JP2003505800A - Geometric design and modeling system using control geometry - Google Patents

Abstract

SUMMARY A method and system for computer aided design (CAD) for designing geometric objects (30, 34) such as surfaces. In the present invention, interpolation and / or fusion (B1 (u, v), B2 (u, v)) are performed between the initial geometric objects (62). The fusion is fast enough that such a fusion target is transformed in real time while the transformation data is being input. Therefore, a user who designs using the present invention can immediately obtain feedback by inputting a correction without having to separately input commands for executing the above-described deformation. A new computer technique is used to perform the fusion between geometric objects (30, 34); this uses a weighted sum of the points on the geometric objects to create The target object (62a, 604) is derived. INDUSTRIAL APPLICABILITY The present invention can be applied to various design fields such as design of bottles, vehicles, ships, and the like, and can also be efficiently used for moving image applications that repeatedly correct the surface of a moving object such as a facial expression.

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to systems and methods for performing computer-aided design, and more particularly, to systems and methods for performing computer-aided design.
Or efficient computer techniques for performing fusion between geometric objects.
. BACKGROUND OF THE INVENTION Computer Aided Design (CAD)
The designers using the computer system for the n) are free from the
For example, when designing the surface), first bind to pass through this object
Start by specifying the characteristic and / or essential sub-elements of the geometric object
Usually, Next, a geometric object that matches the given binding subelement is
The spawning process is started. [0003] More specifically, such sub-elements may be points, curves, surfaces and / or
It may be a higher-dimensional geometric object. For example, a designer designing a surface
, A plurality of curves through which the intended surface may pass may be constructed and arranged (as used herein).
These curves are referred to as “feature straight lines” or “feature curves”. Thus, the geometric properties of the intended surface (eg, differentiability and curvature)
) Is generally sufficient to obey the constraints of the curves placed on this surface.
It is expected to vary substantially only in degrees. [0005] In other words, a surface is created that a designer would normally call "appropriate" to those skilled in the art.
Expect that. Therefore, the designer must construct and arrange such a characteristic curve.
Is usually not easily interpolated from other parts of the surface already designed.
In such areas, the operation is performed so that the intended surface geometry changes. As a more detailed example, when designing a container such as a bottle, the outer surface of the bottle is intended
(A) a characteristic curve in which the surface to be placed is located at the high curvature portion of the bottle surface,
A unique geometric characteristic such as having a shape or contour so that the
First, it may be specified by a partial element such as a partial surface to be provided. In this way, the designer who intends to design the bottle surface satisfies the constraint conditions entered by the designer.
At the same time, design a bottle that is also appropriate. In addition, the designer drills holes as handles.
It is also possible to keep the bottle surface in the proper shape and
By deforming the handle, a handle having a more usable shape may be created. However, the designer of the geometric object (or more generally, the user) inputs the constraint.
In this way, the person's design intention can be expressed easily and efficiently,
Conventionally, there is no CAD system capable of obtaining a geometric object of a shape.
Was. That is, a designer or a user incurs a considerable overhead for an operation.
And / or the designer or user may not be able to
Non-intuitive geometric pairs that require considerable experience to be able to
In some cases, elephant definitions and transformation techniques were used. For example, in many of the conventional CAD systems, a “control point (con
Troll Points) "and specify and / or manipulate specific points
Methods are provided that allow more surface design and / or deformation. And
However, such a method requires a lot of calculation time and is not intuitive.
What is more than local deformation of the surface associated with each such control point is justified.
Not easy. [0011] Furthermore, in some of the CAD systems according to the prior art, individually designated
The surface is defined and defined by what is called a control vector (control vector).
And / or deformation techniques are provided. That is, the direction of these vectors
May be used to define the associated surface shape or contour. However, each control vector usually has a corresponding control vector.
Only corresponds to a single point independently of other points on the surface
Intent does not map well with surface design techniques that use such control vectors
Sometimes. Thus, these techniques at best correspond to the control vector.
It is only possible to locally deform the surface near the point. [0013] Further, such a CAD system according to the prior art includes fusion operation and trimming.
There is a problem with precise operation. For example, along common boundaries
In the case of two geometric objects trying to abut each other, the boundary at this boundary
There is not enough tolerance for each other. [0014] That is, there is a sufficiently large void between these geometric objects, and the "watertightness"
(Watertight) ”is not considered, in which case the machining operation
Problems can occur with composition and other operations such as Boolean operations on solids. [0015] Therefore, a designer or user using CAD can more easily and efficiently use the CAD.
One or more geometric design techniques that enable precise and precise design of geometric objects
It is strongly desired to build a CAD system equipped with In addition, the user
Improve control when defining and / or deforming geometric objects on the computer
In particular, the shape or outline of computer-designed geometric objects can be widely
Graph geometric objects across them, allowing them to be more intuitively controlled
There is a need for systems and / or computer techniques for displaying graphics.
You. <Definition> In this section, basic terms used in the description of the present invention are defined. These definitions are
This is also illustrated in FIGS. A “parameterized geometric object” S is a geometrical object defined as an image of a function f.
Where the domain of f is in a coordinate system (referred to as "parameter space").
Within the embedded geometry, the range of f (range) is in another geometric space
(Called “target space”). Typically, the inverse or pre-image f of a geometric object such as S ^-1 Is a geometrically simpler object than its own image in the object space. For example,
The original image of the curve 170 in the elephant space is a simple line segment 172 in the parameter space.
, L may be used. Then, if S represents a curve in the target space, f
And S may be identified in the expression, in which case, u∈L
A point on the curved line S is expressed as S (u). Similarly, the original image of the surface 204 (FIG. 16) in the object space is stored in the parameter space.
A simple bounded area 180 may be used. And S represents surface 204
Then, (u, v) ∈f ^-1 For (S), points on surface 204 are represented as S (u, v).
Will be revealed. “Contour (side)” 200 (FIG. 16) refers to the geometric
The geometric object (eg, pair) that the modeled object (eg, surface 204) should pass
Curve in the elephant space). That is, such a profile (contour) 200
Is used when generating a geometric modeling object. Therefore, the profile (contour) is used by artists and designers
Is a common natural way of designing in a holistic way;
When defining the characteristic shape of the geometric object (surface) inside, the characteristic curve,
This can be considered using a contour curve. For example, the contour curve on the surface is the geometric shape of the resulting geometric object.
Substantially define the shape, ie its continuity, curvature, shape, boundary, shrinkage, etc.
Is also good. Here, in many design applications, the contour is usually continuous and differentiable.
Note that there is. However, such a restriction is not essential. For example, the contour passes through this
In addition to giving the overall shape or form of the geometric object, this geometry
Gives the texture of the target object. Therefore, if the contour is fractal or fractal-like, the obtained geometric
The surface near the contour of the biological object is given a certain fractal contour
No. The use of higher dimensional (≧ 2) contours is also included in the scope of the present invention.
Note that That is, the contour may be a surface or a solid. Therefore, if the contour is
If at least some of the geometric properties of this contour are locally (i.e.,
(In the vicinity of). Further, the contour (and / or a portion thereof) may be represented in a linear representation (eg,
Surface computing), elliptical expression, NURBS expression, Bezier expression, etc.
It may be a functional expression. But no matter what computational expression
Also have a way to deform or reshape each contour (eg, interpolation)
Note that it is desirable. More specifically, the contour obtained by such a method can be used to define one or more predetermined points.
Pass (or pass), are continuous, differentiable, have minimum curvature
It may be desirable to satisfy certain geometric constraints, such as Further, such a deformation method includes decomposing an outline into partial outlines.
The common boundary (for example, a point) between the sub-contours of the
Note that features that are "possible" may be provided. The “marker” 208 (FIG. 16) refers to the outline 20 in a region near the marker.
Points on the contour that can be moved to change the shape of 0. Mar
Mosquitoes can also deform contours of geometric objects that have contours.
Also used to specify the location of the. “Contour handle” 212 (FIG. 16) is a geometric object tangent to contour 200.
is there. By using such a contour handle, the inclination of the contour at the position of the marker 208 can be adjusted.
By changing the slope (derivative), the shape of the contour can be controlled locally.
Wear. Alternatively, for non-differentiable contours, the corresponding
Control the overall shape of the contour by indicating the overall direction and slope of the contour
be able to. For example, fractal contours or other non-differentiable geometric objects,
, The contour handle should, for example, confine this contour.
May specify a range within the target space; that is, the range is a tubular
The contour may be confined within this tubular region. The contour hand
By changing the length of the contour handle 212, the contour handle 212
For example, the deviation from the straight line between the markers on this contour
Note that The “isoclinic boundary” 220 is an isoclinic ribbon 21
6 is a boundary curve facing the contour 200 on FIG. In one embodiment, contour 200
For each of the above points, there is a corresponding point on the
Such a pair of points is usually orthogonal to the tangent vector at that point on the contour.
Defines a vector 224 (referred to as "Picket"). More specifically, for a parameterized contour, the equi-inclined boundary 220
Can also be considered as a set of pickets at all 200 possible parameter values
You. An “isoclinic ribbon (isoclinic ribbon)” (or simply “isoclinic ribbon” (isoclinic ribbon))
Klein)) refers to a geometric object (eg, surface) 20 in a contour 200
4 (more generally, the geometric object 204) to define the slope
Etc. are geometric objects. Alternatively, the contoured ribbon is a contour 200 with a contoured handle
218a, 218b (described below) and a geometric
It may be regarded as an expression of the object. In other words, the geometric object 204 is oriented along its contour 200 along the
16 and "heel contact". In other words, in one embodiment,
, The geometric object 204 is continuous at equi-incline 216 and the entire contour 200
Must be continuously differentiable along the body. In another embodiment, a similar term as described above in describing the term “contour”
By specifying the possible geometric range of the object 204 by the method,
204 may be constrained by an equal inclination 216. In addition, two for each contour 200
Note that an equi-inclined ribbon 216 may be attached. In particular, a ring that is the boundary between two abutting surfaces (eg, two abutting surfaces 204)
For the gull, there can be a contoured oblique ribbon for each of the two surfaces
. In this case, it can be referred to as a right isometric ribbon and a left isometric ribbon.
. The “equally inclined handle” 228 is a symbol indicating the position of the isometrically inclined ribbon 216 at the marker 208.
A geometric object (eg, a vector) for controlling the shape,
The contour handle and the equi-tilt handle at the f position define a plane tangent to the surface 204.
May be specified. Accordingly, the isometric handle is positioned on the surface 204 (and also near the marker).
Is used to determine the shape of the other underlying geometric object. In particular, the equi-tilt handle 228 is a picket 224 that can be operated by a user. all
All of the contour handles 212 and the isotropic handles 228 (for example, two or more contact surfaces)
) Share a plane at the marker 208 location,
204 is smooth at this marker position (assuming the surface is continuously differentiable
), Otherwise, the surface will have folds and points. Here, at a marker position, a certain handle (equally inclined handle or contour hand)
) From the plane of another handle, along the contour 200 to the surface 204
Note that the pleats can be created intentionally. The part of the outline 200 between the two markers 208 is called a “partial outline” 232. same
Similarly, the portion of the isometric ribbon 216 between the two isometric handles 228 is referred to as a "partial ribbon".
"240. A “partial boundary” 244 is the part of the boundary 220 between the two isotropic handles 228
It is. A vector tangent to the tangent boundary 220 at the position of the eccentric handle 228
The tor 246 is referred to as “ribbon tangent (ribbon tangent)”. In the present invention,
In addition, corrections to the ribbon tangent are also made to the underlying geometric pair, such as surface 204.
Note that it can be used to control and / or change the shape of the elephant
. The isotropic handle 228 may be generalized to specify the curvature of the surface 204
. That is, instead of the equi-tilt handle being a linear vector, the handle is bent.
This is referred to as “ribs 248”. Therefore, these
The ribs provide a bend between surfaces having an accompanying equi-inclined ribbon along a common contour boundary.
It is possible to preserve the continuity of the rate;
It is because it is done. Therefore, if the curvature of such a surface matches the curvature of the corresponding equi-tilt rib,
In both cases, tangency is also ensured. A “deployable surface” is conceptually a flat surface that can be pulled out flat without tearing or shrinking.
It is a surface that is capable, ie, deployable. This is a “scaled surface (ruled
Face)); this latter surface is optional on this surface.
The ruler (ruler) (the straight end of the ruler) can follow along at any point,
Along the entire ruler, find an orientation that allows the ruler to touch the surface.
Is defined as a surface that can On deployable surfaces, along the scale
The normals (surface perpendicular) at are all equal. The “label surface” refers to a feature capable of attaching a label to a container or the like.
Another two-dimensional (deployable or approximately deployable) surface. label
On the surface, a transfer sticker can be used without tearing or shrinking. This surface
Is very tight, usually due to the geometric deformation of the isotropic ribbon 216.
It cannot be transformed. A “trim profile” is used to trim other geometric objects (eg, surfaces).
A geometric object (curve) used as an outline for the object. Trim contour is single correspondence
May have only the equi-inclined ribbon 216;
If it is a surface, it cannot be deformed, so it can be
Cannot be used. [0048] Trim contours (curves) are used to define any surface except the label surface
it can. A surface S fused to one or more other surfaces along a trim contour is a surface S
When overlying a trim profile, it is referred to as an "over built surface". Was
For example, in FIG. 12, the surface 130 is an overlapping surface, and the surface
The face portion is usually not revealed to the designer after trimming. The “convex combination” of the argument Fi is the sum ΣiciFi; where ci is the scalar relation
Scalar multiplication for Fi is assumed to be well defined (Fi is
For example, a vector, a function, or a differential operator), ci ≧ 0 and Σi
It is assumed that ci = 1. If Fi is, for example, a point in space, all of these
It is clear to a person skilled in the art that the set of possible combinations of “Forward evaluation” is one of the techniques for evaluating geometric objects, and the function f (x)
Evaluate f while sequentially incrementing the argument value x to produce a set of sample values from
It is a way to pay. This type of evaluation method is usually fast and efficient, but incremental
No function value is obtained at an intermediate position of The “implicit function” is expressed in the form of f (x) = 0.
The function to be represented. X∈R ^H . Parameter curve or parameter surface
Is converted to an implicit form is called "implicitization".
For example, f (t) = (sin (t), cos (t)) in parameter format
Can be formalized as f (x, y) = x2 + y2-1 = 0. Both forms are
Represents a circle. Vectors are “normalized” by dividing by their length. Therefore,
The normalized vector has a unit length. Divide the vector function by its own gradient
It will be apparent to those skilled in the art that this approximates unit length. Given that pi (t) is a weighting function and a function defined as Σipi (t) Fi (t) is given.
If Σipi (t) = 1 for all t values, then pi will
Referred to as comprising. “G1” continuity is used herein to refer to a geometry defined by a parameter.
The directional vector along a continuous parameter path on a geometric object is, for example, the tangent
Specify the condition of geometric continuity to be continuous without considering the magnitude of the vector.
You. DISCLOSURE OF THE INVENTION The present invention provides a method for real-time processing of an object such as a surface when a user gives an object deformation input.
Computer with sufficient computational power to enable deformation of the
Is a geometric design system. Therefore, modification or deformation of geometric objects
After the user has given the input for
Compared to a conventional CAD system that must be
A major change from the system. In such a CAD system according to the prior art, the design of the user
Feedback is obtained each time a user individually requests. In contrast, the present invention
In, the input is received without the user explicitly instructing to perform the update process.
Immediately after that, the update process is performed in real time. Since the present invention increases the computational efficiency, the user of the present invention is able to
Iterative approximation to the object can be performed more efficiently. Need so much precision
There is no need to calculate design geometric properties with high precision for parts that do not exist
Therefore, the user can proceed with the design quickly. In other words, the ease of correction and the calculation speed at the time of correction allow the user
Can be approximated and / or tried more quickly,
The need to keep in mind that it "does exactly" is reduced. Therefore, the present invention is applicable to a large number of geometric design objects (including machined parts).
It is possible to design the geometric characteristics of qualitative parts to a satisfactory extent over a wide range
In this regard, it has significant efficiency advantages. The CAD system according to the present invention uses two parameterized geometric objects, such as surfaces.
Provide new computer techniques for the fusion between
Metering techniques are possible. In one embodiment of the present invention, the new fusion technique includes:
For example, two parameters each having a unit square as the parameter space
The fusion between the functionalized surfaces S1 (u, v) and S2 (u, v) is performed. For example, (0, 1) is taken as the range of u and v, respectively (further,
Fusion functions B1 (u, v) and B2 (u,
Assuming that v) has surfaces S1 and S2 respectively, the new surface S is given by
Defined by [Mathematical formula-see original document] Here, the obtained fusion surface S is equal to S1 on the boundary of S1, and is equal to the boundary of S2.
The fusion functions B1 and B2 are usually chosen to be equal to S2 in the field.
Note that This condition is that B1 = 1 and B2 = 0 on the boundary of S1.
, S2 on the boundary between B1 and B2 such that B2 = 1 and B1 = 0.
If satisfied, In a more general embodiment, the present invention relates to a method in which a plurality of geometric objects Si (where
, I = 1,..., N) can be used to perform the fusion between
The geometric object is parameterized by the corresponding function fSi,
The domain includes a parameter space PS common to all fSi. Therefore, the gain
In the obtained fusion surface S, each point S (q) corresponding to each point q of PS is fSi (q
) Is determined using a weighted sum of each point obtained from Further, since it is desirable to fuse S with the partial boundary Pi of each Si, S is expressed as P
Interpreted as a function from S to a common geometric space GS with geometric object Si
, S (fSi-1 (Pi)) ⊆Pi. Further, S is also determined for each fSi-1 (Pi).
Can be continuous. Equation (1) above produces a fusion surface (more generally, a fusion geometric object) S
It should be noted that this is a representative example of various formulas for calculation;
Other embodiments are described below in the "Detailed Description" section. In addition, the above equation (1)
Parameter space coordinates (u, v), three-dimensional coordinates (u, v, w), one-dimensional coordinates u, etc.
This formula can be generalized by replacing it with another parameter space coordinate representation of
Please note that Further, the fusion functions B 1 and B 2 also correspond to such another parameter space.
Defined. In addition, such fusion functions B1 and B2 are converted to a surface (more generally,
To interpret as the weight of the weighted sum of points selected from S1 and S2
What you can do is important. Furthermore, this weighted sum idea can be extended in various ways.
You. For example, there are a plurality of geometric objects Si (where i = 1,..., N).
In a more general embodiment, the corresponding weighting / fusion function Bi is for each value of i
Thus, the following modification of the expression (1) may be obtained. That is, Si
S (q) = Σi = 1 for a point q in the common parameter space for ^N Bi (q) Si (q) In another aspect of the invention, a Si geometric object used to generate S
In such a way that at least some of them have dimensions higher than two,
Creation is also within the scope of the present invention. For example, if S1 and S2 are parameters
If it is a solid, it is fused from S1 and S2 using another variant of equation (1).
It is obvious to those skilled in the art that S can be generated as a curved solid. Accordingly, P1 of the surface S1 and P2 of the surface S2 are also set to be boundaries of S.
S may extend between S1 and S2, in which case S is similar to equation (1)
As the weighted sum of the points S1 and S2. In still another aspect of the present invention, formula (1) (or a variation thereof, formula (2)
), (4), (5), (5.2), (5.03), etc.
One or more parameterized geometric objects Si are described in
URBUS expression or isometric reference used for illustration in the description herein
One of some other multi-parameter parameterized computer representations to replace Bonn, etc.
You may have. Further, as will be apparent to those skilled in the art, the underlying geometric pair defining each Si
The elephant (eg, if Si is an isoclinic ribbon, the underlying geometric object is
Mosquito, contour, isotropic handle, contour handle)
What may be different is included within the scope of the present invention. For example, in the Bezier expression or NURBUS expression of Si, “control point” and
And / or use geometric entities derived therefrom to change the shape of Si,
Thereby, the shape of the geometrical object S resulting from this may be changed. In another aspect of the present invention, one or more isotropic ribbons S 1,.
If the fusion surface S is generated from N ≧ 2), the geometrical characteristics of the isotropic ribbon Si
Is changed, the surface S can be deformed. More specifically, one
Point Si (u, v) is changed by changing the shape of the equi-inclined ribbon boundary of two Si
This changes the fusion surface S, which is the weighted sum of these points. In particular, the geometric properties of S (curvature, tangent vector and / or tangent plane,
) Is determined by the shape of the equi-inclined ribbon Si. For more details,
If there is a substantially linear parameterization along the tilt picket,
The longer the relative length of such a picket in an equi-inclined ribbon, the more the shape of S
It is more strongly deformed in the direction of this picket. Further, if the direction of these pickets is changed, the curvature of S changes. sand
That is, the weighted sum of equation (1) or the like forces S to always contact the surface Si with the heel.
So that S touches the heel to the equi-inclined ribbon Si having the picket whose direction has changed.
The shape of S changes. Thus, (a) changing one or more geometric properties of one or more Si (here
The shape is defined as multiple geometrical features such as continuity, differentiability, curvature, higher-order continuity, etc.
This change shall mean a characteristic, and this change may include a change in the shape of Si.
Or (b) changing the parameterization of Si.
The shape of the fusion surface S can be changed by an interactive technique. Such user-interactive techniques for deforming the fusion surface have been
Note that it may be used for high dimensional geometric objects. For example,
Used to determine S if geometric object Si is not a surface but a solid
By changing the shape of one or more of the solids Si thus obtained, the resulting fused solid S is changed.
Can be shaped. The geometric object Si used to generate the fusion geometric object S is
In a manner that can be indirectly modified through another geometric object that can be generated,
What is better is also included in the scope of the present invention. For example, if S is equi-inclined ribbons S 1 and S 2 (corresponding contours P 1 and S 2, respectively)
And P2), and the ribbon S1 is provided at both ends of P1.
Interpolated from contour handles at points, isometric handles, and ribbon tangents
In accordance with the present invention, such handles and / or ribbon tangents are modified.
Provides a user-interactive technique for modifying the fusion surface S
It is. Further, in one example of a user interface technique, only the handle is displayed.
The handle may be represented as being connected to the fusion surface S.
Is shown. Therefore, changing this handle changes the fusion surface.
You. It should be noted that such a user-interactive technique requires a handle by the user.
Note that it can respond to changes in ribbon tangent in real time
I want to be. Therefore, when the user inputs such a change, the user's design intention is immediately
Will be displayed. Therefore, if the present invention is used, communication with the user during the design process is possible.
The interaction is different from the conventional CAD user interactive technique,
It comes closer to the situation in the technique of actually building a geometric model. In another aspect of the invention, the geometric objects generated in the invention
It is possible to impose various geometric constraints. More specifically, geometric
The properties and / or sub-geometry of the object O0 are confined within another geometric object O1
In that case, deforming O1 will result in the properties and / or sub-geometry of O0
Are correspondingly deformed, and as a result, O0 is also deformed. For example, according to the present invention, a point p in the object space is
Or can be defined (ie, parameterized) to stay on top of this
Where O 1 may be a curve, surface, volume, or volume. And change O1
If it is shaped, O0 will also be deformed. Also, instead of the point p, another number such as a curve, a surface, a solid, etc.
The geometric sub-objects may be bound in a similar manner. Further, control points, handles (various handles such as contour handles and isotropic handles, etc.)
), Normals, twist vectors, etc., the properties of the geometric object O0
The constraint may be made by a method, in which case, if O1 is deformed, O0 is also deformed. For example,
By using the geometric object interpolation technique according to the present invention, such as equation (1) and its variants, O1
When the bound properties and / or the partial geometry of O0 are transformed by the transformation of
, The geometric object O0 is efficiently generated in substantially real time (eg, re-interpolation).
)it can. More specifically, in this aspect of the invention, the parent geometric object
The geometric deformation operation depends on the corresponding geometry in the child's geometric object.
Various geometric objects can be connected hierarchically by inducing
Wear. For example, when a fine scale of a large surface is represented by a surface piece, the fine surface
Users can control the shape of large surfaces by attaching pieces to the large surface
It is useful to be able to automatically control the shape of fine surface
You. In addition, other types of geometric objects such as curves, points, three-dimensional deformation spaces, etc.
However, similar hierarchical control can be performed. In such hierarchical control, the deformation and the return to the original undeformed state are repeated.
Used together with the permanent deformation space needed for geometric objects
Note that this is also good. Such control is repeatedly performed for one-time deformation.
Note that this is difficult to achieve in real time. Therefore, by using the hierarchical control of the present invention, such a three-dimensional deformation space can be obtained.
Control of the embedded geometric object and / or the embedded geometric object
The structure allows the geometric object to be deformed with the deformation of the three-dimensional deformation space.
It becomes possible. In addition, one or more such deformation spaces may include surfaces, curves, etc.
When relying on simpler geometries, even if the geometric objects are complex,
Substantial control over is done by manipulating this simple geometric shape
Can be. [0091] Other features and advantages of the invention will be set forth in the Detailed Description section, in which the accompanying drawings are referenced.
It will be described with reference to FIG. [Detailed Description] <1. INTRODUCTION FIG. 1 shows some two parameters, such as between the semi-cylindrical surface 30 and the surface 34.
FIG. 4 illustrates one embodiment of the present invention used to design a surface 62 that interpolates a structured surface.
It is. That is, the surface 62 is generated by a new surface interpolation process;
, The constraints on the shape of the surface 62 are the characteristic curves 54, 58, 60 and these
Provided by a new control geometry (e.g., an equi-tilt ribbon) associated with More details
Alternatively, the surface 62 satisfies the following constraints. (A) One or more geometric properties of surface 30 along characteristic curve 54 are applied to surface 62.
Given. (B) applying one or more geometric characteristics of surface 34 along characteristic curve 58 to surface 62;
Given. (C) Surface 62 interpolates through feature curve 60;
The tangent of the surface 62 along is derived from isotropic ribbons 61, 63 (eg,
So that they are equal). Therefore, using the present invention, the designer can (a) carefully construct and position
A relatively small number of feature curves, and (b) the surface along the range of these feature curves.
Designing the specified surface (via isotropic ribbon) with the desired slope
Can be. Furthermore, using the present invention, the surface designed in this way has a characteristic curve
In addition to properly interpolating the gap, the convexity, concaveness, and / or
Which can be subject to the set constraints. Further, the present invention may be used to fuse a surface area to an object under design.
Can be. For example, FIG. 2 shows an example in which a disk 66 is fused to a cylindrical surface 30.
It is. In addition, the invention can be used to build bosses, dimples, logos, and embossments,
It can also be used to design surfaces recursively, as described in this document.
It will be apparent to those skilled in the art from the illustrations. [0097] At least one embodiment of the present invention is a conventional computer assisted computer in the following respects.
For Computer Aided Design (CAD)
Is different. That is, in the present invention, a desired geometric object (for example,
, Surfaces) are geometrically and computationally independent pieces (eg, 3
(A bounded surface with sides, sides, sides, etc.)
At the boundary between these small pieces, these pieces are
Can be joined. Thus, the desired geometric objects are the boundaries and / or regions between them.
Constraints such as continuity, differentiability, and / or curvature are met on both sides
Using a method to interpolate, fuse and / or trim these sub-objects in an embodiment
, Design by joining multiple unrelated geometrical sub-objects (partial surfaces)
be able to. This is essentially different from the conventional CAD approach in the following points.
You. That is, in the system according to the prior art, the NU having four sides of the hidden surface is used.
RBUS, Bezier, Hermite, Coons, Cordon or Boo
Only the joints are joined together. <2. Fusion between geometrical objects> The geometrical object design technique that is essential in the present invention is based on two parameters such as surfaces.
Fusion between metered geometric objects, and in particular, how to perform such fusion.
As defined in the “Definition” section, “parameterized geometric objects” (for example, tables
Surface) is a (simple) coordinated geometric object (parameter space) such as a bounded plane
) To another (usually more complex) geometric object (object space)
Can be defined as If this parameter space is a bounded plane, for example, two coordinates
Each point in the parameter space is uniquely identified using parameters (denoted by u and v)
can do. If the parameter space is three-dimensional, the bounded plane parameter
For each (u, v) point in the data space, the function computes the point (x, y, z)
) May be attached. By convention, the parameter space of a plane is usually assumed to be a unit square; in this case
, U, v both vary between 0 and 1; yet another parameter space
The use of arrangements and coordinate ranges is also within the scope of the present invention. In one embodiment of the present invention, each unit space has a unit square as a parameter space.
To perform a fusion between the two parameterized surfaces S1 (u, v) and S2 (u, v)
To this end, each surface S1 and S2 is defined by the fusion functions B1 (u, v) and B2 (
u, v); each fusion function takes, for example, (0, 1) as the range.
(Further, it satisfies other properties described later). This gives a new surface
Defined by [0104] Here, the obtained fusion surface S is equal to S1 on the boundary of S1, and is equal to the boundary of S2.
The fusion functions B1 and B2 are usually chosen to be equal to S2 in the field.
Note that This condition is that B1 = 1 and B2 = 0 on the boundary of S1.
, S2 on the boundary between B1 and B2 such that B2 = 1 and B1 = 0.
If satisfied, In FIG. 3, for example, S 1 is surface 30, S 2 is band 34, and one
The boundary is the vertical line 54 of the surface 30 and the other boundary is the curve 58 of the band 34
The surface 62a is S, which runs between these two boundaries and
It is tangent to S1 and S2 in the field. <2.1. Fusion Functions> Fusion functions can be prepared to fuse between various types of geometric objects.
it can. For example, to fuse between two volumes filling a geometric object
May be prepared. However, the new fusion processing of the present invention and the accompanying
To facilitate (and clarify) the description of the associated fusion function, the discussion herein
Is essentially limited to the fusion between two curves or the fusion between two surfaces
I do. Therefore, for the two surfaces S 1 and S 2 to be fused together,
, The fusion functions B1 (u, v) and B2 (u, v) are the fusion functions generated in the present invention.
It is appropriately set to be 0 or 1 on the boundary of the joint surface. In FIG. 4, boundaries 78a and 78b in the parameter space are located in the target space.
Assuming that they correspond to the contours 54, 58 of the fusion surface, such as surface 62a.
For any curve 80, the corresponding original image (eg,
For example, a straight line 86) exists. Note that, for simplicity, the boundaries 78a, 78b and
Although the original image of the curve 80 is a straight line, it does not have to be so. The fusion functions B 1 (u, v) and B 2 (u, v) have a domain that is a unit square.
Then (also for simplicity),
For this point (u, v), this point (u, v) is a boundary curve (eg, a boundary curve
78a, 78b), or more generally, the "closeness" to the original image of the contour curve.
It is important to determine some measure to indicate. Such proximity or distance
The measure may be used to determine the value of the fusion function and / or its result.
. It is to be noted that such a method of calculating the proximity or distance measure in the parameter space is used.
Note that there are various laws. For example, the boundary 78 (or
If the original image is a straight line, such a parameterized distance to the (u, v) point is
And can be easily calculated as the length of a line segment perpendicular to the boundary straight line. parameter
Other techniques for calculating the digitized distance are described later herein (e.g.,
Sections 2.3 and 2.4). Assuming that the parameter space is also a two-dimensional space of (u, v) points,
Function B ^~ i (where 1 ≦ i ≦ N, where N is a constant which is the number of boundary curves) is
Function B of distance function of number ^~ i (Di); where Di is also (u
, V) and B ^~ i (Di) = B ^~ i (Di (u, v)) = Bi (u, v)
) And Di (u, v) is the boundary curve Ci of the surface S (in the target space).
This is a distance function to the original image Ci-1. Here, such a distance function is such that (u, v) is the i-th boundary curve original image Ci-1.
When approaching infinitely (eg, measured at normal Euclidean distance), Di
Note that the condition that (u, v) approaches zero indefinitely
I want to be. Such a fusion function B ^~ Examples of i and the distance function Di are described herein.
It will be described later. Many of the useful fusion functions Bi are B ^~ i (Di), so it is necessary to distinguish
Unless it is necessary, the following description uses the following description:
(U, v), and (b) the fusion function B for some distance function Di ^~ i (Di),
Are used for both. However, if a clear distinction between the fusion functions (a) and (b) is needed, the fusion function
Indicate which fusion function is intended by noting the domain of the combined function
be able to. Now, equation (1) shows that the fusion function B ^~ i (Di) (where i = 1, 2
Note that the same holds true for (Equation 3) If the point (u, v) is close to the i-th original image boundary (i = 1, 2), B ^~ i
(Di) is expected to be small and this point is (in object space) i
It is mapped near the second boundary. The benign set of the fusion function Bi is such that the map S of the fusion surface has a desired outer (contour) curve.
Not only does it allow for coincidence, but also, for example, two or more
The fusion surface obtained between the perimeter curves, such as
In a manner that preserves properties such as continuity. That is, the fusion surface “contacts the heel” with each of the initial surfaces. Also, the fusion function B
It is desirable that i make the new surface appropriate. FIG. 5 shows Bi (where i =
6 is a graph showing a pair of fusion functions desirable as (1, 2). Regarding the contour curves P1 and P2 of the two surfaces S1 and S2, a fusion surface is defined between P1 and P2.
When it is desired to generate the contours, the contours P1 and P2 are represented by a unit square ｛(u, v) | 0 ≦ u ≦
The parameterized original images corresponding to = 0 and u = 1 for 1 and 0 ≦ v ≦ 1｝, respectively.
Then, the following useful properties regarding the fusion functions B1 and B2 are obtained.
Can be (1.1) B1 = 1 at u = 0 and B1 = 0 at u = 1. u = 0
B2 = 0 at u and B2 = 1 at u = 1. (1.2) Di (u, v) = 0 and Di (u, v) = 1 (where i = 1,
If 2), the derivatives B1 'and B2' are zero. Thereby, the fusion surface S and the first
A smooth transition (tangent continuity) occurs between the initial surfaces S1 and S2. Higher order
If the derivative is also zero, higher continuity between the surfaces is achieved and
Is improved. (1.3) B1 + B2 = 1 for all points (u, v). This is "division of 1"
And prepares for the creation of a convex connection of the surfaces S1, S2 with which the new fusion surface abuts.
Note that this ensures that the new fusion surface is not too far from the initial surfaces S1, S2.
effective. Various embodiments exist for the definition of the fusion function. One useful example is
It is as follows. (Equation 4) This gives arbitrarily high order continuity to the fusion function, as well as the initial fusion
Necessary to achieve the same continuity as higher order continuity between surfaces. Another example is above
The purpose is to select a polynomial function having the properties (1.1) to (1.3) described above. Was
For example, select a fifth-order polynomial whose second derivative is zero at D = 0 and D = 1
As a result, useful curvature characteristics can be realized (see section 4.4). In addition to the above-described fusion function, the following fusion function is given as an example. One example is polynomials B1 (x) and B2 (x) that satisfy the following constraints: (Equation 5) Here, additional constraints on higher derivatives (eg, x = 0 and / or
Note that (or equal to 0 in 1) may be further imposed. For example
, Bi ″ (0) = Bi ″ (1) = 0 (where i = 1, 2), the interpolation and
C2 continuity is obtained in the subject undergoing fusion and / or fusion. An example of a polynomial fusion function satisfying these constraints is as follows:
. (Equation 6) Here, as shown in FIG. 6D, B1 (x) represents the six control points P1,.
Note that it may be derived as a Bezier curve having. Furthermore, as below
Note that (Equation 7) (C) Bijective (eg, one-to-one and upward mapping) parameterization function P: [
0.1] → [0,1], the above fusion function configuration uses another fusion function
May be configured using a fusion function for obtaining In one embodiment, P (x)
= 2c (x−x2) + x2, where c is a constant “twist” factor
For example, a new fusion function is obtained as B (P (x)). Therefore, when c = １ ／, P (x) = x. Furthermore, c is strange.
As shown in FIG. 6A to FIG. 6C, the inflection point of the graph of P (x)
Moving. It should be noted that the fusion function (here, c> 1/2) in FIG.
And / or a fusion surface or other geometric object) to obtain x in the graph of FIG. 6B.
= The geometrical properties of the object used for the fusion corresponding to the 0 axis
Note that it will be retained. Reduce real-time computation overhead that occurs when evaluating a fusion function
Therefore, in one embodiment, the values for the fusion function are set prior to the design session.
Table with sufficient resolution, and the closest approximation to the actual fusion function value is
The information may be stored in a memory so as to be efficiently searched for an index. <2.2. Extending the fusion to the N-side region> In one embodiment of the present invention, the parameterized surface Si (where i = 1,.
N and N ≧ 2) to perform the fusion on the area bounded by each edge ei
A new general form is a weighted sum of Si (ui (p), vi (p)) as follows:
is there. (Equation 8) Here, (a) p is a variable representing a point in the common parameter space with respect to the surface Si, and (b) Di (p) is a variable representing the i-th edge ei in the common parameter space up to the original image.
(C) Bj is zero when Dj is zero and simply when Dj increases.
(D) ui, vi is a function of p from the common parameter space to (something)
A parameterization function that transforms into an intermediate parameter space. The sum of the products of the fusion function Bj Note that by dividing by (4), equation (4) is normalized with respect to the fusion function.
I want to be. When N = 2, equation (4) is similar to equation (1), and
Note that this is an extension. That is, when N = 2, the expression (
B1 in equation (4) performs the function of B2 in equation (1), and B2 in equation (4)
Fulfills the function of B1. That is, the subscripts are interchanged between the two expressions
. As an example of equation (4), consider a three-sided area 300 (in the target space) shown in FIG.
Sympathize. If the surface S for the region 300 is generated by applying the equation (4), the following equation is obtained.
Is obtained. (Equation 10) Where the parameterization functions u, v, w are the barycentric coordinates of p;
It will be clear to those skilled in the art. Another method of defining the fusion surface on the N-side region (where N ≧ 4) is shown in FIG.
11 and R12 are used as S1 and S2 in equation (1), respectively.
The first is to apply the edge approach to generate S1 in FIG. Furthermore, the figure
Apply equation (1) to the surface of 35; where S1, S2 in equation (1) are
These are replaced with R11 and R12, respectively, to generate S2 in FIG. Next, FIG.
35, the resulting surfaces S1, S2, respectively, are fused using equation (2).
Here, the fusion functions B1 and B2 are as described above, and
The corresponding Di is also as described above. For example, ribbons R11, R12, R21
, R22 have a common original image, the edges P11, P12, P21, P22 (
34 and 35) used in equation (2) for calculating the distance measure to the pair of original images.
i is expressed as follows: (a) For point P1 of the (common) original image with respect to S1 in FIG.
in (D (P1, P11), D (P1, P12)); where D is P1 and this
(B) For point P2 of the (common) original image for S2 in FIG. 35, D2 (P2) = m
in (D (P2, P21), D (P2, P22)). Therefore, the two surfaces S1 and S2 can be fused to each other using equation (2).
Then, the surface S of FIG. 36 is obtained. In another embodiment that is particularly useful for producing four-sided fusion pieces, the following is described.
Tentative, but limited, versatile method for defining contours and ribbons
Set. (A) All handles are piecewise line segments, and (b) All fusions are performed using the functions B1 (x) and B2 (x) in equation (3.1).
Is Further, in describing this small piece generation technique with reference to FIG.
Use the method. For the contour P, m L, m R: left and right markers of the contour P, respectively hL, h R: left and right contour handles of the contour P, sL, sR: respectively of the contour P Left isometric handle and right isometric handle, bL, bR: left ribs at the left end point and right end point of the isometric boundary R, respectively
Tangent and right ribbon tangent (these ribbon tangents are also known as "boundary handles")
Is). Using the notation of FIG. 37, SL and SR can be defined; where SL is sL and hL
, BL, dL = (sL + bL)-hL
SR is bounded by a line segment corresponding to sR, hR, bR, dR = (sR + bR) -hR.
It is attached. In particular, SL and SR are referred to in the art as “twisted flat surfaces”.
Therefore, SL is called the left-hand twist flat surface, and SR is the right-hand twist flat surface.
It is called Tan surface. In addition, these surfaces are expressed by the following formulas (5.01a) and (5.01b).
Can be evaluated. (Equation 11) Here, the parameters u and v are indicated by a u-direction arrow and a v-direction arrow (FIG. 37).
As shown, it increases in the lateral direction. (Equation 12) Here, too, the parameters u, v increase in the horizontal direction;
Is the direction opposite to the u-direction arrow in FIG. Therefore, the equi-inclined ribbon surface S (FIG. 37) can be defined as follows.
Wear. (Equation 13) Here, for simplicity, the u parameter is the distance required for B 1 and B 2 in equation (3.1).
It is a distance measure. Therefore, when v = 0, S (u, 0) is a contour, that is, a control hand.
Fusion between dollars (hL-mL) and (hR-mR). Further, when v = 1,
S (u, 1) is a resource derived as a fusion of vectors (bL-sL) and (bR-sR).
Note the Bonn boundary. Also, bL and bR are hL and sR-mL along sR-mR, respectively.
And the translation of hR, P is the translation of R, and by such similarity,
Note that the need for data storage in the present invention can be simplified. A plurality of isotropic ribbons S 1, S 2,..., SH in which each Si is generated by the equation (5.02)
On the other hand, such a ribbon is represented by the following equation which is a modification of the equation (4).
It may be used in the form of a general N-side surface. (Equation 14) Here, Dj (s, t) and ui (s, t), vi (s, t) in the formula are
From the distance measure and the N-side piece parameter space (s and t) to the ribbon S
This is a mapping of i to the parameter space (u and v). When using the fusion ribbon Si for N = 2, 3, 4 and N ≧ 5,
Equation (5.02) for the ribbon is a special case of equation (5.03):
First, please note. For example, in equation (5.02), the denominator is 1, and
The distance measure is the u parameter itself, and u and v directly correspond to s and t. The formula for the two-sided surface is the same, except that the base surface is based on the formula (5.02).
(Also referred to herein as a "twisted ribbon").
Therefore, equation (5.02) becomes: (Equation 15) Here, the parameter u is a distance measure. This varies along the direction of the contour curve.
Become Also, in equation (5.04), parameter v is a distance measure. In FIG. 38, the equi-inclined ribbons S1 and S2 move in the u direction and on each of these ribbons.
Parameterized as indicated by the arrows in the v and v directions.
It may be used to generate small pieces. The two contours P1, P2 changing at u
, Using the twisted ribbons S1, S2. [0164] The other two sides P3, P4 are fusion ribbons derived from equi-tilt handles;
That is, P3 is a fusion (using formula (1)) of hR1 and hL1;
And hL1 are S1 and S2 in formula (1); similarly, P4 is hR2
And hL2 fusion. Note that the fusion surface S in FIG. 38 has a tensor product form. this is
, Eq. (5.04) can be understood by decomposing it into a tensor form;
, S2 are derived from equations (5.01a) and (5.01b). sand
That is, S1 is a fusion of SL1 and SR1 (FIG. 38), and S1 is a fusion of SR1 and SR2.
If not. Therefore, the decomposition is as follows. [Equation 16] Therefore, from the last expression above, first, the torsional distortion in the v parameter
If the same surface S can be generated by generating a bon and then fusing at u
I understand. However, since the roles of u and v are symmetric, the twisted ribbon is
May be generated along the data and then fused at v. Therefore, the surface S
Using L3 and SR3, SL4 and SR4 in FIG. 39 are the same as in FIG.
Give the surface S. Thus, in both techniques for deriving S, the inputs, ie, mLi, mRi,
hLi, hRi, sLi, sRi, bLi, bRi are the same; where i is
The contour Pi to be used (i = 1, 2, 3, 4) is specified. In addition, between various inputs
Note that the correspondence is shown in FIG. Therefore, as a whole, the two-sided small piece of the expression (5.04) is a very versatile 4
Provide side pieces. Further, the evaluation can be performed efficiently. Therefore, equation (5.
01a) and equation (5.01b) to develop SLi and SRi in equation (5.05).
When opened, the following formula is obtained. [Equation 17] Here, ( ⁱ , _L )and( ⁱ , _R ) Is the expression (5.01a) and the expression (5.0).
1b) is a suitable matrix. Here, when evaluating the value of this equation, Bi
Note that it will probably be retrieved from a table. Although the above formulation is mathematically sufficient, it can be described in a geometrically intuitive way.
In order to use it, the user must also make a decision. In other words, degenerate
In some cases, mathematical support is also needed. A common example is shown in FIG.
So that two profiles (eg, P1, P2) intersect each other
Is the case. In this case, the contours P3 and P4 (FIG. 38) are of zero length and
Since the end markers are shared (ie, ml3 = ml4 and mr4 = ml4), they are degenerate.
are doing. However, it was noted that equation (5.04) still defines the surface S.
However, it is easily understood that this surface may form a loop at the intersection of the contours.
I can solve it. Maintains handle-like control at the marker while eliminating this looping
For this purpose, the twisted ribbon of the formula (5.04) may be sealed by a function of u.
No. One of the functions that is 1 at u = １ ／ and 0 at u = 0 is
It is as follows. (Equation 18) Therefore, equation (5.01) is changed as follows. (Equation 19) Such a function (5.08) is expected to remove the majority of loops
. The ability to narrow the ribbon at both ends suggests other uses. A scale function as follows: Makes the ribbon thinner at the end of u = 1, and Is thinner at the end of u = 0. This is the effect of creating a triangular (three sides) surface.
It will be apparent to those skilled in the art that this is an efficient method. <2.2.1. Bosses and Depressions from Two Edges> A so-called "boss" shape results from the fusion between two contour edges. This ring
The gusset is, for example, the semicircle of FIG.
780a and 780b. The ribbons 784a and 784b are separate parallel flat
Exists on the surface. When these ribbons are fused, a table can be considered as a boss or depression.
A surface 786 (FIG. 24) is obtained. Here, dome, rocket tip, plateau (mesa)
Shapes of various variants, such as, apple top, etc., can be similarly generated. Further, by rotating the upper semicircular ribbon, the boss can be twisted. this
The method can be used for transitions between tubes, such as in the case of joints.
It will be clear to the trader. In another embodiment, the differential when performing fusion using formula (1) or (4).
Using the neighborhood of each boundary curve (in the target space)
It will be apparent to those skilled in the art that a combination may be made. Therefore, the value ε> 0 is defined
By defining the band and width of each surface along the boundary where the surfaces should be fused
These strips may be used as isotropic ribbons. Therefore, the surface boundary is a contour curve
It becomes a line, and the original image may be used in equation (1) or equation (4). <2.3. Contour Curve> In the present invention, a small number of various well-positioned (object space) rings
Take a contour curve, generate a corresponding surface passing through it, and create a fusion surface based on Equation (1) above.
Therefore, for each surface S1, S2, two parameter space original image curves are
Being present, these curves are the boundaries of the fusion functions B1, B2;
It is a curve which exists at Di = 0 and Di = 1 for the number Bi. As shown in FIG. 7, there may actually be eight curves; this defines the fusion surface.
Can be used to determine That is, two curves 78a are set in the parameter space of S1.
, 78b and two additional curves 7 in the parameter space for S2.
8c and 78d may be present (of course, in many cases,
Are identical.) Furthermore, the curve 78 to the two surfaces 30, 34
And gives corresponding image curves 90, 54, 58, 91;
Have original images 78a, 78b, 78c, 78d, respectively. When S1 and S2 have the same parameter space, the contour 78b is
This is the original image. Further, when S2 at 78d (= 78b) is the contour 58,
78b is included in the original image of each of S1, S2 and the fusion surface 62. When using the present invention for surface design, the user or designer must
The contour is continuously stretched and deformed to allow this initial surface and another
You can also design a fusion surface by creating a new surface between the contour curves.
Conceivable. In the present invention, different types of contour curves or boundary curves may be used.
Please note. In some embodiments of the present invention, such a contour curve C
May typically have a parameter original in parameter space; that is, C-1 (
s) = (u (s), v (s)), where s is the parameterization of the original image
(Eg, 0 ≦ s ≦ 1). Here, a parameterized curve such as C includes (a)
Conic curves such as straight line, parabola, circle, ellipse, Bezier curve, Hermite curve, non-uniform
, Rational B-spline (NURBUS) curve, (b) trigonometric function and exponential function shape
, (C) degenerate shapes such as points.
I want to be. In addition, these curve shapes can be, independently of this, open curves, closed curves, degenerate curves,
Note that it can be classified by another property, such as a compound curve;
Will be obvious to those. The contour curves include curve types (2.3.1) to (23.5) according to the following classification.
Includes curves. <2.3.1. Open curve> An "open curve" is an unconstrained curve in which the endpoints coincide with each other;
For example, both end points may be located freely. In the present invention, the surface (in the object space)
When defining an arbitrary set of curves (contours) to generate
The kind of curve that is used is an open curve; this surface passes through this set of curves
Be bound to be. <2.3.2. Closed Curve> When both end points of the curve coincide, this curve is called a “closed curve”. This is the curve
It means that the start point is the same as the end point of this curve. The closed curve is, for example,
, Surface, area; this is particularly useful in isolating a particular design area
is there. An example of this would be a label surface for the container, such as surface 66 in FIG.
Section). That is, the label surface is wrinkled.
A special surface type called a deployable surface is also used to prevent it from
It is an area that should be settled. Each such label surface is highly constrained
And are usually separated from other design parts by closed curves.
Such curves can also be used for aesthetic purposes in container design). FIG.
FIG. 3 shows an elliptical region 100 fused to a cylinder 108;
0 limits this area. In many cases, a closed curve matches the contact at the endpoint.
Can be made. <2.3.3. Degeneracy> There are various methods for generating a degenerated contour. In one technique, the length
It may be an open curve b or a closed curve having no surrounding area.
The result obtained in such a case is that it can fuse with adjacent surfaces. FIG.
A degenerated disc (ie, a point labeled S1) and a cylinder 116 (ie, S2)
It is a figure which shows the point fusion produced | generated by the fusion between. Here, a simple boss 11
2 are formed on the cylinder 116. More specifically, the appropriate fusion function Bi (only
Then, for i = 1,2), it is possible to obtain a fusion surface between S1 and S2 using equation (1).
Can be. Further, since equation (4) can be used instead of equation (1),
Creating a surface that fuses between a number of points (ie, degenerate contours) and adjacent surfaces
Can also. FIGS. 23 and 24 show additional fusion for degenerate contours.
. FIG. 23 shows the extension between the degenerate contour (point) 714 and the circular end 718 of the cylinder 722.
FIG. 9 illustrates an existing fusion surface 710. More specifically, the fusion surface 710 is
It is a fusion of ribbons 726 and 730;
It is a flat disk with a degenerate contour 714 in the center, and the equi-inclined ribbon 730
And has a circular end 718. Therefore, in equation (1), S1
726 and S2 is an equi-inclined ribbon 730, the distance measure is (each corresponding
(A) on the equi-inclined ribbon 726, the radial distance from the degenerated contour 714, and (b) on the iso-inclined ribbon 730, the distance from the contour 718. be able to. FIG. 24 shows a degenerated contour (point) 754 and a planar ring 758 having a circular curve 760.
And another fusion surface 750 extending between the two.
A central hole 762 having a line 760 as its boundary and penetrating this planar ring
, May be further provided). More specifically, the fusion surface 710 has an equi-inclined ribbon 766 (with respect to the degenerate profile 754).
One) and an annulus 758 (which is, for example, a surface 7 contoured by curve 760).
70 may be used. Therefore, S1 etc.
If the inclined ribbon 766 is used and S2 is used as the ring 758, the distance measure is (each pair).
(In the corresponding parameter space), (a) on iso-ribbon 766, radial distance from degenerate contour 754, (b) on torus 758, distance from curve 760 be able to. <2.3.4. Compound Curve> The new geometric design technique of the present invention can also be used for compound curves.
A composite curve is a general curve of the form that includes another curve as a partial curve;
, The sub-curves may intersect and be twisted, for example, at endpoints
Is also good. When using a composite curve as an outline, etc.
The definition of degree is important. FIG. 10 includes two intersecting partial curves 124, 128.
FIG. In such a composite curve,
The end points of the partial curves may intersect. A partial curve Cj (where j = 1, 2,..., N) of the composite curve C is parameterized.
And have a common parameter space, the partial curve Cj
The distance calculation formula (in parameter space) that determines the distance measure D to the original image is
, As follows. [0203] Here, k = 2,..., N; ? ? D1 (p)? ? ? (D (p)) = d1 (
P) is the distance measure between P and C1; Dk (P) is the distance measure between P and Ck
It is. Therefore, a fusion function B for fusing one or more surfaces to a composite curve C
D (p) can be used as an input to (D). <2.3.5. Trim Curve> In the present invention, the surface can be "trimmed";
, Constrain or limit the surface to only one side of a particular boundary curve (also called a trim curve)
Process. More specifically, for a parameterized surface,
The original image is, for example, in the (u, v) parameter space of the surface, after trimming.
Defines the extent of the original image of the surface to be left. The trim curve may be a contour curve;
The desired trimmed surface is usually one of the trimmed curves of the original untrimmed surface.
It is a part that exists only on the side. An example is shown in FIG. 11; where trimmed
The original surface that is not present is the entire rectangular portion 130. The angled surface 134 is
A "label" surface trimmed from surface 130 along curve 138. It should be noted that trim contour 138 may correspond to one or more adjacent surfaces (eg, surface 142).
Note that an accompanying isometric ribbon (not shown) may also be provided;
In this case, this adjacent surface makes contact with the heel with the isotropic ribbon at the trim profile 138.
You. The use of equi-tilt to modify the shape of such adjacent surfaces is not
This is an important technique for making a smooth transition from a surface to a trim surface. The present invention includes a trim technique for drilling holes in geometric objects.
Note that this is also good. The depression in the front surface of the geometric object is
Protrude through the rear surface, then trim the front surface and remove the corresponding
Can be used, for example, as a handle for containers.
Holes can be created. <2.4. Distance Metrics> Several techniques for calculating distance measures have been described above. In this section,
Additional techniques will be described. The point in the parameter space is the parameter space
Calculates how close to one or more specific geometric object images (curves) in
Efficiency greatly affects the performance of the geometric design and modeling embodiments of the present invention.
give. Generally, such distances in parameter space between points and curves
The discrete measure (which is generally a monotonic function of the usual Euclidean distance metric)
When calculating, how efficiently can we evaluate the complexity of the curves and these measures
Or a compromise is required. In general, the simpler the curve, the faster such a distance can be determined. What
Note that these songs are related to the parameter space curve and its image curve (in the target space).
Lines of the same type (eg, polynomial, transcendental, open, closed, etc.)
Note that this need not be the case. In fact, the parameter space curve is very simple
While pure, it can be an original image of a complex surface curve in the object space. For example, figure
The parameter space curve corresponding to one Bezier curve 58 may be a straight line. Para
Fast distance calculation by keeping the meter space curve as simple as possible
Becomes possible. <2.4.1. Parameter distance calculation for fusion> In this section, distance measures to some candidate parameter space curves
In general, the various monotonic functions of the usual Euclidean distance metric
These methods are described in the order of increasing computational complexity.
I will. A fusion surface is generated between two contour curves P 1, P 2 each having an isotropic ribbon
Where each ribbon is parameterized and the ribbon
As a common parameter space, for example, a unit square plane [0, 1] × [0,
1]. One of the distance functions that can be used for fusion is common
One or the other of the points represented by the coordinate pair (u, v) in the parameter space of
Is a function that depends only on the other coordinate. That is, the contour curves P1, P2 of the equi-inclined ribbon
However, the original images are vertical lines u = k1 and u = k2 (where 0 ≦ k1 ≦ k2 ≦ 1).
If the distance function is such that D1 (u, v) =
(Uk-2) / (k1-k2) and D2 (u, v) = (uk-1) / (k2-k1)
It can be. Furthermore, the original image is defined by the vertical line u = 0 and the parameter space boundary.
If u = 1 (ie, k1 = 0 and k2 = 1), the corresponding
The distance function can be defined as D1 (u, v) = 1-u and D2 (u, v) = u.
Yes, such a simple distance function can be calculated very efficiently. Even if there are more than two original images for the contours to be fused,
To maintain the desired simplicity of the separation calculation, a parameterized distance measure must be calculated.
There are three methods that can be used for Each of these three methods is described below.
This is described below. For example, a path bounded by three boundary curve original images (which are also curves)
The triangular region in the parameter space has three (real) conditions that satisfy the constraint condition r + s + t = 1.
Numerical values) Using the parameters r, s, and t, regarding the vertices v1, v2, and v3 of the triangular area,
Can be parameterized. In other words, a point in a triangular region having vertices v1, v2, v3
p is p = r ^* v1 + s ^* v2 + t ^* It is represented as v3. These parameters r, s, t
Is called “center of gravity coordinates” and is a three-sided table of the surface 300 and the like in FIG. 14 in the parameter space.
Used for face. The area in the parameter space bounded by the original images of the four contours is referred to as (the case of four sides).
B) With a simple extension of a region with a boundary on two opposing sides (referred to as two sides)
is there. In the case of two sides, if parameterized appropriately, only a single parameter u
Can be used to calculate the distance function. In the case of four sides, two parameters
u and v can be used in the same way as their complements (units in parameter space
Assuming a suitable representation, such as a square). Thus, the four in the parameter space
Can be defined as u, v, 1-u, 1-v (that is, the contour
Assume the original image is u = 0, v = 0, v = 1, u = 1). In order to determine the barycentric coordinates for the parameter space area, the original image of the contour is
Assuming that the line segments form a polygon, FIG. 12 (vertices v1, v2, v3, v4, v5
Figure 5 shows a five-sided polygon 148 with
Here, the outline original image is a thick line denoted by 149a to 149e. Determine distance function
First, each side 149a to 149e of this polygon is
By stretching until it intersects another elongated side with 9 in between
That is, a star shape is formed from the original image polygon 148. Thus, intersection 1
50a to 150e are determined in the case of five sides in FIG. As a result, the corresponding
Line segments 152a to 152e from points 150a to 150e to point p in the polygon are constructed
Is done. The obtained distance measure is obtained by calculating the sides 149a to 149e of the polygon 148 from the point p.
Are the lengths of the line segments 153a to 153e. Therefore, from p, the polygon 148
The distance to the i-th side 149 (i = a, b, c, d, e) is many from p
The distance along the i-th line segment 153 to the boundary edge of the square 148. Where
By dividing each distance measure obtained by the sum of all distance measures to the point p,
Note that the distance measure can be normalized. <2.4.2. Straight Line> A straight line is represented by the formula au + bv = c; where a, b, and c are constants.
The normal (unsigned) distance to a straight line is given by: (Equation 23) A more intuitive version corresponding to the Euclidean distance is:
By normalizing, ie, dividing by the length of the gradient, the following equation is obtained. (Equation 24) <2.4.3. Conic curve> The conic curve includes a parabola, a hyperbola, and an ellipse. The general form of a conic curve is
Is represented by (Equation 25) The unsigned distance can be calculated by the following equation. (Equation 26) This can also be normalized by dividing by the length of the gradient, and a more appropriate distance function is
This is the Euclidean distance in the case of a circle. Note that
Farin's "Introduction to Curves and Surfaces" (Academic Press, Inc.
4th edition, 1996), the conversion between the above implicit form and the rational parameter form is given.
Please note that it has been obtained. Therefore, if the conic curve is in implicit form or parameter
Equation (8) can be used regardless of the data format. <2.4.4. Polynomial Curves in Implicit and Parametric Formats> Parameterized curves are described, for example, in the above-referenced Phalan reference.
It is assumed that the data has been converted into the Bezier format by the above method. Vaishnuff (Vai
Mr. shnav) “Fusion of parameterized object by implicit form technique” (ACM stereo model)
(Delling Conference Lecture Record, May 1993)
A way to numerically change to the implicit form curve is given; here, empirical off
By offsetting the curve in a given direction based on the set calculation method, the distance
The separation is measured in a shadow form in the target space. The value of the offset distance that forces the offset to pass through a point is
It is a distance measure. More specifically, for Bezier curves, this distance measure is powerful.
(That is, no failure condition), and the evaluation is sufficiently fast.
It requires only a few Newton-Raphson iterations on average
And may be useful; this will be apparent to those skilled in the art. This is a conic representation
Although it may be an order of magnitude slower than calculating distance measures, the traditional method of calculating vertical distance
It is much faster than the method; this conventional method is also unstable. <2.4.5. Piecewise Parameterized Curve> The present invention is for calculating distance measures on complex curves in parameter space.
It also has a new technique. In FIG. 13, two boundary curves 156a and 156b are
Corresponding sub-curves 160a, 160a,
Assume a piecewise parameterized polynomial curve with 160b. Corresponding part
By connecting the endpoints of the minute curve to line segment 164 (ie, the degree 1 curve),
Number n × 1 Bezier pieces 168 are constructed in unit square representation of parameter space 158
Is done. Here, each small piece 168 has its own second parameter space having coordinates (s, t).
Note that (a) two Bezier sub-curves 160a, 160b (here,
, B1 (t), b2 (t); where 0 ≦ t ≦ 1), each value of t
t0 corresponds to the line segment Lt0 between b1 (t0) and b2 (t0); (b) The line segment Lt0 is Lt0∈b1 (t0) when s = 0, and s = 1 When
Are parameterized by s such that Lt0∈b2 (t0); where
When 0 <s <1, s changes in proportion to the distance between b1 (t0) and b2 (t0).
I do. Therefore, the curves b1 (t) and b2 (t) (and / or
When calculating the distance measure between 64) in the second parameter space,
For any (u, v) point inside the small piece of
The corresponding (s, t) point must be found; then by evaluating this
The distance measure is determined. “S” is a linear parameter (connected at the endpoints by two identical line segments 164)
Corresponding to the point distance between the two corresponding partial curves 160a, 160b
), Simple functions f1 (s) and f2 (s) (for example, f1 (s) = s
And f2 (s) = 1-s) are distance functions for b1 (t) and b2 (t), respectively.
Serves as a number. Here, the parameters u and v are both Bezier functions of s and t.
Note that it can be expressed as a number. More specifically, from the (s, t) coordinates,
u, v) Newton-type algorithm to convert to parameter space coordinates
Can be used; this will be apparent to those skilled in the art. [0233] Another application for determining distance measures that can be used under certain circumstances
Has evaluated such a small piece 168 using a “forward algorithm”.
is there. That is, in FIG. 25, for example, contours 812 and 816 (respectively
, With equi-inclined ribbons 820, 824 abutting the heel against surface 808).
An object space fusion surface 808 is shown. The outline 812 has its original image curve 160a (in the parameter space 158).
The contour 816 is represented by its original image curve 160b (in the parameter space 158).
Where the portion of the parameter space 158 for the surface 808 is
It is a small piece 168. The additional parameter space 828 in s, t is
Can be considered as the original image parameter space for space 158;
The original image of 60a is a vertical line at s = 0, and the original image of curve 160b is s =
1 is a vertical line. In the additional parameter space 828, the point 830 of a sufficiently dense point
Evaluate point (u, v) in piece 168 using the set (eg,
(By determining) the corresponding point p (u, v) on the fusion surface 808
It can be calculated efficiently; this is for the original image curves 160a, 160b
Let the distance functions be D1 (u (s, t), v (s, t)) = s and D2 (
This is because u (s, t), v (s, t)) = 1−s. With this approach
According to this, a fusion surface can be easily and quickly generated. Here, continue with surface 808
This method is particularly effective when trimming is not necessary. <3. Fusion Program> FIG. 17 shows a typical flow of a design / construction operation executed by a user of the present invention.
FIG. Here, the contour handle to construct the accompanying contour
May be required; this profile is used to construct the accompanying
This isometric ribbon is required for the desired shape of the accompanying object (eg, surface).
May be needed to obtain a shape; this object may also be
Is needed to build FIGS. 26-30 illustrate the high level of processing performed in one embodiment of the present invention.
FIG. 4 illustrates the process; this process allows the user to more efficiently and directly
New real-time operation of the shape of the geometric object
To make it work. In addition, the basic principle of the present invention is that
Note that this is a major change. That is, in a normal CAD system, a user can modify a geometric object.
Or input must be given for transformation, and then request that the processing of this input be started
Must. Therefore, feedback on user design is
Obtained each time the user individually requests. In contrast, in the present invention, the update processing
As soon as the input is received, the user does not need to explicitly instruct
Update processing is performed in time. Thus, users of the present invention may be able to use geometric features for virtually all points of interest.
Iterative approximation to the geometric object under design without the requirement to precisely calculate the properties
Can be performed efficiently. In particular, the invention relates to a number of geometric design objects (machines).
A wide range of satisfactory geometric shapes of substantial parts (including machined parts)
It has a significant efficiency advantage in that it can be designed in one go. Therefore, according to the present invention, for a portion of an object that does not require much accuracy,
This eliminates the need for the user to specify the precision of the geometric object being designed. FIG. 26 shows an embodiment of the present invention using a one-dimensional modification of the equation (1) described in the second section.
The steps for calculating the interpolation curve according to the invention are shown. In step 1004
Are the end points of the interpolation curve C (u) to be generated, and the tangent at the end points.
Is obtained. More specifically, both end points of this curve are assigned to variables PT1 and PT2.
. Also, the direction vector for the interpolation curve C (u) at the points PT1 and PT2 is
They are respectively assigned to variables TAN1 and TAN2. Here, PT1, P
Note that T2, TAN1, TAN2 can be provided in various ways
I want to be. For example, one or more of these variables may have a value assigned by the user.
And / or one or more of the other geometric object representations (such as
Derived from another curve, surface, or volume)
Is also good. More specifically, the direction tangent vectors named TAN1 and TAN2 are points
For parameterization of geometric objects (for example, surfaces) on which PT1 and PT2 are placed
It may be automatically determined accordingly. In steps 1008 and 1012, the fusion functions B1, B2 are
It is selected as described in section (2.1). However, the user explicitly specifies
The fusion function for a particular pair of fusion functions is defaulted so that
Note that it may be prepared. However, it should be noted that such a fusion function may be explicitly selected by the user.
Included within the scope of the invention. In this regard, the present invention is directed to the user's geometric design.
Various acceptable fusion functions exist because they are intended to express intent.
Which usually means that the user does not have to consciously determine the precise input,
This is because the intention of the user is generally appropriately expressed. In other words, for the iterative approximation of the final geometric design, a wide variety of fusion functions
It is believed that numbers may be acceptable; this uses substantially the same fusion function
To gradually create and / or modify relatively small portions of the geometric object being designed
By doing so, precise details are gradually created. With respect to another method, the present invention relates to a method for defining precise (geometrically or otherwise) constraints.
In addition, it is also necessary to express the user's intention repeatedly at a high magnification.
High accuracy and / or small scale design features where this is needed.
Can be incorporated into the user's design. In step 1016, the equation (2) applied to the one-dimensional parameter space
Using the transformation, an interpolation curve C (u) is calculated. Point PT1, PT2 and vector
FIG. 32 shows an example of the interpolation curve C (u) in the case where TAN1 and TAN2 are designated.
It was shown to. FIG. 27 shows the nearness of the equi-tilt boundary R (u) for the object S (for example, the surface)
The steps performed in constructing the similarity are shown; where the points PT1, PT
2 defines the contour curve corresponding to the isotropic ribbon boundary approximation to be generated. More details
In other words, the isotropic ribbon boundary approximation generated by this flowchart
It is intended to approximately fulfill the definition of the isoscillary boundary in the section "Justice." More specifically, the isotropic ribbon boundary approximation determined by this flowchart is
For example, along the contour curve generated between PT1 and PT2,
Depending on whether the object S is smooth or not, the portion of the object S between PT1 and PT2, etc.
Works to match the definition of the tilt ribbon boundary. That is, the smoother (curvature
The smaller the variance), the better the match. Next, in step 1104 of FIG. 27, the curve interpolation program shown in FIG.
The ram is the tangent TAN1 to PT1, PT2 and the object (surface) S
, TAN2. Thus, the nearness of the contour of S adjacent to the curve
A similar interpolation curve C (u) is returned. In steps 1108 and 1112, each of the points PT1 and PT2 is
The tangent (ie, picket) along the parameterization of the object S at
The values are substituted into the variables PICKET1 and PICKET2, respectively. Where PIC
KET1 and PICKET2 are usually perpendicular to the vectors TAN1 and TAN2
Note that this is not required. Then, step 1116
And in step 1120, the equidistant ribbon points corresponding to PT1 and PT2 are determined.
And substituted into variables RIBBBON_PT1 and RIBBBON_PT2, respectively.
It is. Next, at step 1124, the curve interpolation program of FIG.
Start again using BON_PT1, RIBBON_PT2, TAN1, TAN2
As a result, an approximately inclined ribbon boundary approximation R (u) is obtained. In some cases,
The equidistant ribbon approximation bounded by the interpolation (contour) curve C (u), corresponding to this
Pickets (PICKET1, PICKET2), and newly generated etc.
Note that the inclined boundary R (u) does not necessarily form a surface.
In fact, curves C (u) and R (u) may be substantially identical (eg, PI
If CKET1 is equal to TAN1 and PICKET2 is equal to TAN2
). FIGS. 28A and 28B show a more precise isotropic ribbon than the approximation obtained from FIG.
The flowchart of the program for constructing the boundary is shown. For more information,
28A and 28B, the path of the given contour curve
In response to the change of the object (for example, the surface) S along the line, the program of FIG.
Repeatedly activated adaptively. In step 1204 of FIG. 28A, one or more markers M _i (However, i =
1, 2,..., N and N ≧ 1) are assigned to a variable MARKER_SET;
Here, these markers are on the surface S and along the contour curve to be generated.
The desired generation order has been made. Note that in one exemplary embodiment, the marker
Mosquitoes may be provided (eg, constructed and / or
Is selected). Further, in this description, the marker M _i Is assumed to be the tangent of S input by the user.
. However, such a tangent vector determines the tangent of the direction of parameterization of the surface S.
It is also included in the scope of the present invention that it may be automatically given by
. In step 1208 of FIG. 28A, the first in the set MARKER_SET
Is assigned to the variable MARKER1. Then, in step 1212,
A determination is made as to whether there are additional markers in the MARKER_SET.
You. If there is, at step 1216 the variable INTRVL is
The parameter increment value for selecting points to be generated sequentially on the curve while incrementing
Enter. In one embodiment, INTRVL has a range of about 10-3 to 10-6 or more.
May be substituted. In step 1220, the value of the next marker in MARKER_SET is
Assigned to variable MARKER2. Next, in step 1224, MAR
KER1, MARKER2 (and associated user-specified tangent vectors
26) is used to start the curve interpolation program shown in FIG.
Interpolation curve C between mosquitoes _j (U) is obtained (where j = 1, 2,...,
Depending on the number of times the Next, at step 1228, MARKER1
, MARKER2, and the value of the interpolation curve C (u), based on FIG.
A boundary approximation is determined, whereby the equi-inclined boundary approximation curve R _j (U) is obtained. Next, in step 1240, the curve C _j (U), R _j (U) Select point on
Default value INTRVL is assigned to the variable u_VAL. this
In step 1244 following _j (U_VAL) corresponds to the variable IN
Assigned to CRMT_PT. Next, at step 1245, the point C _j (U
_VAL) is substituted into the variable S_PT. More specifically, assuming that S does not overlap with itself within ε> 0,
For some ε, C _j A point on S existing in the vicinity of ε is selected. Note that C _j Since (u_VAL) does not need to exist on S, the curve C _j Crosses the surface S
An interpolation curve C that does not exceed 1.5 times any of the undulations _j To the maximum length along
If the value of the variable INTRVL is set to correspond, the interpolation curve C _j Is actually on the surface S
Note that it is considered to be qualitatively or consistent. Next, in step 1246, the point INCRMT_PT is set to the predetermined value of S_PT.
(For example, this predetermined distance may be in the range of 10 -3 to 10 -6)
Is determined. More specifically, the predetermined distance is determined by the user.
May be set and / or modified depending on the application for which the invention is utilized
It may be a system default value. Therefore, INCRMT_PT and
If S_PT is within the predetermined distance, step 1248 is executed;
In the step, the point R on the isotropic boundary approximation _j (U_VAL) is determined and the variable
Substituted for RIBBBON_PT. Next, in step 1252, C _j (
u_VAL), the approximation to the isotropic picket is determined and the variable PICKET
Is assigned to In the step 1254, the point C _j (U_VAL) surface (more general
Specifically, the tangent to S) is determined and assigned to INCRMT_TAN.
This tangent points in the direction of parameterizing S. In step 1256, the vectors INCRMT_TAN and PICK
A determination is made whether the ETs are sufficiently close to each other (eg, within one pixel on the screen).
Is If it is close enough, u_VAL is incremented in step 1264.
And the interpolation curve C _j The next new point above is determined. Subsequent step 1
In 268, the interpolation curve C _j Whether the end of (u) has been reached or passed
A determination is made as to whether It should be noted here that 0 ≦ u ≦ 1 is assumed. Therefore, u_
If VAL is less than 1, step 1244 is executed again, then step
Some or all of the steps up to 1256 are performed;
As theoretically specified in, the equi-inclined ribbon point approximation R _j (U_VAL) is the actual ribo
It is determined whether or not the point is sufficiently close. Returning to step 1246, if INCRMT_PT is not close enough to S
, S, a more precisely specified interpolation curve is determined. That is, the point
S_PT is placed in the marker and inserted in MARKER_SET;
New interpolation ribbon curve C with a smaller deviation from S _j (U) and R _j (U
) Is generated (assuming the continuous differentiability of S). That is, step 1272 is executed, whereby the mask for the point S_PT is
The new marker is created in the MARKER_SET as the current marker is created.
It is inserted between the current marker values MARKER1 and MARKER2. Then
Sets the flag of the marker currently called MARKER2 to unused
Along with (step 1276), in step 1280, the most recently constructed
Interpolation curve C _j (U) and any accompanying ribbon boundary curve R _j (U)
Remove. Then, step 1220 and subsequent steps are performed again.
And a new interpolation curve C _j (U) and ribbon boundary curve R _j (U) is determined. Here, in step 1256, INCRMT_TAN and PICKE
If it is determined that T is not sufficiently close to each other in the target space of S, step
Note that steps 1272 through 1280 and step 1220 are also performed.
I want to be. Returning to step 1268, the interpolation curve C _j The end of (u) has been reached, or
If you have passed, C _j (U) is (between MARKER1 and MARKER2)
) Is a close enough approximation to a point on S and R _j (U) corresponds to a point on S
It is assumed that it is not close enough to the isotropic ribbon. Therefore, the interpolation curve C _j (U
) And the corresponding ribbon approximation R _j Additional markers for which (u) has not yet been determined
If present, consecutive (as marker order) in MARKER_SET
The next pair of markers is determined, as in step 1220 and subsequent steps
Is performed. That is, in step 1284, MARKER1
The value of MARKER2 is substituted, and in step 1288, MARKER_
A determination is made as to whether there is a next unused marker in the SET. Exists
In that case, as described above, step 1220 and subsequent steps
Processing is performed. When all the markers have been used, the obtained curve C _j (U
) And R _j (U) (where j = 1, 2,...)
, Displayed graphically and stored for subsequent operations. Note that the contour curve
C _j By reparameterizing (u), these curves become a single curve C ^~ (
u) (however, C ^~ (0) = C1 (0) and C ^~ Set as (1) = CN (1))
Note that it may be parameterized dynamically. FIGS. 29 and 30 illustrate isometric handles, ribbon tangents, and attendant
By modifying the isometric ribbon, one or more surfaces (more generally, geometric
FIG. 3 is a diagram illustrating, at a high level, a flowchart for correcting an elephant. More details
For simplicity, in the flowcharts of these figures, one or more parts
By the surface Si (where i = 1, 2,..., N and N ≧ 1) (at least partially
) There is a resulting composite surface S0, where these partial surfaces Si are common
Are interconnected (eg, spliced) along the boundaries of
It is assumed that 0 has no discontinuities. Given such a composite surface S0, the flow charts of FIGS.
, Can be described at a high level: In FIG. 29,
Specify one of the geometric properties to be changed (eg, length, direction, curvature, etc.)
The isometric handle and / or the ribbon tangent
Or the partial surface Si to be modified with a change in the ribbon tangent. Next, in the flowchart of FIG. 30, the selected equi-tilt handle and / or
Or, as the user enters a correction for the ribbon tangent,
Corrections are calculated and displayed in real time. Note that the surface (more generally, geometric
Real-time calculation of the modification of geometric objects)
On the other hand, the computational overhead becomes too large,
Note that we could not. Therefore, in the present invention, it is very efficient
Provides a new fusion surface calculation technique where the existing and generated surfaces are correct
By doing so, this overhead was reduced. A more detailed description of FIGS. 29A and 29B is provided below. To step 1400
In this case, there is a contour and an equi-inclined ribbon corresponding to the entire boundary of each partial surface Si.
If not, a contour and an equi-inclined ribbon approximating the entire boundary of each partial surface Si are created.
To achieve. This can be performed using the program of the flowchart in FIG.
Please note that. In step 1404, a marker corresponding to the marker on the surface S0 is
Isometric handle and ribbon tangent are displayed graphically to the user
. In step 1408, one or more additional isotropic ribbons are added to surface S0.
Or extending an existing isotropic ribbon having a contour curve on S0;
Is determined by the user. The user makes such a request
If so, step 1412 is performed; in this step, the user
In addition to the other markers added, (a) the contour touches the boundary of the partial surface Si
At all positions, (b) the contour curve ends on the boundary of the partial surface Si
Markers are added in such a way that each is expanded. Further, an additional marker may be added at the intersection of the curve boundaries. Therefore
For these latter markers, the two separate ribbon tangents associated with them are
May be present (ie, one for each partial surface). Next, in step 1416, each Si (where i = 1, 2,..., N
), The program of FIG. 28 is activated, whereby the desired additional contours and
And equidistant boundaries are obtained. In the program of FIG. 28, a new marker is added.
It should be noted that it is only necessary to activate for the partial surface Si. At step 1420 following step 1416, the newly added equitilt
The handle and ribbon tangent are displayed. Note that in some embodiments,
Initially, only the isotropic handle is displayed, and if the user desires,
Note that it can be selectively displayed. Then, in step 1424, one or more additional markers within the existing contour
It is determined whether the user has requested to add. When there is a request
Has a new additional marker and at least a new
Dollars are determined for these new markers. In one embodiment of the present invention, a case where a new marker is added to an existing contour
Note that this contour changes slightly;
At this point, it will be exactly the same as the surface S0 at another point, and
The interpolated curve generated in the meantime (according to FIG. 26)
This is because it is generated at that time. Thus, a contour with one or more additional markers will generally be adjacent to surface S0.
It will more closely follow the shape of the part. Then, in step 1432, a new additional marker is optionally added
To the user, including the corresponding isotropic handle and ribbon tangent.
It is displayed physically. Steps 1408 to 1420 and steps 1424 to 1420
Note that 1432 does not need to be performed sequentially. Event start user
If the user interface is used, the processing of each new marker is executed individually,
What can be displayed before the user inputs the next new marker position is
It will be apparent to those skilled in the art of user interface design for computers. Therefore
During the continuous execution of steps 1408 to 1420, step 1424
One or more of steps 1432 may be performed. In step 1436, the isotropic handle and / or ribbon tangent is
It is determined whether or not the user has selected as a correction target. Should be modified
It is noted that the isometric handle and / or ribbon tangent is given the identifier ISO.
I want to be reminded. At step 1440, a marker corresponding to the ISO is determined, and
Access is enabled via the variable MRKR. Next, at step 1444
And a set of one or more partial surfaces S1,..., SN adjacent to MRKR is determined.
Access to these adjacent part surfaces is possible via the variable ADJ_SURFACES.
It works. In steps 1448 to 1460, the partial table adjacent to MRKR
The boundary expression of the surface Si is determined (step 1452), and MOD_SET and table
It is inserted into the set of surface boundary representations described (step 1456). More details
Or, for each of the partial surfaces in ADJ_SURFACES, next to MRKR
The boundary of the smallest part of the surface that is in contact with and bounded by the isometric ribbon
The expression data is put into the set MOD_SET. Finally, in step 1464, the program of FIG. 30 is started;
MOD_SET in real time as the user changes the ISO
The part of S0 in the boundary expression included therein is corrected. [0285] In the flowchart of Fig. 30, the identification is performed by the surface boundary expression in MOD_SET.
High-level steps to correct in real time
Note that these surface portions are adjacent to the marker MRKR. Therefore
, In step 1504, an isometric handle corresponding to the marker MRKR and
And / or the first (next) modified version of the ribbon tangent is obtained and substituted into the ISO
It is. Next, at step 1508, the ISO modified isometric handle and
And / or all isometric ribbons with ribbon tangent are regenerated and required by the user.
The latest correction requested is reflected. Note that this is a one-dimensional version of equation (1)
With the MR on each isotropic ribbon including the MRKR.
Modify each such isometric ribbon along its own area between the KR and the adjacent marker
Note that this is the case. Next, in step 1512, the first (next) boundary in MOD_SET
The boundary expression is assigned to the variable B. Then, in step 1516,
A set of equi-inclined ribbons for the (outline) boundary segment is substituted for a variable R. here
Where R is defined as containing at least one isotropic ribbon containing the marker MRKR.
I want to be reminded. In step 1520, a fusion table defined by the contour of the R
A surface is created. The equation used in this step is similar to equation (4)
It is a thing. However, this formula contains an additional function Qi (p)
. It should be noted that, in general, the parameter used when generating the surface S (p) in this step.
The part of the parameter space has 2, 3, 4, 5, or more sides (original contour image)
It should be noted that each side may have the original image of the isotropic ribbon.
You. Thus, for the translation function Qi (p) for each isotropic ribbon Ri of R, R
A point p in the parameter space inside I of the original image of the contour Pi for each isotropic ribbon Ri
, The corresponding point in the target space of the equi-inclined ribbon Ri is determined.
In a manner that can be used in the fusion function in Tep, these points p are Ri
Is preferably translated to a point in the parameter space for. Where the translation function
Note that Qi (p) preferably satisfies at least the following constraints:
I want to. (A) Q i (p) is continuous with respect to the continuous surface. That is, when the point sequence in I converges on the original image of the contour point Pi (u), Qi (p
) Converges to the equi-inclined ribbon parameter space point (u, 0). Next, in step 1524, the surface S (p) is displayed.
In 28, an additional boundary representation to generate an additional fusion surface S (p) is M
It is determined whether it exists in OD_SET. Step, if present
1512 is executed again. On the other hand, if no boundary expression remains,
At step 1532, the isotropic handle and / or rib
It is determined whether there are additional modifications by the user to the tangent. If it exists, at least steps 1504 to 1528 are executed again
Is done. In addition, each step of FIG.
Conform to the MRKR specified by the user while continuously correcting the Bon tangent
Real tie that is made gradually for the isometric handle and / or ribbon tangent
It should be noted that it can be performed sufficiently efficiently in such a way that changes in the system can be displayed. <4. Geometric Design User Interface> The general principles described above apply to a new user interface for computer-aided geometric design.
The foundation of the interface. In one embodiment of the user interface for the present invention, the user interface
A face is provided to define the equi-tilt. Such an interface
The use of a tool allows the designer, for example, to give a constant slope along the entire contour curve.
You can create a reflected ray by requesting it to be perpendicular to the ray direction of this;
Will be obvious to those. More generally, in the new user interface, the input of various constraints
Isometric ribbons, isometric handles that satisfy such constraints, and
And / or a ribbon tangent can be generated. In particular, beam direction, curvature, contact,
It allows the use of global constraints such as bell contours, planar dihedral functions, etc .;
Will be apparent to those skilled in the art. [0297] In one embodiment of the user interface, the user may access a given user, such as a cylinder.
Start with a geometric object. The user then moves to various positions on this cylinder.
Place a marker and draw a contour curve on the cylinder. Use tilt information from cylinder
This allows the contour tangent and / or isometric handle to be used as default.
May be. For example, at each marker position, the contour tangent is
In the plane tangent to the cylinder at The user may then select and modify the marker, add a marker, and / or
May modify the position and orientation of the isotropic handle and / or ribbon tangent.
As the isotropic ribbon is modified in this manner, the cylinder (more generally, the geometric
The target object) reflects the change due to the correction of the isotropic ribbon. Desired shape geometry
Until the target (derived from the cylinder) is obtained, add additional contours and markers.
You can add it in a way like that. One example of these steps is shown in the flowchart of FIG. That is,
In step 1904, the user may view the graphically displayed surface (more generally,
Is a geometric object). Next, in step 1908, the user
Construct a contour curve on the selected surface (object). Next, in step 1912, an equi-tilt ribbon (or at least
) Is generated for this contour. Note that this ribbon / boundary can be
, Can be generated with virtually no additional input from the user. sand
That is, an isoclinic ribbon / boundary can be generated from the contact properties of the surface on which the contour resides.
. More specifically, for a parameterized surface (more generally, a geometric object)
, The parameterized tangent on the surface at a point on the contour is
Can be used to create boundaries. Therefore, the vicinity of the surface on one side of the contour curve is shifted to the first side having this contour.
Can be used to determine the first isotropic ribbon / boundary to the surface;
Is above the seam between the first and second surfaces, the other of the contour curves
May be used to determine a second isotropic ribbon / boundary. [0302] Further, other surface properties may be retained on the iso-inclined ribbon / boundary.
Please note. For example, to keep parameterized tangents at contour curve points
In addition to isotropic ribbons / boundaries, the curvature and higher order (> = 2) derivative continuity with the surface
Surface characteristics such as the above may be retained. It should be noted that equi-inclined ribbons / boundaries provide additional surface properties.
Note that retention is also within the scope of the present invention. In step 1916, using this generated isotropic ribbon / boundary,
Surfaces with curves may be modified; in this regard, FIGS.
This has been described above with reference to the flowchart program. In some embodiments of the user interface, two object space surfaces
And a continuity requirement of a higher order than the tangent plane continuity can be selected.
(For example, curvature continuity)
, Are available for designers. For example, high-order continuity can be applied to isotropic ribbons derived from one surface at a common boundary.
By imposing constraints, it is also possible to create an equi-inclined ribbon to the other surface with a common boundary.
Can be bound as well. Therefore, this operation, under certain conditions,
"Mach b (Mach b)
and) reduce the effect. [0306] Other user interface operations provided in the present invention include the following.
There is (A) "rounding", which is a twisting process
Or modify existing surfaces; this may cause the sharp edges to be rounded or sharpened.
Jagged edges (ie, smooth surface except one point)
Is kinked). In order to perform such an operation in the present invention, the contour curve must be drawn on the surface opposite to the tip.
On top and smoothly blend between the contours (eg, as discussed in Section 2.3.5).
Then, the surface between the contours including the apex is removed. (B) "Embed", an interactive user interface procedure
Take the finished model, scale it, rotate and transform it to separate
As part of the model. <4.1. Define isometric with markers, contours, and user interface
Thing> The explicit contour is a contour curve expressing the intention of the designer. Explicit contour, bunch
May be unbound (free form) or partially bound (trim
). Implicit contours are, for example, visible between the surface fragments due to surface discontinuities.
(For example, formed between the end surface of a cylinder and its cylindrical side surface).
Bends, ie, curves). If the user introduces a surface discontinuity, the implicit contour is automatically generated.
It is. All contours in the model are in explicit or implicit form. <4.1.1. Creation of Marker> The outline marker and the handle are created by the following method. A. Markers are automatically created at the edges of new explicit and implicit contours
. B. Inserted by the designer on an explicit contour (for example, double-clicking a point
By that). From the designer's point of view, one would insert points on the contour. This
Only a few or only a few of the newly placed markers
Is changed in the contour line segment including. Then, add a new marker
Contour handle and isometric handle are determined based on the contour and surface shape
Is done. [0312] One marker may be designated at a plurality of identical points on the same contour (for example,
Contours that form and return to themselves and adhere to themselves). Such a mapping to multiple contour points
The marker designation remains unless this marker is deleted. If two or more contours intersect at a common point having a contour marker,
Each marker with a marker is bound and one marker is moved.
If both move, the match is maintained. The contour marker inserted by the designer can be used to provide contour handle points or
It may be inserted to set a constant iso-inclination value. The outline handle point is
There may be a set of constraints on the isometric handle;
Dollars may be given a value by interpolation of the two closest isotropic handles. <4.1.2. Viewing Markers and Contours> Various constraints may be imposed on the contour handle and the isotropic handle;
In the case of these handles are displayed differently depending on the constraints imposed.
It is. More specifically, the following constraints may be imposed on these handles: (A) Binding the direction of the handle to a specific range, (b) binding the length of the handle to a specific range, (c) binding the handle in the same plane as another handle, and (d) setting the curvature of the handle. (E) binding a handle to follow the transformation of another handle (eg,
Rolling and / or translation). The designer can select the display of the constraint condition by using the display request of the property of the geometric object.
Wear. In one embodiment, for different types of constrained contour markers, different
Displayed in different colors. For example, a non-mutable handle (also called a "fully bound"
) May be displayed in blue. In some embodiments of the user interface, the bound vector
Are "grayed out" so that these vectors
It is made clear to the designer that cannot be changed. For example, in one embodiment,
Fully bound handles are grayed out. <4.1.3. Combine Contours> In one embodiment of the user interface, the intersections at the same X, Y, Z locations
Joining two or more contours together is supported. When deforming the contour
And if the parameterization of the points on each contour is invariant,
Is called a "tie point". Note that such binding points are
It may or may not have an accompanying marker.
Please note. If such a binding point is modified,
Are modified as a group. like this
The binding point may be the end point of the contour, or an interior point (ie, a knot).
(Knot)). Alternatively, the first marker of the first contour exists in the target space range of the second contour.
May be constrained (in the shadow or in the sun). For example, FIG.
In FIG. 42B and FIG. 42B, the user sets the outline marker 2002 (first outline 2003 and first outline 2003).
And constrained on the second contour 2004) along the second contour 2004
Which causes the marker 2002 to move along the contour in the direction of the directional arrow 2006.
When sliding, the contour 2004 in FIG. 42A changes to the contour 2004 in FIG. 42B.
The user interface may have a function that enables the user interface. this
Such a slidable marker 2002 is called a “slide point”. A contour intersection is either a “slide point” or a “binding point”. Also these
Different types of points can be graphically represented by different colors and / or shapes.
May be distinguished. In addition, while the outline slides along another outline,
When the isotropic ribbon for this sliding contour is used to calculate the fusion surface S
, S is recalculated. <4.1.4. Creating Markers and Contours> This user interface supports the creation of contour curves by several methods.
Can be A. As with the data driven technique of FIG.
Draw a contour on the surface; here, to bind this contour to the surface within a given tolerance
, Additional markers may be added. Alternatively, in the second embodiment,
By allowing the user to select all markers that
You may draw. In each case, the contour is drawn over one or more surfaces.
Please note that it may be. Further, in the second embodiment, the user input
The interface supports the following steps to create a suitable contour. (A1) A marker point existing on the surface is specified. Each in parameter space
Generate a fit curve through the points; then evaluate this fit curve to fit in the object space
To obtain a corresponding image. (A2) For each surface where the new contour intersects, the user intersects the surface
The contour type (free form or trim) for the contour part may be designated. table
Trim one side of the surface to the contour drawn on the surface, or add two surfaces
Split into new surfaces. In this case, any penetration into the interior of the surface (non-degenerate
Contours must also intersect surface boundaries at entry and exit points
Note that That is, two surfaces along a common contour boundary are always joined to that contour.
Where, for this contour, these surfaces are classified as follows: (
a) one surface is a trimmed surface and the other is a non-trimmed surface ("free form
(Also referred to as "surfaces"), or (b) both are freeform surfaces. B. Copy contour: The user selects the contour to be copied. This contour is
(Called clipboard). Next, the user can copy
Select (for example, you should keep the contour handle or copy the contour
Attach contour handles to geometric objects). User selects new contour arrangement
(Resize, rotate, mirror, etc.) The user selects a location for a new contour. Note that the new contour is the original contour
Note that it can be bound by the constraints imposed on. For example, a new
The contour may be mirrored about a plane from the existing contour, and
Any change causes a change in the copy. If you create a new contour,
Contour markers are automatically generated at both ends of the new contour. Contour handle and isometric
(Ribbon tangent) The handle is derived from the geometric properties of the surface that the new contour splits
It is. <4.1.5. Modification of Marker and Contour> Modification of a marker and / or (contour, isometric) handle is
Or subject to constraints imposed on the handle. These are the methods listed below.
It is bound by one. A. Select a handle (contour or isotropic) at a specific marker m and
The dollar endpoint is defined as the vertical plane on which it is perpendicular (ie,
Defined by a contour or isometric handle and a contour handle in the plane or m
Movement to be constrained to lie on the
To correct. To modify selected contour and / or isometric handles
In order for the user to enter numerical values for length and angle from the keyboard,
A property sheet in a pull-up format is also available. B. For markers whose original image is constrained to be within the outline original,
For example, interactive repair by dragging such marker points
Positive allows the parent to slide along the contour. In addition, the position is bound
For unmarked markers, the marker point is set to the contour of the parent on which this marker is placed.
Move freely along the route (ie, only by the user's instructions and without any other restrictions).
Note that it can move. [0331] Further, the user can click on each of them or in the designated area (
For example, by selecting all markers within the bounding rectangle),
Note that contour marker points can be selected. In this case, the user
By moving the play instruction device (eg, mouse), all selected
All markers are moved uniformly in the direction corresponding to the movement of the display pointing device.
Can be made. However, the movement of the markers is subject to the constraints imposed on these markers. Was
For example, a bound marker moves only within the limits imposed on it. did
Thus, while the first selected marker moves only within the first contour,
Only the selected marker is positioned within another second contour orthogonal to the first contour.
When moving, one of the following applies depending on the desired moving direction. (I) the first marker is movable, but the second marker is not movable, (ii) the second marker is movable, but the first marker is not movable, (iii) Both the first and second markers are movable, (iv) neither marker is movable. C. Marker and handle constraints are not provided explicitly by the user, but are
It may be set as a default value. Pop-up nature sheet allows users to
Can set or remove specific constraints. D. Contour handle and / or etc.
Set additional constraints on the tilt handle that are dependent on the properties of other geometric objects
You may. For example, if the contour handle and / or
It may be constrained to be perpendicular or parallel to the reference plane. Note that the contour marker
For the position of, even if the constraint condition is set to depend on the characteristics of other geometric objects,
Note that it is good. For example, a marker is bound to be on a split plane.
Wear. The dividing plane is a plane related to the symmetry before and after the bottle is designed.
It is. Another example of such constraints is found in creating symmetric designs;
In other words, a copy of the contour marker that is mirrored with respect to the division plane is
And are bound to be symmetric. E. The surface adjacent to the contour is either C0, C1, or C2 continuous
Where C0 continuity is positional continuity and C1
Continuity is contact continuity, C2 continuity forces a smooth fused surface
. One constraint that can be set for a marker is the distance between the surface surrounding this marker.
Require C1 continuity; this is the tangent vector to the internal marker.
This is done by keeping the lengths of the rules equal. Freeze the contour handle and / or the isotropic handle at the marker (corrector
Contour segment containing this marker, the next two
Reconstructed based on the contour handle of the proximity marker; effectively,
So that the handle reflects the curve constructed by the two markers on either side
Is changed to [0337] Broadly speaking, contour modification is performed by controlling the contour marker position to control the contour shape.
And a feature of the user interface technique for modifying the handle
You. Examples of such user interface techniques are given below. A. Direct method: The contour is directly modified on the object space (three-dimensional) model. this
Is performed by correcting a contour marker and a handle constituting the contour. When the designer modifies a trim contour, the contour always reflects the pattern of the trimming surface.
Exists in parameter space. That is, the trim contour is
Must be modified in the context of the superstructure surface. Trim contour to correct
Or its component), the construction target of the superstructure is highlighted.
It remains highlighted while the user corrects the trim contour
. The designer has the option of turning on the contour and modifying it by the direct method.
You may have. For example, by modifying the contour that defines the surface of the superstructure,
The surface of the substructure is also updated. The contour that trims the surface of this superstructure is
Since it is constrained to be in meter space, the trim profile is also recalculated. B. Design Ribbon Method: This method is used to modify specific areas of the contour
You. By using this, for example, contours that are complicated in one display direction
Correction in the direction can simplify the work of the designer. Designers are the same
Two markers existing on the outline of are designated. Contour segment between two markers
Project in at least one graphical display direction of the contour,
A ribbon is created (not to be confused with an isometric ribbon). A design ribbon is a simple protruding surface (ie, a curve that follows a given direction).
To produce a surface; for example, for a marker at the edge of the contour, the corresponding
By displacing the corresponding contour handle using the isometric handle, the boundary handle
And equidistant boundaries are compensated using, for example, a low-dimensional version of Equation (2).
A surface having an outer periphery consisting of a contour, an isotropic handle, and an isometric boundary.
Define the projecting surface). The three-dimensional contour segment defined between the markers is always
Present in the original image of the design ribbon. The user can use one of the following two methods
Correct the contour by one of them. (B1) Modify the two-dimensional drive curve that draws the design ribbon;
At the end of the ribbon, and by default, this curve
2 is a two-dimensional representation of a defined three-dimensional contour segment. User is a 2D point part
By selecting the set, the drive curve can be "simplified". Every time the user corrects the drive curve point, the ribbon is updated and the three-dimensional contour is also corrected
Exists in the parameter space of the modified and modified ribbon. Against the drive curve
Examples of operations are the same as those listed in the section “Contour markers” (point / tilt correction
, Insert, delete, etc.). (B2) A two-dimensional contour point in the design ribbon is corrected. The user can move in the main display direction
Two-dimensional contours can be directly corrected in a vertical display direction. Two-dimensional points are always
Exists in Bonn's parameter space. Examples of operations are given in the section “Contour markers”.
Same as something (point / tilt correction, insertion, deletion, etc.). There is only one design ribbon per contour segment, per surface
I can do it. Design ribbons can be created, modified, and deleted. Once created
Will be permanent if done; that is, until the designer later modifies this segment
Remains unchanged. The design ribbon only appears when the designer corrects this
. A single profile has multiple ribbons corresponding to multiple surfaces containing this profile.
May be. [0347] Note that, by correcting the contour using the direct method, it is possible to spread between the corrected points.
Note that any design ribbons will be deleted. As a result, there is no ribbon
And the designer must re-designate the ribbon. C. Contour movement: The designer selects two or more contours and moves them simultaneously. sand
In other words, this user interface instruction is placed on the contour (or its segment).
Are selected, and all of them are moved as a unit. D. Merging contours: the designer draws a new contour, which matches the end points of each contour
Can be mounted on existing contours as In addition, designers can use existing contours
You can specify which segments of the to delete. As a result, a new wheel
The contour and the remaining connection part of the existing contour having an end point matching the new contour
Will be merged. Note that by merging the contours,
The set of contour handles, isotropic handles, and ribbon tangents into a single set.
Summarized. E. FIG. Contour separation: one contour can be separated into two at a single point p
. The endpoints of each of the two new contours are constrained to coincide at p. <4.1.6. Deleting Markers and Contours> It is always possible to delete contour markers, except at the endpoints of the contour.
is there. However, in some embodiments of the present invention, the pieces were kept smooth.
Need to replace the marker with a marker with constraints
. Note that the new bound replacement marker is in the same location as the previous marker.
Note that it may or may not be present. If the entire contour is deleted, the user interface
Highlight a geometric object, its outline and its subordinate geometric
Ask the user for confirmation before deleting the target. Therefore, in the present invention,
Dependency information on dependencies between Dell geometric objects is well preserved;
Therefore, when modifying the target used to guide other targets, appropriate additional
Note that the correct is also performed automatically for these other objects. <4.1.7. Contour Markers and Contour Handles> For contour markers, typically two contour handles, two isometric handles and
Note that there are two ribbon tangents;
One contour handle, one equi-tilt for each surface that has a curve
Handle, and one ribbon tangent. However, where some contours gather
In minutes, the number of handles associated with a contour can be much higher;
If it is at the end, it can be less. <4.2. Isometric and User Interface> The tilt of the isometric handle is at the marker and around the contour containing the marker.
In the surrounding part, the surface contact property is controlled. The length of the isometric handle is
Control the body. That is, it controls how much the surface is bulging. Some
The tilt handle is offset from another isometric handle (eg, -10
(To the other side only). Equidistant handles can be placed at any point along the contour
(By inserting a marker on the contour). <4.2.1. Creating Eccentric Handles> The user interface supports binding of isometric handles to each other.
Have been Such a handle is always tangent and of equal length,
Alternatively, it can be constrained to be somewhat offset, etc.
. In one embodiment of the present invention, the user interface includes
Equipped with a pop-up menu to display and change the isometric handle constraint value
I have. <4.2.2. Correction of isometric handle> If the user slides the contour marker along the contour, the user
By fixing the isometric handle to the
) To change the surface; or the two closest neighbors on the contour, etc.
An equi-tilt handle may be obtained by interpolation between the tilt handles (in this case, the dependent table
Surface is not affected). <4.2.3. Deletion of isometric handle> The user interface supports the deletion of the isometric handle. Isometric
When deleting, the following steps apply. <4.3. Special Geometric Objects and User Interface> In the present invention, there are some features that substantially enable the design of objects such as containers.
Special types of geometric objects can be created and manipulated. <4.3.1. Label Surface> The label surface is a special case of the trim surface. Special case of label surface
The signs are as follows. (I) a "watershed" contour running from the bottom to the top of the label; (ii) the label curve between which the corresponding label surface is graduated
Exists (eg, label curve 132 of FIG. 11); (iii) a boundary (trim) contour exists (eg, trim contour 1 of FIG. 11).
38). An important difference that distinguishes the label surface from the other trim surfaces is that the original surface (labeled
(The surface from which the metal surface is trimmed) is a graduated surface. More
Is the curve defining the label surface, the scaled surface is the boundary of these defined curves
Bound to be maintained within. Other surfaces may be fused to the label trim contour, but the trim contour is
That this can only be modified in such a way that it is guaranteed to border the graduated surface
Please note. In one embodiment of the present invention, the two-dimensional “stretched” representation of the label surface is
Can be generated. In other words, the surface is flattened by pushing it flat, so that
It can correspond to one to one. Such representations are designed by the designer on the label surface.
, And then the container is wrapped. <4.3.1.1. Creating a label surface> To create a label surface, the surface of the superstructure to be trimmed must be graduated.
Surface, which can be approximately developed, that is, on any scale line
It must be a graduated surface where all normals are parallel. Next, the user
Perform a normal surface trim step; ie, draw a contour on the graduated surface,
On both sides of the contour (ie, the label surface and the surface portion to be trimmed) (
Part) generate surface, trim label surface and fuse with other surface of trim contour
Let it. It should be noted that the surface part to be trimmed is hidden during normal viewing.
Want (ie, no longer part of the visible model). In order to generate a label surface, the following procedure may be prepared. High
At a higher level, the steps in this procedure are as follows: (I) Confirm that the surface is graduated. That is, if the contour is 4.3.1. Knot
The contour selected by the user is automatically corrected so as to satisfy (i) and (ii).
Correction is supported by the user interface. More specifically, this
To perform the steps, the following sub-steps are performed. (Ii) the user outlines the boundary on a surface that defines the boundaries of the label; (iii) a graphical representation of the label (ie, on its own, characters, designs,
And / or construct a graduated surface with a design) (iv) Give the user this label representation on the label surface (ie this representation)
Attach it graphically. More specifically, the user for attaching the label expression
The interface automatically labels the label expression by grouping type operation
In such cases, the label representation may be rotated, translated, or contracted on the label surface.
Maintains its position on the label during operations such as changing the scale. (V) If the label surface and / or label is not satisfactory, use
Allow the user to cancel the design. <4.3.1.2. Modification of Label Surface> Modification of label surface components is slightly different from modification of trim surface. The portion of the watershed contour that is a straight segment is constrained to maintain linearity. The opposite boundary of the watershed (the other side of the parent graduated surface) cannot be modified. Upper part
Between the boundary and the lower boundary is a simple straight line segment. Upper and lower boundaries
The contour can be modified. These allow you to insert additional free contour markers above themselves.
Are bound to not. The contour marker at the far end of the watershed is marked with a scale.
Is constrained to move only to maintain the surface. This is the graduated surface
As long as it remains, this is expandable (extendable along the same curvature)
, The angle of the end point is readjustable. <4.3.1.3. Deleting label surface> By deleting the label surface, the bundle for all the contours used to create the label surface
The constraint is removed. In addition, all constructs for label surfaces that are invisible to the user
The elephant is also deleted. The constraint of maintaining a graduated surface is also eliminated. But
Thus, the remaining geometric objects are released from the constraints on the label surface,
It can be modified in ways that were not possible before. <4.4. Drilling Tool User Interface> In the present invention, it assists a user to add a hole to a geometric model.
New computer techniques may be provided (e.g., adding a handle to an unhandled bottle).
To add). The information needed to add holes to the model by this procedure is
It looks like this: That is, the loop of the contour segment on the front side surface, the back side
Contour segment loops on the surface, each contour type of contour loops (free form or
Is the trim), and an optional contour, which forms the interior of the hole. <4.4.1. Creating Holes> The Hole Creation Tool guides the user through a series of steps to add holes
I do. FIGS. 22A-22C illustrate the use of the present invention to create a hole 600 on a geometric object 604.
It is a figure which shows the procedure which produces (FIG. 22C). Run to create hole 600
The corresponding steps are as follows. (A) Draw a contour loop 608 on the front surface 612, (b) Draw a contour loop 616 on the back surface (project the contour 608 on the back surface)
May be). Note that isotropic handles are automatically placed on contours 608 and 616.
I want to be. (C) One or more of the contours for one of the contour loops 608 and 616 is free
If the contour is a formal contour, the user must add a new contour (to complete the contour loop).
And / or contours that merge corresponding to such loops may be added.
This allows these contours to be used as if they were a single contour.
Be bound as much as possible. Therefore, after the contour loop has been constructed,
Can be used to remove the surface and remove the original surface blocking the holes. If a trim contour loop is specified, the surface area inside the contour loop is trimmed.
Is done. If specified, the hole creation procedure uses additional contours to define the internal boundaries for the hole.
Place the surface on top and mold. Otherwise, the front and back contour loops
The surface is automatically peeled between the loops. <4.4.2. Modifying a Hole> Modifying a hole modifies the contour markers and contour handles that form the shape of the hole.
Is performed by the function. <4.4.3. Deletion of a hole> Deletion of a hole depends on the components forming the shape of the hole, ie, the contour and
This is done by the ability to delete other geometric objects. <4.5. Consider smoothness using the user interface> Consider the order of the transition between adjacent surfaces (at the contour). In this section, the second
It contains broader suggestions for the general theory mentioned in the section. <4.5. 1. Continuous contour using interface> Given two crossing contour curves, if the following conditions are satisfied,
Derivative continuity at the intersection is guaranteed. (A) the end point of one contour matches the end point of the other contour (position continuity); (b) the fusion function Bi (FIGS. 26 and 27) used to generate the contour
(C) contour handles at intersection markers are collinear and have equal length. The following tangent continuity is a weaker condition obtained by changing the above (c).
It is. (C *) The contour handle at the intersection marker is only collinear. This place
In that case, the length of the contour handle may be different. The designer can break the collinearity of the two contour handles at the intersection marker by
A bend can be created at the marker position. This is a two contour hand
That do not have a common direction. <4.5. 2. Continuous Surface> The concept of tangent plane continuity between surfaces can be defined as follows. That is, two
For each point p at the boundary between the surfaces S1 and S2 of p, the tangent plane T1 (p
) Is equal to the tangent plane T2 (p) of S2 at p. For surfaces that straddle contour boundaries
In order to achieve tangent continuity between markers, it is necessary to add
Contour handles at each other and at the marker,
It must be in a common plane. If this is not met, the contour
Bends on the surface along. [0381] Two or more surface pieces should be generated, and these pieces are placed at a common marker point p.
In the present invention, in the case of binding to
Note that an isometric handle called "" is automatically generated. That is, each contour P (with p) used to define one or more surfaces
, The corresponding automatically generated vector V, which is a vector V with origin at p
There may be a common directional handle created; where V is the contour hand of contour P
Perpendicular to the contour, this contour is
It lies in the constructed common plane and contains the point p. In addition, user in
The interface displays the common direction handle by the user or not
Please note that this is supported. In order to achieve a smooth surface, the contour handle and the isotropic handle
Note that there is no need to match adjacent contours at the marker; these
Need only lie in a common plane. FIG. 18 shows the surfaces 416 and 41
For eight, there are three contour curves 404, 408, 412. Each of the three contour curves intersect at the contour marker 420, and each contour is
Corresponding equi-inclined ribbons 424 (corresponding to contour 404), 428 (corresponding to contour 408)
, 432 (corresponding to the contour 412). Further, the contours 404, 408, 412
And the contour handle and isometric handle associated with the marker 420 are as follows:
It is. (I) Contour handle 436 and equi-tilt handle 440 for contour 404, (ii) Contour handle 444 and equi-tilt handle 448 for contour 408
(Iii) For the contour 412, the contour handle 452 and the isotropic handle 45
6. Therefore, the contour handles and the equi-tilt handles 436, 440, 444, 44
8, 452, 456 all lie within plane 460 (shown as a rectangle using dashed lines).
If present, surfaces 416 and 418 connect smoothly at marker 420
. At any marker, the two isotropic ribbons are similar to the intersection of two contours
Often, they intersect in a manner; that is, two equi-inclined ribbons, one end for each ribbon.
May have a common equi-tilt handle. The different (fused) surface regions S1, S2 (FIG. 43) connected by the composite contour
In order to realize the tangent plane continuity between tangents, the tangent continuity across the contours P1 and P2 must be
Not only is it necessary, but also the tangent continuity between adjacent ribbons R1, R2 is required.
You. That is, the contour P1 (between the markers 2010 and 2014) and the contour P2 (
For markers 2014 and 2018), the respective ribbons R1, R2 are:
When these are considered as surfaces, they must be continuous on a tangent plane,
The handle 2022 must be shared. In many cases, the tangent continuity between ribbons is the tangent continuity between contours, and
, Tangent continuity between the ribbon boundaries required for a smooth transition across the surface piece boundary, and
Note that they are equivalent. Furthermore, the user interface of the present invention
Thus, techniques are provided for ensuring tangential planar continuity between ribbon boundaries;
Note that these techniques were used to ensure tangent plane continuity between contours.
Substantially the same as the law. Thus, according to the present invention, there has been produced from an equi-inclined ribbon according to the present invention.
Tangent planar continuity between adjacent surfaces is obtained. In some situations, the continuity of the composite ribbon is intentionally broken, and
Folds across the surface can be formed; the folds
Does not match with contours that match along. However, in some embodiments of the present invention,
Can create a "shade-shaped outline" that matches this fold. <4.5.3. Curvature continuity> Surface appearance quality depends not only on tangent planar continuity but also on higher derivatives
You. The user can actually feel the discontinuous change in surface curvature;
In particular, specular highlights and anti-
When displayed by projection texture mapping, this is well applied. Users should be aware of unsightly artifacts known as “Mach bends”.
Can be. Therefore, the degree of continuity during the transition is increased to the curvature continuity.
This will improve this problem. According to the analysis, the curvature of the surface defined by the equation (1) or (4) is Bi
And the second derivative of Si. The dependence on Bi is not obvious;
Thus, the fusion surface is selected such that the second derivative is zero, and the surface function Si is given by the curvature
Is advantageously determined. The cosine square function in section 2.1 satisfies this condition.
Fulfill. There is also a fifth-order polynomial that satisfies this. For example, in equation (3.1)
This is the polynomial B1 (x). The curvature of the fusion surface generated by equation (1) or (4) depends only on Si
(Ie, Bi ″ = 0), the method of the previous section for achieving tangent continuity
Similarly to the above, it is possible to increase the degree of curvature between the boundary surface pieces Si. To do this, simply place the corresponding contour and isometric handle on the contour boundary.
What is necessary is just to define so that these 2nd derivatives may correspond in each marker along.
However, each contour handle 212 may be considered as a one-parameter linear function.
Note, therefore, that the second derivative is zero. Therefore, curvature continuity
Is achieved; however, the curvature across the contour is “flat”, ie, zero. This is useful at each point where there is a bend on the contour, but at other locations.
Is not desirable. To correct this situation, move the straight handle to a parabolic arc
What is necessary is just to replace it with a curved rib like this. Therefore, the handle becomes an arc and the marker
In mosquitoes, the curvature matches a given arc. [0398] For all handles, such as contour handles, isometric handles, and boundary handles,
The idea of giving non-zero curvature and zeroing out the second derivative of the fusion function
Is extended, the Mach band effect is reduced. <4.5.4. G1 Continuity Using Roll, Yaw, and Magnitude Representations> In the present invention, handle vectors (eg,
, Isometric handle) is provided;
Here, the G1 continuity between the surfaces connected by this contour (as defined in the “Definition” above)
Is defined). In this method, referred to herein as the roll-yaw method,
Three scalar quantities called roll, yaw, and mag (magnitude)
Specifies the vector V; where roll and yaw are at point P on the curve
A tangent vector T at point P, a vector N perpendicular to the curve at point P,
Is determined using The yaw component of the vector V represents the angle deviation from T at P
You. For example, if the vector V is in the direction perpendicular to T, the yaw value is (at least
0 ° (in one coordinate system) and the vector V is in P in the same direction as T
The yaw value is 90 °. For the roll component of vector V, this scalar
The amount indicates the amount of rotation around T about the axis of rotation; here, this angle is measured.
The reference axis at this time is the vector N at P. [0402] Therefore, the vector N represents the roll 0 °, and its rotation angle is calculated using the right-handed system.
In the range of -180 ° to 180 °; this will be apparent to one skilled in the art. Be
For the mag component of the vector V, this simply represents the length of the vector V. here,
An arbitrary vector expressed in three-dimensional Cartesian coordinates is, for a given T and N,
Note that it is possible to convert one to one into the notation of the rule, yaw, and mag. [0403] Note that the vector N may be selected from vectors in a plane perpendicular to T.
I want to be reminded. However, this does not ultimately determine N. Therefore, define N
There are several ways to do this. Such a method for determining N
The first one simply selects a constant vector VC, then the expression N = T × VC
N is determined. However, in this method, if T and VC are collinear,
In this case, N is undefined. In order to obtain the value of N even when the result of this equation is a zero vector, N must be
It can be approximated in the linear topological neighborhood. In contrast, N
In the second method, the Fresne-Serrare coordinate system of the underlying curve is selected.
Good; this will be apparent to those skilled in the art. However, the Fresne-Séret coordinate system is discontinuous at the inflection points along the curve.
Can get. Thus, in the present invention, complex (ie, three-dimensional) curves
Provides a way to create a reference coordinate system that also has minimal rotation;
When defining the vector N irrespective of the direction and shape of the curve and its tangent vector T
Difficulties are reduced. As described above, the roll-yaw method achieves G1 continuity over a contour.
Provide a new way for For example, consider the arrangement shown in FIG.
, A contour having a left isometric ribbon LR and a right isometric ribbon RR is shown.
Each isometric ribbon LR, RR has two corresponding isotropic handles at its ends;
That is, HL1 and HL2 for LR and HR1 and HR2 for RR.
It is. With respect to an arbitrary point pp on the contour, the end points of the contour P are called HP1 and HP2.
Assuming it has dollars, the contour for the surface bounded by the contour is also
The continuous continuity is determined by the interpolated isometric values IL and IR. In addition, IR
Interpolated from HR1 and HR2 (based on the technique of the present invention), IL is HL1
And HL2. Thus, as will be apparent to those skilled in the art, G1 continuity across contour P
As for IL and IR, at least in the opposite direction (collinear).
In addition, as will be apparent to one of skill in the art, for ILs HL1 and HL2
Cubic Hermitian interpolation between HR1 and HR2 for IR
G1 continuity when IL and IR are formed using the Hermitian interpolation
Is that HL1 and HR1 are equal-length opposite vectors.
Is Rukoto. Further, the same is required for HL2 and HR2.
. However, instead of interpolating the isometric values IL, IR in Cartesian space, the interpolation is
When performed in a (roll, yaw, mag) space, the G1 continuity is tighter.
Realization, that is, the roll values of HL1 and HL2 match.
it can. Thus, this is to ensure G1 continuity at any point on the contour P
Does more than just say that HL1, HR1, and HP1 must be coplanar.
No request is made (the same applies to HL2, HR2, and HP2). Sa
In addition, if the isotropic handle is curved instead of straight, the same condition is imposed.
Please note that More specifically, the tangent vector to the equi-tilt handle at a point common to the contour P
May be used in place of any corresponding isotropic handle vector shown in FIG.
good. Therefore, as will be apparent to those skilled in the art, Cartesian
Convert the vector to roll, yaw, and mag vectors, then use the coplanar constraints described above.
Is satisfied, so that the surface extends G1 continuously across the contour P.
A computer step that implements the roll-yaw method of ensuring that
I can prepare. <4.6. Embedding Model in Model> In the present invention, each part of the surface bounded by the contour is independent of each other.
It is possible to design. For example, replace the triangle on the surface with a free-standing surface model.
It may be designed as Dell. The designer then obtains a model of a satisfactory design.
Until required, contours and skewed ribbons can be added as needed (obvious to those skilled in the art).
Is used). Then, this small piece is deformed, rotated, and attached to the triangle of another model.
You can do it. Therefore, a model that has been precisely finished is embedded in another model after design.
You can go in. By maintaining this coupling, this process can be used at the level of detail control.
Can be That is, for example, if you look at the model from a distance,
Parts do not need to be displayed; however, as the model approaches,
Combine the embedded objects to show the parts. Following two types of embedding
Will be explained in the section. <4.6. 1. Rounding Technique> In FIG. 20, a small fusion surface is defined between two intersecting surfaces 484,486.
The ridge is rounded. This fusion surface 480 fuses from narrow surface bands 488,490.
Where the original image of this narrow surface band is in parameter space
This is a “small” offset of the ridge 482 from the original image. This processing is directly performed by the equation (1).
Application, the two surfaces 484 and 486 share a common parameter space (not shown).
)). This new surface type is a new evaluation that is particularly efficient in the specific case described.
Routines will be introduced. <5. Evaluation> First, consider the evaluation of two-sided fusion; other forms are derived from this basic form.
Think to be guided. Since it is important, it is described again. Equation (1) is as follows.
is there. [0415] What is to be determined in the evaluation of the surface S is the fusion function Bi and the equi-inclined ribbon Si.
is there. The fusion function is calculated as a one-variable function of the distance in parameter space
. As described in Section 2, the evaluation of the distance function is based on the fact that the original image in the parameter space is
It varies significantly depending on how complex it is. Once determined, the actual fusion value can be calculated by a simple table lookup;
, The fusion function is tabulated and stored in memory at a sufficiently high resolution;
Searched according to value. Consider the fusion function B1 (x) in equation (3.1). The function is evaluated at x = 0, 0.01, 0.02,..., 0.99, 1. this
These values of 1001 (101) are stored as an array. Given a point X
Is used to identify the closest value in the array, for example, between 0.52 and 0.53.
used. Then use B (0.52) or B (0.53) as function value
Is done. [0419] Depending on what the distance function and the isotropic ribbon function are,
There are many techniques. The explanation in this section assumes a computationally simple model.
Attention is drawn to methods that do, but nonetheless, have significant design flexibility. FIG.
At 1, an equi-inclined ribbon 508 (S1), 516 (S2) is provided. They are
Parameters u and v are parameterized from 0 to 1. Contour 5
For each fixed value of v along 04, the corresponding picket on the equi-inclined ribbon 508 is
If it is a straight line segment (eg, line segment 512), it will be apparent to those skilled in the art.
As such, the isotropic ribbon is a graduated surface. Therefore, the point (u, v) is found
In locations where this occurs, the parameter u provides a distance measure along the scale line.
Offer. It is assumed that each isometric ribbon 508, 516 is a graduated surface. Furthermore, para
The original image of each of the contours 504 and 506 in the meter space is the contour itself, and
The distant measure is the value of the u parameter of the point (u, v0) on the equi-inclined v0 scale line.
Assume. Since the equi-inclined ribbons 508 and 516 are graduated surfaces,
For data v0, add the appropriate offset vector to the previous value
, A set of equidistant points along line segments 512 and 520 can be scanned. initial value
Is Si (0, v0). The offset vector is given by the following equation. [0421] Here, n is an eye to be scanned from one end of the equi-tilt ribbon (original image) to the other end.
This is the number of desired points on the fill line. As desired from a design point of view, the fusion function is divided into one, ie, B1 = 1
If the constraint of -B2 is imposed, equation (1) becomes as follows. [0423] In one embodiment, using this form and the previous simplification, for each point
, Three vector additions (for S1, S2, and "+"), one table lookup (B
1 (u, v)) and one scalar multiplication.
. This is after initialization and finding each Si (0, v) and (Equation (10)
(Using) the offset vector T0. Point on S
To scan the set of, we simply need to increment the parameter v, which gives
Points along the scale at u can be calculated. In the case of a defined four-sided surface (section 4.6.1.), Some Si
On two sides; but otherwise, first fused longitudinally across the ribbon
I do. More specifically, in the case of the v-roof in FIG.
Same as 35; however, the u roof in FIG.
is there. A four-sided surface results from all four centroid fusions. In FIG. 33, four contour curves P11, P11,
P12, P21 and P22 are shown. In FIG. 33, the contour curves P11 and P12 are
It is used together with the corresponding isotropic ribbons R11 and R12 to produce the fusion surface S1.
. Although S1 is evaluated to be exactly the case of the two sides described above, generation of S2 (FIG. 35)
, U, v parameters are inverted, which is different. In this case, the isoclinic R
21, the straight line segment on R22 corresponds to the case of fixed u and v-scan;
This situation is incompatible with rapid scanning. However, in FIGS. 34 and 35,
It is desirable to fix only one parameter and scan the other. In one embodiment
In this regard, the problem is to define a different definition for the isoclites R21 and R22.
Will be more resolved. In other words, each of these ribbons can be created by simple user input.
This is the fusion of the two graduated surfaces defined. For example, consider the equi-inclined ribbon R21.
I can. This is described in Section 2.2 and shown in FIGS. 37-39.
Fusing two bi-primary surfaces 1950, 1952 in a manner similar to the technique
And may be defined as follows. That is, the contour P of the biprimary surfaces 1950, 1952
The tangent edges on 21 are contour handles 1956, 1960; boundary handle 1
964 and 1968 are tangent to the ribbon boundary 1972 and the bilinear surface
To form the opposite edge. The remaining two line segments 1976 and 1980 are user input
It is. Now, second, fix v (u roof) and add a single vector offset
Scanning can be performed. As a result, points on the equi-inclined ribbons S21 and S22 are obtained.
In each case with the same amount of work as obtaining the points on the v-roof. In addition, new
The points on S2 must be calculated by fusing the points. Counting the operations, 11
Vector addition, five scalar multiplications, and one table lookup. This increase
Is a fusion of these three, three for the v roof and three for the u
One for the fusion of the two roofs. For a general N-side surface, it is necessary to first calculate the distance on each ribbon.
is there. The parameters can be calculated using the N-side parameterization technique of Section 2.2. Next
Then, these distances are substituted into the fusion function of equation (6). These vary between 0 and 1.
Is adjusted to The parameters for the ribbon must be set from the distances thus given.
Absent. That is, one parameter is the distance (from the contour). The other para
The meter determines where the parameter lines of FIG. 12 meet at the edge of the N-sided polygon.
Can be derived by Where the polygon has sides of length 1
Assume. After these parameters can be calculated, all necessary sums are calculated by equation (4).
You can calculate. <6. Applications> The present invention can be used in various computer design areas. For more information
The following is a brief description of some fields to which the present invention can be applied. <6.1. Container design> The free-form design of containers such as bottles has traditionally been intuitive and cumbersome.
there were. The present invention alleviates these disadvantages. <6.2. Automotive Design> In the automotive industry, the present invention relates to automotive body design and automotive component design.
Available to More specifically, according to the present invention, it is possible to deform a portion or an outline.
Because of its ease, straightforward deformation of parts and depressions is possible, and
The fitting of the components into the recesses can be designed more easily. <6.3. Aircraft> According to the present invention, high-precision trim operations and surfaces required in the aircraft industry
Perform patch operations. <6.4. Shipbuilding> One of the characteristics of the shipbuilding industry is that the hull and propeller (screw) design is required.
That is. Hull and propeller design is based on the physics of water flow constraints.
Can be pushed forward. Satisfying such constraints is within the scope of the present invention.
include. <6.5. Conventional CAD / CAM applications> For application to engine, piping layout, and sheet metal product design,
And a function of fusion. The present invention is particularly efficient when performing such operations.
And the surface can be easily deformed; these advantages are
It is particularly useful in various fields. <6.6. Other Applications> The following list describes other applications in which the present invention can be used in computer assisted designs.
In the field. Design of home electronics and appliances, resin injection molding
Mold design, tool and die design, toy design, geological modeling, geography modeling
Deling, mine design, art and entertainment, sculpture, fluid dynamics, meteorology, heat flow, electromagnetic
Science, plastic surgery, burn masks, orthodontics, prosthetics, clothing design, shoes
Design, architectural design, virtual reality design, visualization of scientific data, trainees
Geometric model for (eg medical training). The foregoing description of the present invention has been presented for purposes of illustration and description. Sa
Moreover, this description is not intended to limit the invention to the form disclosed herein.
Not something. Therefore, from the above disclosure, experience and knowledge in related technologies
Changes and modifications derived based on the above are included in the scope of the present invention. The above embodiment is a book
While describing the presently best mode for carrying out the invention,
The present invention may be implemented by modifying the above-described example or another embodiment according to necessary changes depending on the application.
And make it possible to use it. Attachment claims
Boxes shall include modifications of the embodiments to the extent deemed possible by the prior art.
You. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a surface 62 generated in the present invention;
In addition to interpolating between 30 and 34, in a predetermined direction according to the equi-inclined ribbons 61 and 63,
It passes through the curves 54, 58, 60. FIG. 2 shows a modification of the surface of FIG. 1; this surface 30 is used in the method of the invention.
It has a disk 66 fused to it. FIG. 3 illustrates a fusion surface 62a created between surfaces 30, 34 in the present invention.
Note that this surface 62a passes through curves 54 and 58;
This is performed according to a new surface generation calculation formula (formula (1)) described in the specification. FIG. 4 shows a pair of a geometric entity in a parameter space and a geometric entity in a target space.
FIG. 7 is a diagram showing the relationship; straight lines 78a and 78b in the parameter space are
Each has a target aerial image of curves 54 and 58;
The straight line 86 has a target aerial image called a curve 80. FIG. 5 is a graph of two fusion functions B1, B2 used in some of the embodiments of the present invention.
FIG. FIG. 6A is a graph of another fusion function that can be used in the present invention. FIG. 6B is a graph of another fusion function that can be used in the present invention. FIG. 6C is a graph of another fusion function that can be used in the present invention. FIG. 6D is a graph of another fusion function that can be used in the present invention. FIG. 7 is a diagram further illustrating a correspondence relationship between geometric entities in a parameter space and a target space.
It is. FIG. 8 illustrates an elliptical region 100 fused to a cylinder 108 in the present invention;
Note that the closed curve 110 is obtained by transforming the ellipse from the deformed portion of the cylinder 108 fused to the closed curve.
Define the area. FIG. 9 illustrates a simple projection 112 generated on a cylinder 116 by the method of the present invention.
You. FIG. 10 shows a composite curve 120 (described below) including two intersecting partial curves 124 and 128.
FIG. FIG. 11 illustrates the original surface 130 from which the label surface 134 is trimmed. FIG. 12 shows a distance from a point p inside a polygon having vertices v1, v2, v3, v4, and v5.
FIG. 4 illustrates one computer technique for determining a measure;
A distance measure to an edge is determined using the corresponding apex 150 generated by the radiation process.
Is determined. FIG. 13 shows two boundary curves 156a, 156a, in parameter space (ie, unit square).
FIG. 156b is a diagram showing an area piece 168 between the coordinates (s, t).
Can be parameterized itself; where s is the opposite subcurve 16
0a, 160b linearly with the distance between two corresponding points on the pair
Varies; and t lies on each of the pair of sub-curves 160a, 160b.
Determine corresponding points. FIG. 14 shows an area having a side surface and a ribbon defined by three surfaces S1, S2, S3.
In the present invention, this region is expressed by using Expression (5) described later.
A surface strip for 300 can be generated. FIG. 15: General computer geometry concept and new concept underlying the present invention
FIG. These figures are defined in the “Definition” section above.
Note that these terms are used to illustrate the terms. FIG. 16 shows a general computer geometry concept and a new concept underlying the present invention.
FIG. These figures are defined in the “Definition” section above.
Note that these terms are used to illustrate the terms. FIG. 17 is a flow of a design construction operation performed by a user of the present invention while designing a geometric object.
It is a block diagram which shows the typical example of. FIG. 18 shows three contour curves 404, 408, 412 encountered at the position of the contour marker 420.
Note that the surfaces 416 and 418 are equiangular
For dollars (as opposed to marker 420), a smooth
Combine. FIG. 19 shows a contour curve defining a surface 480 forming a chamfer between surfaces 484 and 486.
It is a figure showing x and y. Note that the contours x and y are usually the intersections of the surfaces 484 and 486.
It is defined using distances 488 and 490 from 482. FIG. 20 is a diagram illustrating an example of calculating a fusion surface from isotropic ribbons 508 and 516 according to the present invention.
It is a figure showing an example. FIG. 21A is a diagram showing a procedure for generating a hole 600 in the present invention. FIG. 21B is a diagram showing a procedure for generating a hole 600 in the present invention. FIG. 21C is a diagram showing a procedure for generating a hole 600 in the present invention. FIG. 22 shows a fusion surface 710 according to the present invention;
722 extends between the degenerated contour (point) 714 and the circular end 718. 23 shows a plane having a degenerated contour (point) 754 and a circular curve 760 according to the present invention.
FIG. 139 shows a disc 758 and a fusion surface 750 extending therebetween. FIG. 24. Fusion of the present invention to fuse surfaces between semi-circular ribbons 784a, 784b.
FIG. 4 shows the result of the technique; the resulting surface 786 shows the two ribbons
Fused between. FIG. 25 has a point p (u, v) determined using the “forward algorithm” in the present invention.
FIG. 9 shows a fusion surface 808 that changes;
, Itself parameterized using points in additional parameter space 828
And points 830 in the additional parameter space are contours 812, 816 (object
Distance measure of the original image (in parameter space 158)
Used to efficiently determine FIG. 26 illustrates an embodiment of the present invention using a one-dimensional embodiment of the new computer technique of the present invention.
5 is a flowchart showing steps for calculating an interpolation curve in the calculation. FIG. 27 is a flow chart showing steps performed when constructing an approximation to an isoclinic boundary of an isoclinic ribbon.
It is a chart; the boundary is on the opposite side of the contour with respect to the equi-tilt ribbon. FIG. 28A is a flowchart of a program for constructing a more accurate isotropic ribbon boundary than the approximation obtained in FIG. 27;
It is a low chart. FIG. 28B is a flowchart of a program for constructing a more accurate isotropic ribbon boundary than the approximation obtained in FIG. 27;
It is a low chart. FIG. 29A is for a marker on one or more contour curves defining a boundary for a partial surface Si, etc.
By changing the geometric properties of the tilt handle and / or the ribbon tangent,
5 is a flowchart for correcting one or more partial surfaces Si of the composite surface S0. FIG. 29B, etc. for markers on one or more contour curves defining boundaries for the partial surface Si
By changing the geometric properties of the tilt handle and / or the ribbon tangent,
5 is a flowchart for correcting one or more partial surfaces Si of the composite surface S0. FIG. 29C is for a marker on one or more contour curves defining a boundary for a partial surface Si, etc.
By changing the geometric properties of the tilt handle and / or the ribbon tangent,
5 is a flowchart for correcting one or more partial surfaces Si of the composite surface S0. FIG. 30A shows the partial surface Si when the user corrects the isometric handle and / or the ribbon tangent.
In order to correct in real time,
It is a flowchart of a program. FIG. 30B shows the partial surface Si when the user corrects the isometric handle and / or the ribbon tangent.
In order to correct in real time,
It is a flowchart of a program. FIG. 31 is a diagram illustrating an example of an operation performed by a user performing an operation of changing a surface shape according to an embodiment of the present invention.
9 is a flowchart showing higher-level steps to be performed. FIG. 32 shows a parameter used in the flowchart of FIG. 26 for calculating the interpolation curve C (u).
It is a figure which shows the numerical example of a meter graphically. FIG. 33 is a diagram showing four contour curves P11, P12, P21, and P22;
It is necessary to create a surface surrounded by
It is defined by these four contours (and their accompanying oblique ribbons). FIG. 34 shows a four-sided piece from two two-sided fusions using the four contour curves of FIG. 33 (FIG. 36).
FIG. 5 illustrates an intermediate surface created during the performance of one method of creating the surface. I mean
, The fusion surface S1 (FIG. 34) is equidistant ribbons R11, R12 (contours P11, P12, respectively).
The fusion surface S2 (FIG. 35)
Are generated using the contours R21 and R22 (respectively for the contours P21 and P22). 35 shows a four-sided piece from two two-sided fusions using the four contour curves of FIG. 33 (FIG. 36)
FIG. 5 illustrates an intermediate surface created during the performance of one method of creating the surface. I mean
, The fusion surface S1 (FIG. 34) is equidistant ribbons R11, R12 (contours P11, P12, respectively).
The fusion surface S2 (FIG. 35)
Are generated using the contours R21 and R22 (respectively for the contours P21 and P22). FIG. 36 shows the fusion obtained by derivation from S1 (shown in FIG. 34) and S2 (shown in FIG. 35).
FIG. 5 is a view showing a joint surface S; S is shown in Section 5 of “Detailed Description” described later.
It is generated based on equation (11). FIG. 37 shows a method for generating a surface S from two surfaces SL and SR in one embodiment of the present invention.
FIG. 4 shows the geometric objects used. In particular, this figure is shown in FIGS.
1 illustrates the notation used. FIG. 38 illustrates one embodiment of the present invention for generating four side pieces. FIG. 39 is a view showing another embodiment of the present invention for generating the four side pieces generated in FIG. 38;
You. FIG. 40 shows a notation correspondence between the geometric object of FIG. 38 and the geometric object of FIG. 39;
FIG. FIG. 41 is a diagram showing an example of the geometric arrangement of FIG. 38; contours P3 and P4 of FIG.
Degenerate. FIG. 42A illustrates markers 2002 constrained to remain on contour curves 2003, 2004.
It is a figure showing a movement. FIG. 42B shows markers 2002 bound to remain on contour curves 2003, 2004.
It is a figure showing a movement. FIG. 43 shows that a tangent plane continuity between two fusion surfaces S1 and S2 is ensured.
FIG. 7 is a diagram showing a combined contour curve of a filter and binding to the corresponding isotropic ribbon.
. FIG. 44 illustrates a contour P and an associated contour P for explaining conditions for realizing G1 continuity on P
FIG. 4 shows isometric ribbons RL, RR and various handles.

[Procedure for Amendment] Submission of Translation of Article 34 Amendment of the Patent Cooperation Treaty [Date of Submission] March 27, 2001 (2001.3.27) [Procedure for Amendment 1] Item name] All drawings [Correction method] Change [Contents of correction] [Fig. 1] FIG. 2 FIG. 3 FIG. 4 FIG. 5 FIG. 6A FIG. 6B FIG. 6C FIG. 6D FIG. 7 FIG. 8 FIG. 9 FIG. 10 FIG. 11 FIG. FIG. 13 FIG. 14 FIG. FIG. 16 FIG. FIG. FIG. FIG. FIG. 21A FIG. 21B FIG. 21C FIG. FIG. 23 FIG. 24 FIG. 25 FIG. 26 FIG. 27 FIG. 28A FIG. 28B FIG. 29A FIG. 29B FIG. 29C FIG. 30A FIG. 30B FIG. 31 FIG. 32 FIG. 33 FIG. 34 FIG. 35 FIG. 36 FIG. 37 FIG. 38 FIG. 39 FIG. 40 FIG. 41 FIG. 42A FIG. 42B FIG. 43 FIG. 44

────────────────────────────────────────────────── ─── Continuation of front page    (81) Designated country EP (AT, BE, CH, CY, DE, DK, ES, FI, FR, GB, GR, IE, I T, LU, MC, NL, PT, SE), OA (BF, BJ , CF, CG, CI, CM, GA, GN, GW, ML, MR, NE, SN, TD, TG), AP (GH, GM, K E, LS, MW, SD, SL, SZ, UG, ZW), E A (AM, AZ, BY, KG, KZ, MD, RU, TJ , TM), AE, AL, AM, AT, AU, AZ, BA , BB, BG, BR, BY, CA, CH, CN, CU, CZ, DE, DK, EE, ES, FI, GB, GD, G E, GH, GM, HR, HU, ID, IL, IN, IS , JP, KE, KG, KP, KR, KZ, LC, LK, LR, LS, LT, LU, LV, MD, MG, MK, M N, MW, MX, NO, NZ, PL, PT, RO, RU , SD, SE, SG, SI, SK, SL, TJ, TM, TR, TT, UA, UG, US, UZ, VN, YU, Z A, ZW (72) Inventor Haigen, Lance             Boulder, Colorado, United States             ー, Towenty Ace Street             335 (72) Inventor Heigen, Scott             Longmont, Colorado, United States             To spruce avenue 1813 F term (reference) 5B046 FA15 FA18                 5B050 AA08 BA08 BA09 EA13 EA19                       EA24 EA28                 5B080 AA09 AA11 FA15

Claims (1)

Claims: 1. A method for determining a fused geometric object, comprising: a plurality of parameterized geometric objects Si, where i = 1, ..., N, and , N ≧
2. For each of the two, preparing a mapping fSi from the parameter space PS to a common geometric space GS containing Si, in which: (A1) a plurality of parameterized geometrics At least one object Si0 has two dimensions or more; (A2) fSi ^-1 (Pi) The Si portion Pi where fSi is continuous at the point (Pi) is
A step of calculating a function S at each of a plurality of points q in PS;
Thereby, one corresponding point S (q) in GS is obtained. However, in the step, the following (B1) and (B2) are satisfied, and (B1) S (q) is at least fSi0 (q). One fSj (q) (however,
j ≠ i0), S (fSi0 ^-1 (Pi0)) ⊆Pi0 and S (fSj ^-1 (Pj)) ⊆Pj, and (B2) S is fSi0 ^-1 ( Pi0) and fSj ^-1 (Sj) are continuous, and the above step is satisfied; and the expression of the corresponding point S (q) is displayed as an expression of a geometric object that fuses between Si0 and Sj. The above method, comprising: 2. (a) each of the mappings fSi is a parameter mapping for parameterizing Si; (b) each of the Si is a surface; and (c) each of the Pi is one (D) the point S (q) is included in the surface defined by the function S, and the curve Pi is included in the outer periphery of the surface. The method of claim 1. 3. The method of claim 2, wherein each of said Pis is interpolated from a plurality of points. 4. The method of claim 1, wherein the points in the parameter space PS are represented by a multiple of a predetermined coordinate value, and each coordinate has a predetermined range. 5. The method of claim 1, wherein said calculating step includes determining S (q) as a function of at least a weighted sum of fSi0 (q) and fSj (q). . 6. The computing step comprises determining one or more corresponding weights of the weighted sum for at least some of the points S (q) and each weight w is one of the geometric 6. The method according to claim 5, wherein the points of the biological object Si are determined (scaled) at a constant rate. 7. A method for modifying a representation of a surface by a user, the method comprising: a first surface having a first curve approximately included in the first surface. Graphically displaying one surface; a second curve, wherein the point is at each point on the first curve, or
Graphically displaying the second curve approximately indicating the tangent of the first surface at that point; and graphically displaying the second curve relative to the first curve. Changing the position of a part to change the contour of the first surface. 8. The method of claim 7, wherein each point on the first curve lies within a predetermined distance of the first surface. 9. The method according to claim 8, wherein the predetermined distance is in a range of 10 ⁻³ to 10 ⁻⁶ . 10. The method of claim 7, wherein the first curve is a contour curve interpolated from at least two points on the first surface. 11. The method of claim 11, wherein a point on the surface between the first and second curves is used in determining a point on one or more of the first surface and the second surface. The method of claim 7, wherein 12. The method of claim 7, further comprising interpolating points of the first curve from surface tangents to points on the first surface. 13. The method of claim 7, wherein the step of changing includes changing one of a direction and a length of a vector representing a tangent to the first surface. Method. 14. A method of modifying a representation of a surface on a computer system, the method comprising: graphically displaying a particular surface having first and second curves set thereon. Invoking, by a user of the computer system, a user interface technique for deforming the particular surface, thereby: (A1) determining a point on a first geometric object representation; Wherein the first geometric object representation is used to evaluate a desired contour of the particular surface at a majority of points on the first curve representable by the computer system. (A2) a second determination for determining a point on a second geometric object representation, wherein the first determination is for representing first data to be performed. The second geometric object representation represents second data used to evaluate a desired contour of the particular surface at a majority of points on the second curve representable by the computer system. (A3) generating a modified version of the specific surface, wherein there are a plurality of new points on the modified version that are not on the specific surface. And each of said new points comprises: (a) at least one point obtained from said first geometric object representation; and (b) at least one point obtained from said second geometric object representation. Generating, which is determined as a function of a point; launching, wherein is executed; and graphically displaying the modified version. The method according to claim. 15. The method of claim 14, wherein at least one of said first and second geometric object representations includes a representation of a surface. 16. The step of generating, for each of one or more of the new points, a weighted sum of at least one point on each of the first and second geometric object representations. 15. The method of claim 14, comprising calculating. 17. The step of calculating includes, for each of one or more of the new points, setting one or more corresponding weights of the weighted sum and each of the weights w 17. The method according to claim 16, wherein corresponding points pw in one of the first and second geometric object representations are scaled. 18. The step of determining at a fixed rate comprises: for each point q of the new set of points Q and at least one of the corresponding weights wq for the new point q. Determining the distance-like measure Dwq, the distance-measure Dwq includes: (a) parameterizing the original image (play image) of the new point q; ) The original image parameterization of a point sq lying on both the modified version and the geometric object representation containing the point pwq for the weight wq. 18. The method of claim 17, wherein the method comprises: 19. For q1 and q2 of the set Q, the original image parameterization of q1 is determined by the original image parameterization of sq1 as compared to whether the original image parameterization of q2 is close to that of sq2. 19. The method according to claim 18, wherein Dwq1? Dwq2 if close. 20. A method for modifying the representation of an N-dimensional geometric object by a user of a computer system, wherein N is greater than or equal to 2, wherein the method comprises: a first geometric object having N dimensions. Graphically displaying on the computer system, wherein a lower-dimensional second geometric object is embedded in the first geometric object; A third geometric object, the points of which indicate a rate of change of one or more measures of the first geometric object at a point of the second geometric object. Graphically displaying the third geometric object, and changing one or more geometric properties of the third geometric object relative to the second geometric object. , Whereby said first geometric pair Changing the geometric properties of the elephant. 21. For each of the first, second, and third geometric objects, the dimensions of the geometric object are linear independent vectors required to represent all points of the geometric object. 21. The method of claim 20, wherein the minimum number is. 22. The one or more geometric properties of the first and third geometric objects include one or more of: tangent direction, tangent vector length, and curvature measure (measurement). 21. The method of claim 20, comprising: 23. A method for generating a geometric object on a computer system, the method comprising: preparing a representation of a curve; for each of a plurality of points on the curve, a first at that point. Obtaining data indicative of the shape of the surface of the first surface; determining a representation of the first surface including the curve; and generating a representation of the second surface having a contour that is a function of points of the first surface. Generating. A method comprising: 24. The method of claim 23, wherein the first surface includes an isotropic ribbon relative to the second surface, and wherein the curve is a profile for the isotropic ribbon. 25. The method according to claim 25, wherein the first and second surfaces include the curve as a boundary, and the first and second surfaces have the same tangent plane at each point of the curve. 24. The method of claim 23, wherein: 26. The method of claim 23, wherein said determining comprises providing the first surface as one of a deployable surface and a label surface. 27. The generating step includes determining the second surface as a fusion surface between the first surface and at least one additional surface, and determining the second surface as a fusion surface between the first surface and at least one additional surface. 24. The method of claim 23, wherein substantially all points on a surface of the first surface are a function of points on the first surface and points on the additional surface. 28. A method for generating a representation of a geometric object, the method comprising: obtaining a first surface, a portion of which is an expandable surface; and constructing a closed curve boundary for the expandable surface. And wherein the boundary identifies the interior of the closed curve on the first surface; and only the interior of the first surface is displayed substantially alone graphically. Trimming the first surface to approximately the boundary; and graphically applying the label to the interior so that the label substantially covers the interior. 29. The method of claim 28, wherein the step of obtaining includes identifying the first surface as a graduated (ruled) surface. 30. The step of constructing generates the boundary as a profile curve having a corresponding equi-inclined ribbon for use in deriving the fusion surface having the boundary as a boundary to the fusion surface. 29. The method of claim 28, comprising. 31. The method of claim 30, wherein the points of the fusion surface are derived from a weighted sum of points from the isotropic ribbon and at least one other surface. 32. A method for modifying a representation of a geometric object, the method comprising: a first display step of displaying a first geometric object representation having two or more dimensions; Displaying the additional geometric object representation of the second geometric object representation, wherein the shape and position of the additional geometric object representation are indicative of the shape of the first geometric object representation; Said steps wherein one or more of said additional geometric object representations have one or more dimensions; and two steps: (A1) the shape of one or more of said additional geometric object representations; Changing the position; and (A2) re-displaying the modified first geometric object representation indicating the change to the additional geometric object representation simultaneously; It said method characterized in that it comprises. 33. The additional geometric object representation includes a graphical representation displayed as being connected to the first geometric object representation when displayed on a computer graphic output device. 33. The method of claim 32, wherein: 34. The method of claim 32, wherein the additional geometric object representation comprises one or more user selectable points, vectors, curves, and surfaces.
The method described in. 35. The changing step includes a user inputting a substantially continuous chronological change request to change the additional geometric object representation, and wherein the changing is performed. During the input of one of the requests, the re-displaying step graphically displays a corresponding modification to the first geometric object representation for one or more of the previously entered requests for changing the time series. The method of claim 32, wherein the sub-steps are performed simultaneously. 36. At least one of said displaying and re-displaying steps comprises determining said first geometric object representation as at least some of said additional geometric object representations. 36. The method of claim 35, comprising: 37. The step of determining includes calculating a weighted sum of points P to obtain a point q of the first geometric object representation, wherein the points P are the additional geometric 37. The method of claim 36, wherein the method is obtained using a geometric object representation. 38. The weighted sum comprises weights, each weight being obtained using a corresponding fusion function, each of the fusion functions having a range of values from 0 to 1; The method of claim 37, wherein each of the fusion functions is dependent on a q parameter play image for determining a weight to which the fusion function corresponds. 40. The system of claim 32, wherein each of the first geometric object representation and the additional geometric object representation is represented in a three-dimensional coordinate space.
The method described in.