JP3187809B2 - Object surface shape data creation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION   The present invention will be described in the following order. A Industrial application fields Summary of invention B C Conventional technology Problems to be solved by the invention D (Figs. 1 and 2) Means for solving problem E (Fig. 3) F action (Fig. 3) G Example (G1) Representation of a triangular patch (Fig. 3) (G2) Representation of a quadrilateral patch (Fig. 3) (G3) Principle of triangular patch and quadrilateral patch connection (fourth
(Fig.) (G4) Two-dimensional connection of a quadrilateral patch to a triangular patch
Continued (Fig. 5) (G5) Two-dimensional connection of a triangular patch to a quadrilateral patch
Continued (Fig. 6) (G6) Patch connection processing procedure (Fig. 7) (G7) Effect of the embodiment (G8) Another embodiment (FIG. 8) Effect of H invention A Industrial application fields   The present invention relates to a method for creating surface shape data of an object, for example,
For example, CAD (computer aided design) or CAM (computer ai
ded manufacturing)
It is suitable for application when forming the shape of an object.
You. Summary of invention B   The present invention provides a framework processing for specifying a rough shape of an object.
Forms many framework spaces surrounded by boundary curves
And the object represented by a predetermined vector function in this framework space
Three sides adjacent to each other when forming the detailed surface shape of the body
About the shared boundary of the shape framework space and the quadrilateral framework space
And the triangular detail surface shape and
And smooth connection of quadrilateral detail surface shapes.
The object with an appropriately smooth surface shape
Can be shaped. C Conventional technology   For example, the shape of an object with a free-form surface using CAD techniques
When designing a shape (giometric modeling), generally
The designer has to create multiple
Specify a point (this is called a node), and
Using a predetermined function of the boundary curve network connecting the nodes of
Data, so-called wire
Create a surface represented by frames. Thus the boundary curve
Can form a framework space surrounded by
(Such processing is hereinafter referred to as framework processing).   The boundary curve network formed by such framework processing is
A rough sketch of the object that the designer itself is trying to design
Shape using a boundary curve that includes each framework space.
Surface shape that can be expressed by a predetermined vector function
If it is possible to interpolate a curved surface,
Freeform surface (quadratic function) designed by Zaina for the object
Which cannot be specified in the above).
Here, the curved surface set in each framework space constitutes the entire curved surface
This constitutes a basic element, which is called a patch.   Conventionally, in this type of CAD system, a boundary curve network
As a vector function to express, for example, veg
It consists of a Bezier formula and a B-spline formula.
A cubic tensor product is used.
Ideal for expressing free-form surfaces that have no sign
It is believed that.   In other words, a free-form surface with no special features in shape
Is the projection of a given point in space onto the xy plane.
Make sure that the projected points are regularly arranged in a matrix.
When the number of projection points is represented by m × n,
A quadrilateral patch expressed by the cubic Bezier equation
It is known that it can be easily stretched by using. Problems to be solved by invention D   However, this conventional mathematical expression is used for songs that are characteristic in shape.
Apply to a surface (eg, a curved surface with a greatly distorted shape)
In some cases, there are difficulties in connecting
Computational operations must be performed.
Data processing is complicated and huge.
Was.   Especially when a curved surface with an extremely distorted shape was framed
In this case, the regularity of the specified point array may be disturbed.
Thus, as shown in FIG.
When only a framework that leaves a rectangular patch can be created
Can occur.   In the case of Fig. 1, the nodes specified by the designer For processing the surface given by
A quadrilateral which can be easily connected between patches
Adjacent nodes are sequentially framed to form a patch.
This is a framework processing based on the concept of
However, the nodes specified by the designer are
Is determined based on the requirements of
Between the nodesCan not avoid leaving a triangular patch surrounded by
No.   However, in the past, a triangular patch was smoothed into a quadrilateral patch.
No way to connect to it has been proposed, and in practice
It is extremely difficult to generate a smooth surface on a surface.
Was thought to be.   In such a case, as shown in FIG.
A triangular patch (ie, a node Center point of a triangular patch) surrounded by 3 new framework surfaces CN₁, CN_Two, CN_ThreeThree sides
Pull out this framework curve CN₁, CN_Two, CN_Three
, A triangle patch and a quadrilateral patch connected to it
Modification framework that re-divides into a quadrilateral patch again
Process all patches by quadrangle patch
And then execute the process of connecting patches.
Such a method can be considered.   But in this way, in effect, the computer
Framework processing to modify a quadrilateral patch into a quadrilateral patch
A separate program must be prepared, and
It is unavoidable that the computational processing of the user becomes enormous.   The present invention has been made in consideration of the above points, and
The disorder of the array of nodes
Four sides obtained as a result of framework processing for specifying a rough shape
If a triangular framework space remains between the
When the boundary curve network is given as
Also modified the triangular framework space (or quadrilateral framework space)
Triangular detail surface shape (or four sides) directly and smoothly without processing
Objects that can be connected to each other
It is intended to propose a method for creating body surface shape data.
is there. Means for solving problem E   In order to solve such a problem, in the present invention, CAD
Using the device, make sure that the boundary curve is
Form multiple framework spaces that represent the approximate shape of a single object
In each framework space, the position within each framework space
In the order specified by the parameters u and v that are specified sequentially at predetermined intervals.
By calculating the vector function by specifying the following, each framework
Find the position vector data at each position in the space,
Detail surface shape data representing the detailed surface shape of the object
In the method for creating surface shape data of an object for creating
Triangular framework with two boundary curves as common boundary COM
Tangent plane continuity
Of control edge vector data that satisfies
Control points in the triangle and quadrilateral framework spaces.
By setting each, each other at the shared border COM
Connected triangular patches Triangular detail surface shape and quadrilateral patch consisting of Surface shape data to form a quadrilateral detail surface shape consisting of
And the control edge vector data is transferred to the shared border COM.
Control edge vector data in the direction along the line and shared boundary COM
Control edges in a triangular framework space to traverse
Four sides so as to cross the vector data and the shared border COM
Including the four control edge vector data
Only, the condition of continuation of the tangent plane
A triangle that represents each triangle detail surface shape across the world
Patch And a quadrilateral patch representing the detailed surface shape of the quadrilateral Of first and second tangent vectors towards COM and shared boundary COM
Tangent formed by the third tangent vector pointing in the direction
To make the faces the same, adjacent triangular details
Shape or triangular patch And quadrilateral detail surface shape, ie quadrilateral patch Is displayed on the display means, and the point
Normal vector or triangle detail surface shape or triangle
Patch And quadrilateral detail surface shape, ie quadrilateral patch Displaying contour lines inside
Check the smoothness of the connection state and correct internal control points.
It was to so. F action   Triangular and quadrilateral frames adjacent to each other
Between the tangent plane continuity of its shared boundary COM
The internal control points that satisfy the condition are
By setting each in the quadrilateral framework space, three sides
Surface detail, ie triangular patch And quadrilateral detail surface shape, ie quadrilateral patch Can be directly connected to satisfy the condition of tangent plane continuity.
As a result, the triangular framework space and
Adapts the surface shape of the details of objects with mixed quadrilateral framework space.
Can be easily generated with positive smoothness. G Example   An embodiment of the present invention will be described below in detail with reference to the drawings.   As shown in Fig. 3, adjacent triangular framework spaces
And the quadrilateral framework space (representing the rough shape of the object)
Each as a detailed surface shape that represents the surface shape of the details of the object
Tensioned surfaces, first and second patches Defines the boundaries they hold together (this is called the shared boundary)
Satisfies the condition of tangent plane continuity by the method described below
Connected. (G1) Representation of a triangular patch   In the case of this embodiment, a boundary representing the boundary of the triangular framework space.
Boundary curve and patch attached to this triangular framework space Is Is expressed using a vector function consisting of a cubic Bezier equation, such as
Manifest. In equation (1) Is a position vector representing one end of the common boundary COM, and the other end
Position vector And the first patch Position vector And the second patch Position vector Together with a node specified at the time of framework processing.   Thus the first patch The triangular patch consists of nodes Is surrounded by three sides consisting of the three boundary curves
I understand.   Nodes of these boundary curves The shared boundary COM between the two control points Is represented by a third-order Bezier equation defined by Likewise
Then a node Boundary curve between, The boundary curves between each two control points Is represented by a third-order Bezier equation defined by   In the equation (1), E and F are in the u direction and v
Direction shift operator, patch Control point represented by the position vector For With the relationship here u ≧ 0 (4) v ≧ 0 (5) u + v ≦ 1 (6) It is.   Further, in the expression (1), u and v are in the u direction and v
The direction parameter, as shown in FIG. For each node Seat with the u axis in the horizontal direction and the v axis in the vertical direction
Patch using markers (u, v) Can be represented on the free-form surface.   With this definition, each point on the shared border COM
And the first patch Tangent vector taken in the u direction of Is the first-order partial differentiation of the equation (1) with respect to the parameter u.
And by It is represented by here Is a node From control point And the control edge vector toward
The first patch For the following equation By the control edge vector Can be represented. Ie Is the control point of the shared boundary COM The first patch from Control point Indicates the control edge vector going to Is the control point of the shared boundary COM From control point This shows the control edge vector going to.   Also, the first patch at a point on the shared border COM Tangent line in the v direction (ie, the direction along the shared boundary COM)
Khutor Is the first order partial differentiation of equation (1) with respect to parameter v.
And It is represented by here Is a contact From control point The control bias vector towards
For shared boundary COM, By the control edge vector Can be represented. Is the control point From Indicates the control edge vector going to Is the control point Node from This shows the control edge vector going to. (G2) Expression of quadrilateral patch   In this embodiment, the boundary of the quadrilateral framework space is represented.
Boundary curve and patch attached to this quadrilateral framework space
That is, the second patch formula Is expressed using a vector function consisting of a cubic Bezier equation, such as
Manifest. Node in equation (11) Is located at the other end of the shared boundary COM, as shown in FIG.
Khutor To the second patch Position vector Together with a node specified at the time of framework processing.   Thus the second patch Is a nodeIt can be seen that it is surrounded by the four boundary curves.   This second patch In the shared border COM, the first patch As described above for the two control points Is represented by a third-order Bezier equation defined by
In contrast, the node Boundary curve between Boundary curve between, The boundary curves between each two control points Is represented by a third-order Bezier equation defined by   Also, in equation (11), the shift performance in the u and v directions
Arithmetic elements E and F are patches Control point represented by the above position vector For With the relationship Where the parameters u and v are u, v∈ [0,1] …… (14) Takes a value from 0 to 1 as represented by Defined like this
The second path at a point on the shared border COM.
Tsuchi In the u-direction (ie how to traverse the shared border COM)
Ivy tangent vector Is to perform first-order partial differentiation of equation (11) with respect to parameter u.
By It is represented by here Is the contactFrom the second patch Control point And the control edge vector toward
The second patch About By the control edge vector Can be represented. here Is the control point of the shared boundary COM From the second patch Control point Indicates the control edge vector going to Is a node From control point This shows the control edge vector going to. (G3) Principle of connecting triangular patches and quadrilateral patches   By the way, the framework processing as shown in FIG.
In the two adjacent framework spaces that have been created,
Each triangular patch using the surrounding control points And quadrilateral patch , The surface at the shared boundary COM is generally smooth
It doesn't matter. Therefore, two
Patch Each connection so that the connection
Tsuchi Control points inside By re-setting, the free-form surface
Recalculate the interpolation. By doing so, the boundary curve network
All patches over the entire curved surface
By being able to connect easily, many things
The external shape of the body can be expressed without becoming unnatural.   The smooth connection at this shared boundary COM is
Control edge vector that satisfies the condition of continuation Is realized by seeking   Condition of tangent plane continuity at all points on shared boundary COM
Must be satisfied by the first patch. Tangent vector in the u direction for (Represented by equation (7)) and the tangent vector in the v direction
Le (Represented by equation (9)) and the second patch Tangent vector in the v direction (Represented by equation (15)) are on the same plane.
Is required, and to achieve this,It is good to reset the parameters to satisfy the condition of
No.   In equation (17), μ (v) and ν (v) are scalar functions
so, μ (v) = κ₁(1-v) + κ₂v …… (18) ν (v) = η₁(1-v) + η₂v …… (19) Is selected.   Therefore, substituting equations (18) and (19) into equation (17) gives
And substitute (8), (10), and (15) into (17)
And as a result the unknown κ₁, Κ
₂And η₁, Η₂Satisfies the condition of tangent plane continuity
Two patches while adding Can be connected.   In practice, equations (7), (9), (15), and (18),
The expression (19) has terms expressed by (1-v) and v.
And the left and right sides of equation (17) are (1-v)^Three, V (1-v)^Two,
v^Two(1-v), v^ThreeCan be expanded and arranged in the form of a sum of terms. Follow
Condition that the coefficient parts are equal to each other for each term of the expansion equation
If you set Is obtained, and thus the four unknowns
κ₁, Κ₂And η₁, Η₂Can be solved.   Here, the tangent plane is the u direction at the point of the common boundary COM
And the plane formed by the tangent vectors in the v direction
Therefore, patching at all points of the shared border COM Are the same, the condition of continuation of the tangent plane holds.   That is, any point on the shared border COM The condition for continuation of the tangent plane in (v = 0 to 1) is shown in FIG.
Can be determined as shown. That is, the first patch For the direction across the shared boundary COM (ie, u direction
Tangent vector (Represented by equation (7)), and the direction along the common boundary COM
Tangent vector (ie, v-direction) Normal vector (represented by equation (9)) Is It is represented by Also the second patch For the direction across the shared boundary COM (ie, u direction
Tangent vector (Represented by equation (15)), and
Tangent vectorNormal vector (represented by equation (9)) Is It is represented by Under these conditions, in order for a tangent plane to be continuous,
Line vector Must lie on the same plane, so that the normal vector
Torr Will face in the same direction.   In order to satisfy the condition of continuation of the tangent plane in this way,
In equations (20) to (23), first, the control side vector
Le Is determined, whereby the control edge is obtained from the equations (21) and (22).
vector Should be determined. Control edge vector Means that the shared boundary COM is a node specified by the designer Control point based on Are specified at the time of framework processing.
Control points based on the vector Control edge vector indicating And the control point Control edge vector indicating Can be determined under the condition of continuation of a tangent plane.   Control edge vector As a selection method of, for example, v
Tangent vector in the transverse direction due to changes in Can be set on condition that the rate of change of is constant. This
Then the control edge vector Is A known control edge vector, such as Can be determined based on   As a result, in equations (20) to (23), the unknown is κ₁,
κ₂And η₁, Η₂So this simultaneous equation is
Unknown κ₁, Κ₂And η₁, Η₂Seeking
Under the condition of tangent plane continuity.
Side patch To the quadrilateral patch Can be connected smoothly via shared border COM
You. (G4) Two-dimensional connection of a quadrilateral patch to a triangular patch
Continued   By the method described above with reference to FIG.
The triangle patch and quadrilateral patch of
You can connect satisfactorily, but use this technique.
As shown in Fig. 5, based on the nodes specified by the designer,
Any direction with respect to the triangular framework space formed
(That is, two-dimensionally
Each adjacent quadrilateral frame space
Think about putting up.   To make such a connection, it is necessary to set
Triangular patches are adjacent to each other via three sides
Simultaneously connect with the quadrilateral patch set in the quadrilateral frame space.
Connect quadrangular patches while satisfying the condition of planar continuity.
I need to go. Such a connection method is used for two-dimensional connection.
It is called a continuation method.   In the embodiment of FIG. 5, one triangular patch is used.For each of the three sides that make up
Patch, ie In the manner described above with reference to FIG.
Three subpatches that satisfy the condition of tangent plane continuity
Generate and overlay these three sub-patches on top of each other
By using a vector function expression such as
And combine them. In this way, three subpatches are stacked
By combining, three adjacent to each of the three sides
Quadrilateral patches In two dimensions so that the condition of tangent plane continuity is satisfied at the same time
Connect a free-form surface with a triangular patch Can be created as   In FIG. 5, first, a boundary curve forming three sides
Three patches via the shared border COM1, COM2, COM3 Triangle patch adjacent to At the intersection of the shared boundaries COM1 and COM2
Parameter v in the direction along the shared boundaries COM1 and COM2
Assign the u coordinate axis. Shared boundaries to match this
Quadrilateral patches adjacent via COM1 and COM2 V and u coordinate axes are selected.   Shared border COM1 patch With respect to the position position when the parameter u is set to u = 0.
Represents a vector (ie, a boundary curve). Also shared border COM2
Is a patch Position vector when parameter v is set to v = 0
Torr (ie, boundary curve). Further sharing boundary COM3
Is a patch , Parameters u and v were set to u + v = 1
Represents the position vector of time (ie, the boundary curve).   When such a coordinate system is set, the central triangle frame
Triangle patch stretched over the space Is the following formula as the detail surface shape Is defined by a vector function represented by.   In this equation (27), the first term Is a quadrilateral patch Share a triangle patch through the border COM1 To the first tangent plane
Sub-patch or first sub-detail surface shape. Also
The second term of equation (27) Is a quadrilateral patch Share a triangle patch through the border COM2 The second set to satisfy the condition of the tangent plane continuation
Represents a sub-patch or second sub-detail surface shape. Further
The third term of equation (27) Is a quadrilateral patchShare a triangle patch via the border COM3 The third set to satisfy the condition of the tangent plane continuation
Represents a subpatch or third sub-detail surface shape.   Thus, equation (27) is a triangular patch. Through the shared borders COM1, COM2, COM3 forming three sides
Quadrilateral patches to connect Satisfies the condition of continuation of the tangent plane
Like three subpatches stacked on top of each other
Show one patch expressed by a vector function
I have.   In equation (27), α (u, v), β (u, v), γ
(U, v) are parameters u and v as variables, respectively.
Is a scalar quantity expressed as Is defined by   It is clear from substituting equations (28) to (30) into equation (27).
As shown, the triangular patch expressed by equation (27) Is the position of v = 0, u = 0, 1−uv = 0 (that is,
First, on the first, second, and third shared boundaries COM1, COM2, and COM3
Position) , The first, second, and third
Triangle patch at the location of the shared border COM1, COM2, COM3 Is a quadrilateral patch It can be seen that they are connected under the condition of continuation of the tangent plane.
Thus, on the three sides of the triangle patch, these quadrilateral patches
The switches are simultaneously connected to the tangent plane via the sub-patches.
It can be connected to a triangular patch so that the condition holds.
Wear. (G5) Two-dimensional connection of a triangular patch to a quadrilateral patch
Continued   In the method described above with reference to FIG. A triangle patch must be connected to each of the four sides
Consider when it is necessary.   For example, as shown in FIG.
Tsuchi Via four shared boundaries COM1, COM2, COM3, and COM4
Then a triangular patchAre connected, each shared boundary COM1, COM2, COM3, CO
M4 is calculated using the above equations (20) to (23).
Control edge vector Can determine two inside the quadrilateral patch
Control point A quadrilateral patch Can be set within.   Thus including the eight control points found for the four sides
Quadrilateral patch consisting of Is Is defined by a vector function represented by.   Where δ (u, v) and ε (u, v) are
A scalar function represented by parameters u and v as variables, Is defined by   As is clear from equation (32), the first term in equation (31) Is v = 0, or v = 1 (that is,
Tangent plane continuity condition for the bordered COM1 and COM4)
That can be connected to a patch adjacent in the v direction by satisfying
Indicates a subpatch.   On the other hand, as is clear from equation (33), equation (31)
Second term of Is that if the parameter u is u = 0 or u = 1 (that is,
(Representing COM1 and COM4)
Satisfies the condition of plane continuity and contacts with adjacent patches in u direction
Represents a second subpatch that can be followed.   Thus the quadrilateral patch represented by equation (31) Is the second subpatch The three sides adjacent via the shared border COM1 and COM4
Shaped patch In contrast, the method described above for equations (20) to (23)
Therefore, they are connected so as to satisfy the condition of continuation of the tangent plane.   At the same time, a quadrilateral patch expressed by equation (31) Is the sub-patch of item 1. The three sides adjacent via the shared border COM2 and COM3
Shaped patch By the method described above with respect to equations (20) to (23).
They are connected so as to satisfy the condition of planar continuity.   Thus, the quadrilateral patch at the center of FIG. For the four supply boundaries COM1 to COM4, respectively.
Three-sided patch Can be connected smoothly.   In the above description, in FIGS. 5 and 6, the center
Triangle patch in the section And quadrilateral patch Connect a quadrilateral patch and a triangular patch to
The connection processing method when connecting is explained.
The connections between the rectangular patches are as shown in Equations (31) to (33).
Can be connected using the method described above.   That is, in FIG. Three rectangular patches connected to And the quadrilateral patch around it Are all related to the u direction and the v direction as shown in equation (31).
To be expressed using two subpatches
The adjacent patches in the u and v directions are tangent plane continuous
It is good to connect while satisfying the conditions of
No.   On the other hand, as shown in FIG.
H Four triangular patches connected to And the quadrilateral patch around it Is connected, as described above with reference to FIG.
If you use the connection method centering on the triangular patch as it is
good. (G6) Patch connection processing procedure   The triangular patch described above with reference to FIGS.
For the two-dimensional connection of quadrilateral patches, use a CAD device
FIG. 7 shows an apparatus for creating surface shape data of a touched object.
It can be realized by executing a processing procedure. In FIG.
In step SP1, the connection processing procedure is started.
Then, the computer is patched at step SP2.
Data. This patch data is, for example,
When designing a curved surface, position it separately in three-dimensional space.
To be specified and framed in a boundary curve network.
And is obtained by If there is no abnormality in the framework processing,
Adjacent patches surrounded by boundary curves are shared boundaries
It has COM, and therefore uses the connection process described below.
Each patch is connected to the tangent plane
Can be connected smoothly under the matter.   The computer reads the patch data in step SP2.
When reading, it corresponds to the surface represented by the cubic Bezier equation.
Of the required number of control points when extending on the boundary curve
(3 pieces for a triangular patch, 3 pieces for a quadrilateral patch
Are set to 8) and shared with the nodes at the vertices of each framework space.
Then, the interpolation operation in the patch is executed.   This interpolation operation is (27) for the triangle framework space.
Set the sub-patches expressed by the formulas (30) to (30),
Sub-patches expressed by equations (31) to (33)
Means to set.   The computer connects in the next step SP3.
Triangle patch at the center of power (In the case of Fig. 5) or a quadrilateral patch (In the case of Fig. 6) and its surrounding quadrilateral patch (Fig. 5) or a triangular patchAfter designating (FIG. 6), the process proceeds to step SP4.   In this step SP4, the three sides to be connected
Common border COM between rectangular patch and quadrilateral patch (Fig. 3)
The nodes at both ends of the shared boundary COM Whether the control edge vector is on the same plane
Find out. Ie nodes Control edge vector at Are not in the same plane, the condition of continuation of the tangent plane does not hold
Will be. Nodes at the same time If the control edge vectors are not on the same plane,
The condition of plane continuity is not satisfied.   So the computer gave a positive result in step SP4
Is obtained, the process proceeds to the next step SP5. to this
If a negative result is obtained,
By rotating control edge vectors that are not on the same plane
After making corrections on the same plane, proceed to the next step SP5.
No.   This step SP5 is a triangular patch Specify the order of creating the three subpatches (Fig. 5), and
Is a quadrilateral patch The creation order of the two sub-patches shown in FIG. 6 is designated.
Thus a triangular patch Or quadrilateral patch To the surrounding quadrilateral or triangular patch.
Can determine the condition of continuation of the tangent plane in a fixed order.
You.   Subsequently, the computer moves to step SP7 and
Triangle patch in fixed order Or quadrilateral patch A control point to be set inside is calculated. Thus, in FIG.
Triangle patch Four adjacent four sides with the three sides as shared boundaries
It is represented by three subpatches that connect the shape patches smoothly.
One triangular patch can be created. Also the
Fig. 6 Quadrilateral Patch Of the four adjacent four
Smoothly connect to the triangular patch in u and v directions 2
Creating a quadrilateral patch with two subpatches
Can be.   Then, the computer moves to the next step SP8.
Judge whether or not all patches have been connected.
When it is obtained, return to step SP3 above and make a new connection.
To specify a triangular patch or quadrilateral patch
Therefore, the above-described sub-patch creation process is repeatedly executed.
You.   Eventually, all the patches are connected and the above-mentioned steps are completed.
If a positive result is obtained in SP8, the computer
Move to step SP9 and surround each patch using a display device
Normal vector at each point of the boundary curve and in the patch etc.
Displaying the high line makes the patch connection smooth.
Is displayed so that the operator can check it visually.
You.   Looking at this display, the operator can proceed to the next step SP10.
The normal triangle on the shared boundary
And whether they match with each other for the quadrilateral patch.
If you can confirm it and it does not match, go to step SP11
Investigate the cause and make numerical corrections as necessary.
Thus, a series of patch connection processing procedures are described in step SP12.
And end. (G7) Effect of the embodiment   According to the above embodiment, the node specified by the operator is
Thus, when the framework processing is performed, the three sides are
A quadrilateral framework space on each of the three sides of the framework space
Adjacent or 4 of the quadrilateral framework space as shown in FIG.
A three-dimensional curved surface such that a triangular framework space is adjacent to one side
When specified, a triangular patch or quadrilateral patch is
Adjacent quadrilateral patches under the condition of tangent plane continuity, or
Can be connected to a triangular patch. About to hide
As described above with reference to FIG.
Since there is no need for processing to reframe the polygon,
Smoothly connected with relatively little computer computation
A free-form surface can be easily obtained. (G8) Other embodiments (1) In the above embodiment, the free-form surface according to the present invention
The creation method is used when the designer designs the shape of the article.
Although the embodiment when applied as a means to be used has been described,
The invention is not limited to this, and can be applied to various shape creating means.   For example, as shown in FIG.
Machine tools based on the original model produced using materials such as
Applied to a product model machine that makes a product model using a machine
If this is done, first in step SP21,
The created original model is mounted on a three-dimensional measuring instrument and three-dimensional data
Make   In the next step SP22, this data
Generate a curved surface in a curved surface creation device that implements a surface creation method
I do. Thus, in step SP22, the adjacent patches are
Free-form surface data representing a free-form surface connected smoothly
can get.   Then, in the next step SP23, the free-form surface data
After converting to an algorithm that indicates the tool path of the machine tool,
In step SP24, for example, NC
By controlling the machine tool with a switch, the product model can be
Make.   If constructed as shown in Fig. 8, it was created manually.
It is possible to automatically make a product model based on the original model
Wear. Therefore, materials for making original models created by humans
Therefore, select materials that are easy to process by hand.
To make product models of any material freely
Can be. (2) In the above-described embodiment, the third order is added to the framework space.
Described the case of putting a patch expressed by the Bezier formula
However, the real number of the mathematical expression is not limited to this, and may be fourth or higher. (3) Further, in the above-described embodiment, the Bezier equation is used.
Described the case where a patch was set up.
But not limited to this, spline type, Coons
Expressions, other vector functions such as the Furgason expression
A number may be used. Effect of H invention   As described above, according to the present invention, the rough shape of an object is
Two-dimensionally expand in any direction by the specified framework processing
Free-form surface representing detailed surface shape of object on curved boundary curve network
The triangle frame space and the quadrilateral frame space
Are adjacent to each other, these adjacent framework spaces
In addition, a triangular detail surface that satisfies the condition
Connect shape and quadrilateral detail surface shape directly. Thus
Relatively simple operation amount makes it easy to achieve proper smoothness.
The detailed surface shape data of one object can be created.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic diagram showing a boundary curve network in which a triangular framework space and a quadrangular framework space are mixed and expanded in arbitrary directions;
FIG. 2 is a schematic diagram showing a boundary curve network re-framed in a quadrilateral framework space, FIG. 3 is a schematic diagram showing the principle of a method for creating surface shape data of an object according to the present invention, and FIG. FIG. 5 is a schematic diagram illustrating an embodiment in which a quadrilateral patch is connected two-dimensionally to a triangular patch, and FIG. 6 is a quadrilateral. FIG. 7 is a schematic diagram showing an embodiment in which a triangular patch is two-dimensionally connected to a patch, FIG. 7 is a flow chart showing a patch connecting procedure, and FIG. 8 is an application of the present invention to a product model machine. 6 is a flowchart showing a processing procedure in the case.

Claims (1)

(57) [Claims] Using a CAD device, a number of framework spaces surrounded by boundary curves and representing the rough shape of the object are formed by the framework processing, and positions in the framework spaces are sequentially determined at predetermined intervals in each of the framework spaces. By sequentially specifying the designated parameters and calculating a vector function, position vector data at each of the positions in each of the framework spaces is obtained, thereby generating detailed surface shape data representing the detailed surface shape of the object. In the method for generating surface shape data of an object to be simulated, a boundary curve space and a quadrilateral frame space adjacent to each other with one boundary curve as a shared boundary are represented by control edge vector data satisfying a condition of continuation of a tangent plane. By setting internal control points in the triangle frame space and the quadrilateral frame space, respectively, Generating detailed surface shape data for forming the connected triangular detailed surface shape and the quadrilateral detailed surface shape, the control edge vector data includes control edge vector data oriented in a direction along the shared boundary, and the shared boundary And three control edge vector data directed to the quadrilateral framework space to traverse the shared boundary and four control edge vector data directed to the quadrilateral framework space to traverse the shared boundary. The first and second tangent vectors from the common boundary to the triangle detail surface shape and the quadrilateral detail surface shape, respectively, across the common boundary and the third tangent vector in the direction of the common boundary. Tangent planes formed by the tangent vector of the triangle and the adjacent triangle detail surface shape and the quadrilateral detail surface shape are displayed on display means. Both, by displaying the normal vector of the point on the shared boundary, or the contour lines in the triangle detailed surface shape and the quadrilateral detailed surface shape, confirm the smoothness of the connection state in the shared boundary. A method for creating surface shape data of an object, wherein the internal control points can be modified.