JP3187807B2 - Object surface shape data creation device - 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 invention D Means for solving problem E (Fig. 1) F action (Fig. 1) G Example (FIGS. 1 to 11) Effect of H invention A Industrial application fields   The present invention relates to an apparatus for creating surface shape data of an object, for example,
If CAD (computer aided design) or CAM (computer
Free-form surface in aided manufacturing
This is suitable for application when generating a deformed shape. Summary of invention B   The present invention relates to the surface shape of an object in CAD, CAM, etc.
In the data creation device, detail surface shape from shared boundary
Generate and share using higher-order vector functions
At the boundary and the nodes at both ends of the boundary,
By setting a line vector and internal control points,
Connect multiple matching patches to have a smooth free-form surface
can do. C Conventional technology   For example, using a CAD method, an object with a free-form surface
When designing shapes by computer,
In addition, the designer must be able to
A boundary curve that connects the specified points
The network is calculated by a computer using a predetermined function.
Is expressed in a so-called wire frame
Create a curved surface. Thus surrounded by a boundary curve
Many framework spaces can be formed (such as
The 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 is trying to design
Shape, and use the boundary curves surrounding each framework space.
Surface that can be represented by a predetermined vector function
Interpolation operation can be performed as the surface shape of the details of the body
In other words, the designer who designed the object as a whole
Generate a curved surface (meaning that cannot be specified by a quadratic function)
Can be Here, the curved surface set in each frame space is
Form the basic elements that make up the entire curved surface and patch it
Call.   Conventionally, in this type of CAD system, a boundary curve network
As a vector function to express, for example, veg
D consisting of Bezier equation and B-spline equation
The following tensor product is used, for example,
Ideal for mathematical expression of free-form surfaces without features
It is believed that. Problems to be solved by invention D   However, this conventional mathematical expression is used for songs that are characteristic in shape.
When applying to surfaces (for example, curved surfaces with greatly distorted shapes)
If the patch is difficult to connect to each other,
Because it is necessary to perform mathematical operations,
There is a problem that the arithmetic processing by the data becomes complicated and enormous.   The present invention has been made in consideration of the above points,
To take advantage of the simplicity of the mathematical expression of the product,
Adjacent to have a two-dimensional spread with simple mathematical expressions
Simple contact between tangent patches under the condition of tangent plane continuity
By continuing, complex surfaces can be expressed in simple mathematical expressions.
Free-form surface work that can be operated by interpolation formula
It is intended to propose a synthesis method. Means for solving problem E   In order to explain 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
Is determined by parameters u and v sequentially specified at predetermined intervals.
By sequentially specifying and calculating vector functions, each framework
The position vector data at each position in the space
This gives the detailed surface shape data that represents the detailed surface shape of the object.
In an apparatus for creating surface shape data of an object for creating data,
An order higher than the order of the first vector function representing the boundary curve
Of the patch represented by the second vector function of
Part surface shape Constructs PT17 of the boundary curve network consisting of boundary curves
Surrounded by multiple boundary curves concentrated on the control points
Detail surface shape First means for specifying the surface shape First and second detailed surface shapes adjacent to each other First details about the shared boundary COMj consisting of boundary curves between
Surface shape And the first derivative of a second vector function representing
Details of surface shape First connection vector in the direction traversing the shared boundary COMj of
And second detail surface shape As the first derivative of a second vector function representing
And the second detailed surface shape Tangent vector in the direction across the shared boundary COMj of
And the first-order minute relation of the first vector function representing the shared boundary COMj
A third tangent vector in a number and direction along the shared boundary COMj
And the first and second tangent vectors and the third
The tangent plane formed by the connection vector is the same
As the first and second detail surface shape By setting the control edge vector of the first and second
Details of surface shape At the shared boundary position between
A second means for performing a subsequent COMj process, and one
Concentrated on the node at the end or at both ends
Detail table for all common boundaries COMj with continuation of tangent plane
Surface shape Third means for performing the connection processing of
2 Detail surface shape Is displayed on the display means, and a point on the
Connected first and second detailed surface shapes Check the connection status by displaying the normal vector of
And the control edge vector Of the first and second detail surface shapes by changing And a fourth means capable of adjusting the connection state.
You. F action   As shown in FIG. 4, a node PT17 of the boundary curve network is formed.
Control points The boundary curves that concentrate on The shared boundaries COM1, COM2, COM3, and COM4 are configured.
Control point The surrounding tangent vectors are the tangent vectors of the shared boundaries COM1 to COM4
Satisfies the condition of tangential plane continuity with
It satisfies the condition of tangent plane continuity for boundaries COM1 to COM4
Sea urchin control edge vector If you ask for a neighboring patch Are smoothly connected at sharing boundaries COM1 to COM4. In this way, along with the central part of the shared boundaries COM1 to COM4
All bounded by boundary curves concentrated at the nodes at both ends
Detail surface shape Can be connected smoothly.   Detail surface shape that spreads such connections two-dimensionally in all directions
Condition , One after another, the entire boundary surface network
Can form smooth and detailed object surface shapes
You.   The detail surface shape As a vector function to represent,
Select a vector function of higher order than the vector function
The degree of freedom in setting the tangent vector
And as a result, the boundary surface
It can be easily connected. G Example   An embodiment of the present invention will be described below in detail with reference to the drawings. (G1) The principle of patch connection   In this embodiment, the rough shape of the object is specified.
To the bounding curve and the framework space
The patch is a vector function of Using the Bezier equation expressed by
Expressed as a detailed surface shape. here, Is stretched between adjacent framework spaces as shown in Fig. 1.
Curved surface, first patch And the second patch Is one of the boundaries held by
It consists of a position vector representing the position of the end, and the expression (1)
Control points represented by vectors Based on the first and second patches Express the free-form surface above.   E and F in equation (1) are shift operators, and
Tsuchi Control point represented by the above position vector For the following equation: With the relationship   Further, in equation (1), u and v change between 0 and 1.
The first and second parameters as shown in FIG.
Patch Control points for From the u-axis in the horizontal direction and the v-axis in the vertical direction.
Patch using parameters u and v Can represent coordinates on a free-form surface.   Further, in the equation (1), m and n represent a Bezier surface,
Represents expression using m-th and n-th arithmetic expressions.
You. In the case of FIG. 1, m = 3 and n = 3 are selected and the third order veg
D) A free-form surface is expressed using the equation
hand Has 16 control points, namely Can be expressed as Also the second patchSimilarly, 16 control points Can be expressed by   Two patches like this Is a boundary tune created by the framework processing by the designer.
It is stretched on a wire network and has a shared boundary between these two patches.
Has COM. Here, set along each boundary curve
Control points are used to convert each boundary curve into a third-order veg
Set to represent by the equation, put between both ends of each boundary curve
Four control points are designated. In contrast, the boundary song
The control points inside the framework space surrounded by lines are
Using a third-order Bezier equation to form a free-form surface in the braided space
It is set to perform interpolation calculation. Thus each framework sky
The intervening surface is represented by 16 control points.   By the way, the boundary curve network formed by the framework processing
A free-form surface in each of many framework spaces
When a patch is created by using
In general, the curved surface is not smooth. So this implementation
In the example, two patches with a shared border COM To connect smoothly at the shared border COM.
Re-set the control points of the patch and use these control points
Re-interpolate the free-form surface to be patched. to this
Moreover, over the entire surface framed by the boundary curve network
That can be connected smoothly.
Therefore, the external shape of many objects can be naturally expressed.   The connection at this shared boundary COM is a condition of tangent plane continuity
Control edge vector that satisfies Is realized by seeking Control edge vector Is the control point The first patch from Control point next to It is a vector heading to. Also, the control edge vector Is the control point From the second patch Control point next to It is a vector heading to. Further control edge vector Is the control point Vector towards control point Vector towards control point It is a vector heading to.   Thus, the surface around the shared boundary COM is the control edge vector Using these control edge vectors.
Find the conditional expression for surface continuity. The condition of tangent plane continuity is first
For each point on the line of the shared boundary COM, a first patch Tangent vector in the u direction of the second patch Tangent vector in the u direction of the second patch Is the same as the tangent vector of the shared boundary COM that specifies the v direction of
That is, they exist on one plane. Where the tangent plane is shared
The tangent vectors in the u and v directions at each point on the boundary
Called the plane formed by
Patch 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 is determined as shown in Fig. 2.
Can be Ie patch For the direction across the shared boundary COM (ie, u direction
Tangent vector And the tangent in the direction along the shared boundary COM (ie v direction)
vector Normal vector Is Represented by a patch The tangent vector in the direction across the shared boundary COM And tangent vector in the direction along the common boundary COM Normal vector Is It is represented by   Under such conditions, in order to be tangent plane continuation,
Tangent vector Must be on the same plane, so that
Khutor Will face in the same direction.   here,   The vector function that satisfies the condition of the tangent plane continuity is
formulaExpressed by In equation (6) as well as Is the patch at point (u, v) on the shared boundary COM Tangent vector in the u direction (ie, the tangent vector in the transverse direction)
Torr).   In this embodiment, as shown in FIG.
The adjacent framework space of the boundary curve network expressed by d
Connect using the following Bezier equation: That is, two adjacent
Patch Is the fourth-order Bezier equation, And the tangent vector in the transverse direction of equation (6) The vector function obtained by performing the first-order partial differentiation of equation (7)
number, Is used. However, in equations (8) and (9),It is.   On the other hand, the shared border COM uses the third order during framework processing.
Vector function expressed by Bezier equation, that is, Is generated using Therefore, in equation (6),
Tangent vector in the direction along the boundary COM Is the vector function obtained by first-order partial differentiation of equation (12).
The word become. However, It is.   Also, the scalar functions λ (v), μ (v), and ν in equation (6)
(V) λ (v) = (1−v) + v (15) μ (v) = κ₁(1-v) + κ_Twov …… (16) ν (v) = η₁(1-v)³+ Η₂(1-v)^Twov + η₃
(1-v) v^Two+ Η_Fourv^Three                     …… (17) Is selected, and this is substituted into the equation (6).   Scalar functions λ (v), μ in equations (15) to (17)
(V) and ν (v) are the terms of (1-v) as mathematical expressions.
, V, and their product terms, μ (v) and ν
(V) contains the unknown κ₁, Κ₂And η₁, Η₂, Η₃,
η₄Contains. Thus, the expressions (15) to (17)
When substituting into expression (6) and expanding, the left side of expression (6) and
Both the right sides are (1-v)⁵, V (1-v)⁴, V^Two(1-
v)³, V^Three(1-v)², V^Four(1-v), v^FiveTerm sum of
Be able to organize them into shapes. Exhibition obtained in this way
For each term in the open equation, the coefficient parts are equal to each other.
Sea urn unknown κ₁, Κ₂And η₁, Η₂, Η₃, Η₄Choose
, The continuity condition of the tangent plane at the shared boundary COM
Control edge vector that satisfies
can do.   By the way, the cubic Bezier expression
In the shared boundary COM expressed by
When trying to connect a free-form surface represented by
And the tangent vector in the transverse direction expressed by equation (9) as well as Is a quartic equation, whereas the shared boundary expressed by equation (13)
Tangent vector in the direction along the world COMIs represented by a quadratic equation. Therefore, the condition of tangent plane continuation was obtained
Substituting λ (v), μ (v), ν (v) into equation (6)
The degrees of the terms on the left and right sides when expanded
Will be.   It should be noted that ν (v) in equation (17) is 4
Unknowns η₁, Η₂, Η₃, Η₄That is included
In this way, the condition for continuation of the tangent plane is satisfied.
To reset the control edge vector to be added,
The large number of possible terms increases the degree of freedom,
Surface shape of a free-form surface with strong morphological features
Even so, it is necessary to satisfy the condition of tangent plane continuity.
You can set your point.   Here is a general free-form surface with few geometric features
The continuity condition of the tangent plane for the surface shape of an object
In this case, two unknowns are usually sufficient. Accordingly
In that case, η₂, Η₃To η₁, Η₄According to the following equation η₂= 2η₁+ Η₄                      …… (18) η₃= Η₁+ 2η₄                      …… (19) Control by two unknowns.
An edge vector can be set.   Substituting equations (15), (16) and (17) into equation (6)
By expanding and rearranging and setting the coefficient part of each term to be equal
hand, And the unknown κ₁, Κ₂Passing
And η₁~ Η₄By controlling the
Control edge vector that satisfies Can be set.   In equations (20) to (25), the control edge vector Are two as described above for equations (8) and (9).
Patch Represents the control piece vector when connecting by the following formula
ing. On the other hand, the control edge vector Is expressed by a cubic expression as described above for expression (13).
Is a control piece vector in a direction along the shared boundary COM to be controlled.   By using such a control piece vector, 3
Separated by a boundary curve network expressed by the following Bezier equation
Free-form surface expressed by the fourth-order Bezier equation
Stretching shows a very distinctive shape
Make the shared boundary of the boundary curve network satisfy the condition of tangent plane continuity.
It can be connected smoothly. (G2) Two-dimensional connection method   The two-dimensional connection is, as shown in FIG.
That connect the framework space divided by multiple directions
In this way, many framework spaces are expanded in all directions.
Can create a free-form surface by connecting
it can.   When making such a two-dimensional connection, the
The nodes inside the curved surface are 3
Boundary curves more than books are concentrated. For example, the nodes in Fig. 3
PT₁₈, Three boundary curves are concentrated and the node PT₉, PT
_Ten, PT₁₁, PT₁₆, PT₁₇, PT₁₉, PT_{twenty two}, PT_{twenty three}Has four borders
The boundary curves are concentrated, and the nodes PT₈Has five boundary curves
concentrate.   Therefore, in the case of this embodiment, these boundary curve networks
Two, three, four, five frames adjacent to internal nodes
Free-form surface expressed by a fourth-order Bezier equation for the braided space
Are formed so as to satisfy the condition of continuation of the tangent plane. Scratch
Of the boundary curve network expressed by the cubic Bezier equation
A free-form surface (4
Which is expressed by the following Bezier equation).   For example, in FIG.₁₇Four
Tsuchi In the case of connecting, is shown in FIG. 4 corresponding to FIG.
As the node PT₁₇COM1, COM2, COM shared boundaries
3, COM4 (hereinafter referred to as COMj, j = 1, 2, 3, 4)
For each of the above equations (20) to (25)
Unknowns so as to satisfy the condition of tangent plane continuity described
κ₁, Κ₂, Η₁~ Η₄By setting each share
Find the control edge vector around the boundary.   The condition of the tangent plane continuity at each shared boundary COM1 to COM4 is
Patch Depending on the type of framework to be implemented,
This means finding an appropriate control edge vector. (G3) Conditions depending on the form of the framework   The form of the framework is a system that becomes nodes at both ends of the shared boundary COMj.
Point (Fig. 1) Control toward the direction of adjacent patches
Edge vector Are parallel to each other. (1) When both are parallel   In Fig. 3, the node PT₁₇Boundary COMj that focuses on
Control points at both ends of (j = 1, 2, 3, 4) , Two control edge vectors heading in the u direction Are parallel to each other,
In order to satisfy, η in equations (20) and (25)₁
And η₄But η₁= 0, η₄= 0 (26) Must. Where η₂And η₃To η₂= 2η₁+ Η₄                      …… (27) η₃= Η₁+ 2η₄                      …… (28) If you choose the relationship η₂= 0, η₃= 0 (29) Becomes   The relation between the equations (26) and (29) is changed to the equations (20) to (25).
Substituting into the j-th (j = 1, 2, 3, 4) sharing boundary
The conditional expression for the tangent plane continuation is Can be expressed as   From Equations (30) and (31), the control edge vector at one end Is And from equation (34) and equation (35),
vector Is Becomes Substituting equation (36) into equation (32), the control edge vector Ask for And substituting equation (37) into equation (33),
Torr If you ask for Becomes   κ₁j and κ_TwoIf j is not equal, from equation (36) If you can decide Can be determined from equation (37). If you can decide Can be determined. Simultaneous equations (38) and (39)
By Can be determined. Satisfies the condition of tangent plane continuity
You can connect as you do.   On the other hand, κ₁j and κ_TwoWhen j is equal to each other,
κ₁j = κ_TwoAssuming that j = κj, this is expressed by equation (36), equation (37),
By substituting into equation (38), the control edge vector Is It can be expressed as.   Equations (40), (41), and (42) are the control edge vectors Can be determined, the control edge vector Means that you can decide. (2) When one is not parallel   In FIG. 3, the shared boundary COM5 is a control composed of one node.
Point Control edge vector Control points are parallel to each other and at the other node Control edge vector Are not parallel. In this case, η₁,
η₄Is obtained from the equations (20) and (25). η₁= 0, η₄$ 0 …… (43) And η₂, Η₃The relationship is η₂= Η₄, Η₃= 2η₄                …… (44) Becomes Substituting this relationship into equations (20) through (25) gives
The condition of tangent plane continuity is Becomes From this result, the unknown κ based on equation (45)₁j
Is found. In addition, the control side vector is obtained from equations (45) and (46).
Le IsBecomes Furthermore, from equations (51) and (47) Is obtained.   Based on such a relationship, the unknown κ_Twoj
And η_Fourj can be obtained, and (49) and (50)
Control edge vector from formula To Can be obtained as   Furthermore, from equations (53) and (48) Is obtained, the control edge in equation (51) is obtained.
vector Determine the control edge vector And the control edge vector in equation (53)
Torr Determine the control edge vector Can be determined.   Further control edge vector Is solved by solving equations (52) and (54) simultaneously.
And You can ask as follows.   Thus, the unknown κ₁j and κ_Twoj is equal to each other
Control edge vector that satisfies the condition of tangent plane continuity
Can be calculated. On the other hand, κ₁j and κ_Twoj
Are equal to each other, the equations (52) and (54)
Since the determinant of the simultaneous equation becomes 0, this simultaneous equation
Can not solve. Then η₂, Η₃Is unknown
Connecting patches in tangential plane continuity
Can be.   The above is the control point Control edge vector Control points are parallel to each other and at the other node Control edge vector Are not parallel to each other, but the opposite is true.
And the control point Control edge vector Are not parallel to each other,₁j and κ_Twoj
Around the shared boundary, provided that
You can find your side vector. (3) When both are not parallel   In FIG. 3, the shared boundary COM6 is a control consisting of nodes at both ends.
Point Control edge vector at Are not parallel to each other. This place
If η₁And η₄Is expressed by the equations (20) and (25)
From η₁≠ 0, η₄$ 0 …… (57) Must be in a relationship.   Where κ₁j and κ_TwoWhen j is not equal to each other,
From Equations (20) and (21), the control edge vector Is By substituting equation (58) into equation (22),
RIt can be seen that there is a relationship.   From equations (24) and (25), the control edge vector But And substituting equation (60) into equation (23)
Than It can be seen that there is a relationship.   Therefore, in equation (58), the control edge vector Determine the control edge vector And the control edge vector in Eq. (60)
Torr Determine the control edge vector Can be determined.   In addition to this, simultaneous equations consisting of equations (59) and (61)
And η as above₂= 2η₁+ Η₄, Η₃= Η₁+ 2η
₄Control edge vector by solving You can ask as follows.   On the other hand, κ₁j and κ_TwoWhen j is equal to each other,
The determinant of the simultaneous equations consisting of equations (61) and (63) is 0
Therefore, this simultaneous equation cannot be solved. Then η
₂, Η₃By solving as an unknown
Patches can be connected. (G4) Control edge vector Decision   Control point of shared boundary COMj (j = 1, 2, 3, 4) If one of the control edge vectors is not parallel, equation (51)
And (53), as described above, the control edge vector Is determined, the control edge vector And thus the condition of tangent plane continuity holds.
The control edge vector can be set to stand.   Similarly, control points Are not parallel, the equations (58) and (60)
As described above, the control edge vector Is determined, the control edge vector Can be determined, the condition of tangent plane continuity
You can set the control edge vector so that
You.   This control edge vector Is determined by, for example, the control point in FIG. Is shown as when four boundary curves are concentrated
So each control point All the paths enclosed by the boundary curve
By finding the condition of the tangent plane continuity for Tsuchi,
You can decide. (1) Control edge vector in the case of   Control edge vector Is the control point that constitutes one node of the shared boundary COMj Is the condition of the above equations (20) and (21) related to the surroundings
From the following two equations It is necessary that In addition to this,
The shared boundary COMj and the (j + 1) th shared boundary COM (j +
1) A patch surrounded by About the control point Control edge vector And the control edge vector from the tip The position specified by the sum of
When M (j + 1) simultaneously satisfies the condition of tangent plane continuity
Contains the control edge vector Should be the same as the position specified by the sum of
From these control edge vectors, Holds. Here, in Expressions (64) to (66), j is j = 1, 2, 3, 4 (However, j + 1 = 1 when j = 4) ... (67) It is.   Thus control points Expressions (64) to (6) for the j-th shared boundary COMj
6) If you summarize the formula and display the formula, Can be expressed as   In equation (68), two unknowns Included, but in the same way other shared border CO
About M (j + 1), COM (j + 2), COM (j + 3)
If the conditional expression of tangent plane continuity is obtained, the following four expressions Can be obtained. Thus the control edge
vector Can be determined. (2) Control edge vector in the case of   The other control point of the shared boundary COMj (j = 1, 2, 3, 4) Is also the same as described above for equations (64) to (68).
And the control point The condition of the tangent plane continuity can be obtained for the surrounding patches.
It can be expressed as follows, corresponding to equations (64) to (68).
obtain. j = 1, 2, 3, 4 (However, j + 1 = 1 when j = 4) (76)   Therefore, the control point is calculated using equation (77). Four shared boundaries COMj (j = 1, 2, 3, 4)
The following four simultaneous equations Set up control edge vector Can be solved for (3) For special conditions   In this way, each shared boundary COMj (j = 1, 2, 3,
4) control points that constitute the nodes at both ends About four patches connected under the condition of tangential continuity
can do.   In FIG. 4, the control edge vector Are parallel and Are parallel, the unknown κ₁, Κ₂Regardless of the value of (6
The determinants of the simultaneous equations of equations 9) to (72) are zero. This
In the case of η₂, Η₃Using determinant as unknown
By avoiding that becomes zero and making it indefinite, (J = 1, 2, 3, 4) can be obtained.   Control point The same applies to. (G5) Patch connection processing procedure   As described above with reference to FIG.
The connection process is based on the surface shape of the object using a CAD device.
The processing procedure shown in FIG.
And can be realized by:   In FIG. 5, the connection processing procedure is performed in step SP1.
Is started, the computer goes to step SP2
Read patch data. This patch data is
Designer designs surface shape of free-form object
When we do, we need to frame a boundary surface network in a three-dimensional space.
Is obtained. If there is no abnormality in this framework processing, the boundary
Objects represented by adjacent patches surrounded by curves
The detailed surface shape has a common boundary COMj.
By the connection process described below, this shared boundary COMj
For example, four patches (J = 1, 2, 3, 4) under the condition of tangent plane continuity
Can be connected.   The computer determines the rough
When reading patch data representing the surface shape,
Represented by a fourth-order Bezier equation on the boundary curve represented by the Bezier equation
Set the 25 control points required to create a curved surface
To execute the interpolation calculation in the patch. Where the boundary curve
Control edge vector is used as reference position data for interpolation calculation
Can be   Thus, as described above with respect to FIG.
Control point consisting of nodes at both ends of COMj And this control point Two control points based on a cubic Bezier equation between And three control points based on the fourth-order Bezier equation are set.
You.   Four patches that are adjacent in this way Controls representing the cubic Bezier equation for the boundary curve
A point and 5 representing the fourth-order Bezier equation used in connection
And four control points are specified and surrounded by four boundary curves.
Nine control points are designated inside each patch. This
Here, the control points set based on the cubic Bezier equation are
Based on fourth-order Bezier equation used when connecting switches
Calculate control points (ie, unknown κ₁, Κ₂And η₁
~ Η₄Is determined).   Thus the four adjacent patches To the surface expressed by the fourth-order Bezier equation
be able to.   The computer divides these four surfaces into their shared boundaries.
Specified across the boundary COMj (j = 1, 2, 3, 4)
Control edge vector composed of control points , Two adjacent patches satisfy the condition of continuation of the tangent plane.
Connected by a curved surface represented by the
Four patches at each end of the field are tangent plane continuous
Set the control points around the nodes to satisfy the condition.   That is, in the next step SP3, the computer
4 patches to connect After specifying (j = 1, 2, 3, 4), go to step SP4
Move on. This step SP4 consists of four paths to be connected.
Control points at both ends of the common border COMj Whether the control edge vector is on the same plane
Find out. Ie control points In the formulas (20) to (25), (69) to (72)
Condition holds, and the control point In the formulas (20) to (25), (78) to (81)
For each condition to be satisfied, Control edge vectors must be on the same plane
It is.   The computer obtains a positive result in step SP4.
Proceeds to the next step SP5,
If a fixed result is obtained, the same
By rotating the control edge vector that is not in the plane,
After correcting on one plane, the process proceeds to the next step SP5.   This step SP5 is the control point For each of the three control points in between, Control edge vector heading to Find the position vector that satisfies the condition of the tangent plane
And set again.   In this embodiment, this step is performed by a computer.
Connection of two adjacent patches in the operation in SP5
Are the control points at both ends of each shared boundary COMj For the surrounding patches, a control that satisfies the condition of tangent plane continuity
Your side vector (Equations (64) to (81)). In addition to this, the framework
At both ends of the shared boundary COMj
Depending on the shape of the boundary curve, the control edge vector in the u direction is flat
Use different formulas based on the condition
To obtain the control edge vector.
(Equations (26) to (63)).   Thus, the computer will be able to
Connect under the condition of tangent plane continuity, and
Connect control points around control points under tangent continuity conditions
Finish the process. And then on to the next step SP7
Using a display device, place each point on the boundary curve surrounding each patch.
Display normal vectors and contours in patches.
Allows the operator to see if the connection is smooth.
Displayed for visual confirmation.   For example, as shown in FIG.
Point Unknown κ in₁And κ₂Are different from each other,
The operator proceeds to steps SP2 to SP5 as shown in FIG.
At the common boundary COMj of the surface generated by the connection process
That the normal vectors are the same
It can be checked visually with the line vector.   Note that the shared boundary COMj is connected by the continuation of the tangent plane.
If not, as shown in FIG.
The normal vector above is displayed to open.   Looking at this display, the operator proceeds to the next step SP8.
Then, for each patch, the normal vector on the shared boundary COMj is
You can check whether they match each other, and if they do not match
In step SP9, investigate the cause and, if necessary,
To make numerical corrections. Thus a series of patch connection processing
The procedure ends at step SP10. (G7) Effect of the embodiment   With the above configuration, the operator can
Two-dimensional expanse spanned by the framework space formed
Adjacent patches so that their first-order derivatives are shared boundaries.
Can be connected so that they are tangent plane continuous
And thus the entire boundary curve network with large features
It is possible to obtain a curved surface creation device capable of forming a kana free curved surface.
Can be.   Thus, the framework of the boundary curve network expressed by the cubic equation
The space is stretched using a curved surface expressed by a quartic equation
Thus, the condition of tangent plane continuity at the shared boundary COMj
Number of unknowns η to set a satisfying control edge vector
Can be increased. By the way, a curved surface expressed by
If we try, the number of unknowns η will be two, but
Then, it can be increased to four, and the degree of freedom is large.
It will be good.   This increase in the number of unknowns is due to the boundary curve network.
If the curved surface represented by has fairly distinct geometric features (e.g.,
For example, if there are sudden irregularities on the surface of the object)
Connect framework space smoothly under the condition of tangent continuity
Means that you can.   For example, as shown in FIG.
Create a curved surface S that bends partially like a wire net
If necessary, for each framework space,
All patches can be stretched smoothly under the following conditions,
This means that, as shown in Fig. 10,
The display of the line vector must be the same for adjacent patches.
Can be easily confirmed. (G8) Other embodiments (1) In the above-described embodiment, the control forming the node
Point To connect patches when four boundary curves are concentrated
, But the number of concentrated boundary curves is limited to this
Instead of three or more j boundary curves are concentrated
Can be connected by the same connection method.   For example, the control points in Fig. 11 As shown in the figure, the hem spread where five boundary curves are concentrated
For curved surfaces, connect this under the condition of tangent continuity.
Can be (2) In the above, the fourth-order Bezier equation is used to
The case where the interpolation operation of TSU is performed has been described.
The number is not limited to this, and may be fifth or higher. (3) Further, in the above description, patch interpolation is
D) The case where the equation was used was described, but it is not limited to this.
Plein type, Coons type, Ferguson (Fur)
using other vector functions such as gason)
Is also good. Effect of H invention   As described above, according to the present invention, the detailed surface shape is shared
Generated using vector functions of higher order than the world
Surface shape data of various shapes including special shapes
Data can be generated, and the control points
Detail table with appropriate smoothness required for object shape
By making it possible to generate surface shapes,
Great freedom between the detailed surface shapes to be placed in the framework space
Can connect in degrees. Therefore, a free-form surface with strong geometric features
Can be connected smoothly.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic diagram showing control edge vectors used for a boundary curve network expressed by a cubic equation, and FIG. 2 is a diagram showing conditions of continuation of a tangent plane at a shared boundary in FIG. FIG. 3 is a schematic diagram showing a frame form formed by two-dimensional connection of patches, and FIG. 4 is a schematic diagram showing control edge vectors used in the object surface shape data generating apparatus according to the present invention. FIG. 5 is a flowchart showing a connection processing procedure used when connecting patches, FIG. 6 is a schematic diagram showing an example of a framework, and FIG. 7 is a diagram showing a connection according to an embodiment of the present invention. FIG. 8 is a schematic diagram showing a display when the shared boundary in the case is connected under the condition of tangent plane continuity, FIG. 8 is a schematic diagram showing a connection state not satisfying the condition of tangent plane continuity, FIG. FIG. 11 and FIG. 11 are schematic diagrams showing other connection examples. COM, COM1 to COM6 ... Shared boundaries.

Claims (1)

(57) [Claims] Using a CAD device, a number of framework spaces surrounded by boundary curves and representing the general shape of the object are formed by the framework processing, and in each of the above-mentioned framework spaces, positions in the respective framework spaces are sequentially determined at predetermined intervals. By sequentially specifying the designated parameters and calculating the 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 apparatus for generating surface shape data of an object, a boundary curve is formed of the boundary curve for the detailed surface shape represented by a second vector function having a higher order than the first vector function representing the boundary curve. First means for designating the detail surface shape surrounded by a plurality of boundary curves concentrated on control points constituting the nodes of the net; For shared boundary corresponding with the boundary curve between the first and second detailed surface shapes adjacent one surface geometry, 1 of the second vector function representing the first detail surface shape
A first tangent vector in a direction transverse to the shared boundary of the first detail surface shape and the second tangent vector and the second tangent vector;
A second tangent vector in a direction transverse to the shared boundary of the second detailed surface shape, the second tangent vector being the first derivative of the second vector function representing the detailed surface shape of the second vector function; And calculating a third tangent vector in a direction along the shared boundary, which is a first derivative of the vector function of 1, and formed by the first and second tangent vectors and the third connection vector. By setting the control edge vectors of the first and second detailed surface shapes so that the tangent planes are the same, the first and second detailed surface shapes are tangent at the shared boundary position between them. Second means for performing a process of connecting under the condition of planar continuity, and the details under the condition of tangent plane continuity for all of the shared boundaries concentrated at the node at one or both ends of the shared boundary. Surface type A third means for performing a shape-like connection processing, displaying the connected first and second detailed surface shapes on a display means, and connecting the first and second connected surfaces at a point on the shared boundary. The connection state can be confirmed by displaying the normal vector of the detailed surface shape, and the first and second can be changed by changing the control side vector.
And means for adjusting the connection state of the detailed surface shape of the object. 2. 2. The method according to claim 1, wherein the boundary curve network is represented by a cubic vector function, and the detailed surface shape data of the object spanned in the framework space is calculated using a cubic vector function. An apparatus for creating surface shape data of the object described. 3. 2. The object surface shape data generating apparatus according to claim 1, wherein the detailed surface shape data of the plurality of objects is framed so as to be sequentially connected in a two-dimensional direction.