JP3187808B2 - 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 B Outline of the invention C Conventional technology D Problems to be solved by the invention E Means for solving the problems (FIG. 5) F function (FIG. 5) G embodiment (G1) Principle of triangular patch connection (Figs. 1 to 3) (G2) Two-dimensional connection of triangular patches (Fig. 4) (G3) Confirmation of connection under the condition of tangential plane continuity ( G4) How to set internal control points (Fig. 5) (G5) Patch connection processing procedure (Fig. 6) (G6) Other embodiments (Fig. 7) Effect of invention H A Field of application in industry Regarding the device for creating surface shape data of objects
For example, CAD (computer aided design) or CAM (compute
r aided manufacturing)
It is suitable to be applied when generating the shape of a connected object.
is there. B. Outline of the Invention The present invention relates to a framework space for specifying a rough shape of an object.
Form a detailed surface shape represented by a predetermined vector function
The three sides of the triangular framework space
So that they can be connected under the condition of tangent plane continuity
Three sub-detail surface shapes, and these three sub-details
By superimposing and synthesizing part surface shapes
Adjacent detail surface shape adjacent to the triangular detail surface shape
The shape can be easily formed two-dimensionally. C Conventional technology For example, the shape of an object having a free-form surface using the CAD method
When designing a shape (geometric modeling), generally
The designer has to create multiple
Specify a point (this is called a node), and
The boundary curve network connecting the points of
The so-called wire-free
Create a curved surface represented by a Thus to the boundary curve
Can form many framework spaces 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 is trying to design
Shape using a boundary curve that surrounds each framework space.
A surface that can be represented by a predetermined vector function
If it can be interpolated as the surface shape of the details of
Free songs on objects designed by the designer as a whole
Generate a surface (say what cannot be specified by a quadratic function)
Can be. Here, the curved surface set in each framework space is the whole
Form the basic elements that make up the curved surface of a
Huh. 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.
Ideal for expressing free-form surfaces that have no special features
It is believed that there is. In other words, a free-form surface with no special features in shape
Is equivalent to projecting 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 years 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. D Problems to be Solved by the Invention However, this conventional mathematical expression is a tune having a shape characteristic.
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. Especially when curved surfaces with extremely distorted shapes are framed
In most cases, the specified array of points is regular
Therefore, a quadrilateral patch is set up in the framework space.
In conventional methods such as this, a smooth free-form surface is formed.
It was extremely difficult in practice. The present invention has been made in consideration of the above points, and
Designated by framework processing to specify rough shape
Array of points is randomly arranged without regularity
Form smooth, detailed surface shapes even when
To create an object surface shape data
It is something to try. E. Means for Solving the Problems In order to solve such problems, 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,
As the framework space, the first boundary curve, the second boundary curve and
And a triangular framework space surrounded by a third boundary curve
When executing the framework processing, the first boundary curve is shared
First adjacent detail surface consisting of adjacent patches as field COM1
shape Connected to satisfy the condition of tangential plane continuity
First sub-detail surface shape And the adjacent pad with the second boundary curve as the shared boundary COM2
Second adjacent detail surface shape Connected to satisfy the condition of tangential plane continuity
Second sub-detail surface shape With the third boundary curve as the common boundary COM3
Third adjacent detail surface shape Connected to satisfy the condition of tangential plane continuity
Third sub-detail surface shape Into a triangular framework space by superimposing and synthesizing
Triangle detail surface shape with desired triangle patch to be formed
data Is a position vector representing internal control points such that
Data as well as the three-sided continuation condition
Adjacent triangular detail surface shape consisting of shape patches Between COM1, COM2 and COM3
From the boundary COM1, COM2, COM3 to the shared boundary COM1, COM2, COM3
Across the adjacent detail surface shape And sub-detail surface shape And the first and second tangent vectors pointing to
Third tangent vector in the direction along the fields COM1, COM2, COM3
So that the tangent plane formed by the
Rectangular detail surface shape To set position vector data of internal control points
First means to make a triangle-shaped detail surface shape Are sequentially designated to designate the first, second and third internal control points.
The second means to determine and the triangular detail surface shape First, second and third adjacent detail surface shapes adjacent to The normal vector of the point on COM1, COM2 and COM3
Torr or triangle detail surface shape By displaying the contour lines inside the screen on the display means,
Check the smoothness of the connection in the fields COM1, COM2 and COM3.
The first, second and third internal control points can be modified
A third means is provided. F action Form by framework processing to specify the rough shape of the object
Triangular detail surface shape formed in the formed triangular framework space
Condition Are the shared boundaries COM1, CO formed by the three sides
A system that satisfies the condition of tangent plane continuity in M2 and COM3
Three detailed surface shapes set by points Are generated by superimposing and synthesizing. Thus the triangle detail surface shape Is two-dimensional under the condition of tangent plane continuity on its three sides
Can be generated. G Example Hereinafter, an example of the present invention will be described in detail with reference to the drawings. (G1) Principle of Triangular Patch Connection In this embodiment, as shown in FIG.
Node specified in the program Boundary curve connecting nodes closer to each other based on
To perform the framework processing, thereby creating a boundary curve network.
The three-dimensional curved surface represented by
The rough shape of the object is specified by the interval. The boundary representing the boundary of the framework space thus framed
Display the surface curves of the object curves in the boundary curves and each frame space.
The patch applied as a detailed surface shape is Vector function in cubic Bezier form, such as Is expressed using. In equation (1) Extends between two adjacent framework spaces, as shown in FIG.
Curved surface, ie, first triangular patch And a second triangular patch Of the boundaries that the company holds (this is called the shared boundary)
It is a position vector representing the position of the end, and the position vector of the other end
Le And the first patch Position vector And the second patch Position vector Together with this, it constitutes a node specified at the time of the framework processing. Thus, the first and second patches Are nodes It can be seen that it is surrounded by the three boundary curves. Nodes of these boundary curves The boundary curve between them constitutes the common boundary COM and the two control points Defines a third-order Bezier equation. In contrast, the first patch Nodes Boundary curve between, The boundary curves between each two control points Stipulated by Also, the second patch Boundary curve between, The boundary curve between the two control points Stipulated by In the equation (1), E and F are in the u direction and the v direction.
Direction shift operator, patch Control point represented by the above position vector For the following equation: With the relationship Here, u ≧ 0 (4) v ≧ 0 (5) u + v ≦ 1 (6) Further, in equation (1), u and v are in the u direction and v direction.
And the first and second parameters as shown in FIG.
Patch For each node From the u-axis in the horizontal direction and v-axis in the vertical direction
Patch using parameters u and v Can represent coordinates on a free-form surface. When defined in this way, each point on the shared border COM
The first patch In the u direction of the
The tangent vector obtained is obtained by converting equation (1) for parameter u
By performing first-order partial differentiation, 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. here Is the control point of the shared boundary COM The first patch from Control point The control edge vector going to Is the control point From control point This shows the control edge vector going to. Similarly, on the shared border COM, the second patch The tangent vector in the u direction of
By performing first-order partial differentiation on u, It is represented by here Is a node From the second patch Control point And the control edge vector toward
The second patch For the following equation 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 the control point From control point This shows the control edge vector going to. Furthermore, the first patch at each point on the shared boundary COM The tangent vector in the v direction on the side is obtained by using equation (1)
By performing first-order partial differentiation on It is represented by here Is a node From control point The control edge vector going to
For shared boundary COM, By the control edge vector Can be represented. here 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. By the way, two adjacent
Triangle patch in framework space , The surface at the shared boundary COM, that is,
The surface shape of an object is not generally smooth. So book
In the invention, two patches with a shared border COM So that they are connected smoothly at the shared border COM.
Tsuchi Control points inside And set the patch using these internal control points.
Interpolate again the free-form surface to be set on the surface. To hide
Moreover, over the entire surface framed by the boundary curve network
That can be connected smoothly.
The appearance of many objects so that they do not appear unnatural.
Can appear. Smooth connections at this shared boundary COM are tangent plane continuous
Control edge vector that satisfies the condition Is realized by seeking Condition of tangent plane continuity at all points on shared boundary
Must be satisfied by the first patch. The tangent vector in the u direction is given by (7)
And the second patch At the tangent vector in the u direction (expressed by equation (9)).
And the first patch Tangent vector in the v direction (represented by equation (11))
Need to be on the same plane
In order to do Reset the parameter to satisfy the condition of
No. Where λ (v), μ (v), ν (v) are scalar functions
Λ (v) = (1−v) + v (14) μ (v) = κ ₁ (1-v) + κ ₂ v ... (15) ν (v) = η ₁ (1-v) + η ₂ v …… (16) Therefore, substituting equations (14) to (16) into equation (13) gives
Substituting equations (7), (9) and (11) into equation (13)
Then, the unknown κ is calculated so that the equation (13) holds. ₁ , Κ
₂ And η ₁ , Η ₂ Satisfies the condition of tangent plane continuity
Two patches while adding Can be connected. In practice, equations (7), (9), (11), and (14)
The expression (16) has a term of (1-v) and a term of v
Therefore, the left and right sides of equation (13) are (1-v) ^Three , V (1-v) ^Two ,
v ^Two (1-v), v ^Three Can 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 from equation (17), κ ₁ , Η
₁ Can be solved, and from equation (20), κ ₂ , Η ₂ Solve
Can be Equations (18) and (19) and κ ₁ , Κ ₂ ,
η ₁ , Η ₂ Unknown using Can be solved. Here, the tangent plane means the u-direction and the
And the plane formed by the tangent vectors in the v and v directions
Therefore, at each point of the shared border COM, When the tangent planes are the same, the condition of continuation of the tangent plane holds. That is, any point on the shared border COM The condition of continuation of the tangent plane is determined as shown in FIG.
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, (G2) Two-dimensional connection of triangular patches Two adjacent ones are obtained by the method described above with reference to FIG.
Of the triangular patch so that the continuity of the tangent plane is satisfied.
However, using this method,
As described above, based on the nodes taken at random,
As with many formed triangular framework spaces,
As if it were expanding in two directions (that is, two-dimensionally spreading
To put a triangle patch in the frame space
Think. Triangle patch phases randomly arranged in this way
To connect each other, the three sides of one triangle patch
Three adjacent threes satisfying the condition of the tangent plane
Must be connected to a rectangular patch. Such a connection method
Is called a two-dimensional connection method. In the present invention, three triangular patches are formed.
For each side, for each adjacent triangular patch
The continuity of the tangential plane is obtained by
3 sub-patches to satisfy the requirements
The three sub-patches are superimposed on each other
One by using a vector function expression
Synthesized into a patch. In this way, three subpatches
Are adjacent to each other by overlapping
Satisfies the condition of tangent plane continuity for three triangular patches
Create a free-form surface that can be connected two-dimensionally to add
be able to. For example, in FIG. Attention is paid to the triangular patch surrounded by
Like this triangular patch Boundary curves composing the three sides COM1 and CO
Three patches adjacent via M2 and COM3 Connection method when connecting two-dimensionally
I do. In FIG. 4, first, the first patch Node at Parameters along the sharing boundaries COM1 and COM2 based on
Data u and v coordinate axes are assigned. To match this
To the second and third adjacencies via shared boundaries COM1 and COM2
Patch The coordinate axes of v and u Select based on In contrast, via shared border COM3
The fourth patch adjacent to Is a node facing the shared boundary COM3 U axis and v axis are selected based on Thus, the shared boundary COM1 is composed of the first and second patches. , The position when the parameter v is set to v = 0
Represents a vector (ie, a boundary curve). Also shared border CO
M2 is the first and third patches The position when the parameter u is set to u = 0
Represents a vector (ie, a boundary curve). In contrast,
The bounded COM3 is composed of the first and fourth patches. , Parameters u and v were set to u + v = 1
It represents the position level at the time (that is, the boundary curve). When such a coordinate system is set, the triangle frame space
The first patch to stretch Is Is defined by a vector function represented by. The first term in equation (25) Is a second patch via the shared border COM1 And the first set to satisfy the condition of continuation of the tangent plane.
Indicates a subpatch. The second term of equation (25) Is the third patch via the shared border COM2 And the second set to satisfy the condition of tangent plane continuity
Indicates a subpatch. Furthermore, the third term of equation (25) Is the fourth patch via the shared border COM3 And the third set to satisfy the condition of the tangent plane continuity
Indicates a subpatch. Thus, equation (25) is the first patch Through the shared borders COM1, COM2, COM3 forming three sides
Triangular patch 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 (25), α (u, v), β (u, v), γ (u, v)
Are parameters represented by parameters u and v, respectively.
In the empty function, Is defined by Equations (25) to (28) are for the first patch. Has been described, but this first patch Three patches connected to In exactly the same way Is defined by (G3) Confirmation of connection under the condition of tangent plane continuity Four types of connection that should be connected to each other according to equations (25) to (31)
If you represent a trilateral patch, the first patch Inside the three shared boundaries COM1, COM2, and COM3
Control points that satisfy the conditional expression (FIG. 2) can be set by equation (25).
This can be confirmed as follows. First, the triangular patch shown in Fig. 4 Of the first sharing boundary COM1 of
Finding by setting v = 0 in equation (25)
Can be. However, when v = 0, equations (26), (27),
From equation (28), α (u, v) = 1, β (u, v) = γ (u, v) =
It becomes 0. Substituting this condition into equation (25),
If the switch is expressed by equation (1), the first sub-patch is The sigma corresponding to the first shared boundary COM1 as represented by
It is expressed by the equation of surface continuity. Similarly, the second patch Is based on equation (29) Becomes the curve represented by Expressions (32) and (33)
In the case of the shared boundary COM1 in FIG. 4, the nodes in FIG. As the first and second patches Nodes common to Is used, so that equations (32) and (33) are the same song
By drawing a line Holds. This means that the patch when v = 0 Curves indicate that they are at the same position. Next, regarding the shared boundary COM1, the first and second patches are used. Tangent line in the u direction (that is, along the shared boundary COM1)
When the vector is calculated based on the equation (1), become. Therefore, from equations (35) and (36), Holds, the path in the direction along the shared border COM1
H It can be seen that the tangent vectors are equal to each other. Further, the first and second patches In the v direction at v = 0 (ie, traversing the shared boundary COM1)
Tangent vector) If you ask for become. Therefore, the first and second patches Tangent vector in the v-direction (ie, transverse direction) Is Is the same as Therefore, as is clear from equations (32) to (40), (2
5) and two adjacent patterns expressed by equations (29)
Tsuchi Satisfies the condition of tangent plane continuity at the shared boundary COM1
You can confirm that it is such a patch. Next, the first patch And the third patch Compatible with expressions (32) to (34) for shared boundary COM2 between
Then, as shown in equations (41) to (43), two patches The position vectors representing the curves when u = 0 are
Is equal to Therefore, the boundary curves of the two patches must be in the same position
I understand. Next, corresponding to the equations (35) to (37), the equations (44) to
As shown in equation (46), two patches Tangent vectors in the v direction at u = 0 are equal to each other
Become. Furthermore, corresponding to the equations (38) to (40), the equations (47) to
As shown in equation (49), two patches Tangent line in u direction (i.e., transverse direction) at u = 0
Khutor Are equal to each other. From the calculation results of Equations (41) to (49), the first
Patch And the third patch Satisfies the condition of tangent plane continuity at the shared boundary COM2
It can be seen that they are connected as follows. And the first patch And the fourth patch The curve at u + v = 1 for the shared boundary COM3 between
Corresponding to equations (32) to (34), equations (50) to (52)
When asked as shown, two patches Are equal to each other. . Therefore, the boundary curves of the two patches are in the same position.
You can see that Next, formulas (53) to (5) are made to correspond to formulas (35) to (40).
8) As shown in the equation, two patches Tangent vectors in u and v directions at u + v = 1
Are equal to each other. Like this, two patches Of the curve at u + v = 1 in the u and v directions
Equal to each other is the direction along the boundary curve
The tangent vectors of
Tangent to the direction across the boundary curve at u + v = 1
vector as well as Are also equal to each other. Therefore the first patch And the fourth patch Satisfies the condition of tangent plane continuity at the shared boundary COM3
It can be seen that they are connected as follows. (G4) How to set the internal control point As described above with reference to FIG. 4, the first patch Is, as shown in equation (25), three
Sub-patch 1 represented by the vector function of the sum of the expressions
By putting up a pair of patches, the position of each of the three sides
Tangent plane continuation at shared boundaries COM1, COM2, COM3 in
Two-dimensionally adjacent triangles to satisfy the condition
H can be connected. If such a patch is set up in a triangular framework space,
The boundary curve representing the boundary of the rectangular patch is shown above in FIG.
As mentioned, three nodes And two control points between each node Is uniquely determined when executing framework processing
I have. Patch against this Control point set inside Is actually three in the vector function of equation (25)
So that the condition of tangent plane continuity holds for each side
Then, a control point is set for each item. Thus, 3 inside
One control point With greater freedom
The triangular patches can be connected two-dimensionally in degrees. Now, internal control points The common position vector If expressed as (25), equation (1), equation (26), (2)
7) By substituting equation (28) and expanding it, Is obtained. However, in connection with the parameters u and v, (2
5) In the equations (28), the parameter w is introduced by the following equation 1-uv = u (60). As a result, equation (1) becomes Expressions (26) to (28) can be expressed as Can be expressed as In equation (59), the control point The terms corresponding to other nodes and control points except for the term
Vector components for fixed points specified during processing
Therefore, for each of the three terms in equation (25),
Satisfies the condition of continuation of the tangent plane corresponding to the three sides
Control points Is a term that can be calculated as a fixed value when calculating
is there. On the other hand, the control point The term corresponding to (i.e., the sixth term) is Three control points set inside the Has a substantial content. Therefore, the coefficients of the other terms except the sixth term in equation (59)
(Α + β + γ) may be calculated as α + β + γ = 1 (65), while the sixth term of equation (59) is And the contents to be calculated.
One patch Corresponding to three shared boundaries COM1, COM2, COM3 surrounding
point Multiply the coefficients of α, β, and γ by
It is necessary to calculate the vector
One control point obtained by synthesis is an internal control point It represents that it becomes. Therefore the control point Is from equation (66) Three control points like Can be represented by (67) and (62)
By substituting Equations (64), the triangular patch
Control points set internally when originally connected Is Can be determined by Therefore, the actual control point To set the triangle patch, as shown in FIG.
Specify the conditions of tangent plane continuity for the shared boundaries COM1, COM2, COM3
Satisfactory control points Should be set. (G5) Patch connection procedure 2 of the triangle patch described above with reference to FIGS.
The dimensional connection is the surface shape of the object using a CAD device
The procedure shown in FIG. 6 is executed by the state data creation device.
Can be realized. In FIG. 6, 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 the surface shape of a free-form object
At that time, we decided to frame the boundary curve network separately in three-dimensional space
Is obtained. If there is no abnormality in this framework processing, the boundary
Adjacent patches surrounded by curves are shared border COM
Therefore, leveraging the connection process described below
Of each tangent plane at the common boundary COM
Can be connected smoothly down. The computer reads the patch data in step SP2.
When reading, the curved object represented by the cubic Bezier equation
When setting the surface shape of details on the corresponding boundary curve
Set the required six control points (two on each side)
In the patch with the nodes at the top of the triangular framework space
Is performed. This interpolation operation is performed, for example, as described above with reference to FIG.
In addition, the subpatches expressed by the equations (25) to (31) are
It means to set each. Then, in the next step SP3, the computer
4 patches to connect Then, the process proceeds to step SP4. This step SP4 is the first patch And second to fourth patches for connecting the same About the nodes at both ends of the shared boundaries COM1 to COM3 Whether the control edge vector is on the same plane
Find out. Ie nodes Control edge vector at Are not on the same plane, the condition of continuation of the tangent plane does not hold.
Will be. As well as nodes Tangent plane if the control edge vector is not coplanar at
The continuity condition does not hold. . So the computer gave a positive result in step SP4
Is obtained, the process proceeds to the next step SP5.
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 creation of the three subpatches in
Second, third and fourth triangular patches Tangent planes at the shared boundaries COM1, COM2, COM3
Be able to determine the condition of continuation. Subsequently, the computer moves to step SP7 and
Triangular patches in fixed order Control points to be set inside Ask for. Thus the triangular patch of Figure 4 Of the three adjacent
Triangle patch Creating one triangular patch that connects smoothly to the
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.
By specifying the power triangle patch,
The process of creating a finger is repeatedly executed. 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.
And the normal vectors on the shared boundaries COM1 to COM3 are
Check if the patches match each other
If they do not match, in step SP11
Investigate the cause and make numerical corrections if necessary. Hide
A series of patch connection processing procedures at step SP12.
Complete. (G6) Other Embodiments In the above-described embodiment, the third-order database is stored in the framework space.
I described the case of putting a patch expressed by the Jie formula,
The order of the expression is not limited to this, and may be fourth or higher. Further, in the above-described embodiment, the expression is expressed by the Bezier equation.
I mentioned a case where a patch was set up,
Not limited to this, spline type, Coons type,
Other vector functions such as the Furgason equation
It may be used. In the above-described embodiment, the triangular patch is used. Triangle patch on three sides Although the embodiment in which the
H The shape of the patch connected to the three sides is limited to a triangle
However, other shapes such as a quadrilateral may be used.
Even if it is a triangular patch Satisfies the condition of continuation of tangent plane with three sides of
Such a two-dimensional connection can be realized. In this case, as shown in FIG.
This is also the case when the triangular framework space is mixed between
Can be easily connected in two dimensions.
Thus, for example, the shape of the corner of the object is rounded
This can be effectively applied to the generation of a free-form surface. H Effects of the 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
Landing a free-form surface on a curved boundary curve network
Based on the triangular framework space based on the nodes set in the
One triangular detail surface when forming a boundary curve network
Condition of tangent plane continuity for three shared boundaries surrounding the shape
Three control points that satisfy
Triangular details controlled by points
To form the surface shape of the part
For a framework space that expands two-dimensionally sequentially
Free tunes with large degrees of freedom and practically sufficiently connected
Easily create surface shape data for surface objects
it can.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic diagram showing a boundary curve network in which a triangular framework space extends in an arbitrary direction, FIG. 2 is a schematic diagram showing a method of connecting two triangle patches, FIG. 3 is a schematic diagram for explaining the condition of continuation of the tangent plane, FIG. 4 is a schematic diagram showing the connection relationship of each side of the triangular patch, and FIG. 5 is set in the triangular patch. 3
FIG. 6 is a flow chart illustrating a patch connection processing procedure, and FIG. 7 is a schematic diagram illustrating an application example of the present invention. COM1, COM1 to COM3 ... 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 to be processed, a frame process is executed so as to include a triangular frame space surrounded by a first boundary curve, a second boundary curve, and a third boundary curve as each of the frame spaces. A first sub-detail surface connected to the adjacent first adjacent detail surface shapes using the first boundary curve as a shared boundary so as to satisfy a tangent plane continuity condition. A shape, a second sub-detail surface shape connecting the adjacent second detail surface shape with the second boundary curve as a shared boundary so as to satisfy a condition of tangential continuity, and the third boundary curve Is formed in the above-mentioned triangular framework space by superimposing and synthesizing a third adjacent detail surface shape connected to an adjacent third adjacent detail surface shape so as to satisfy the condition of tangent plane continuity by using as a shared boundary. In addition to generating position vector data representing an internal control point such that desired triangle detail surface shape data is generated, the triangle detail surface shape and the first, First and second tangents at the common boundary between second and third adjacent detail surface shapes from the common boundary and across the common boundary toward the triangle detail surface shape and the adjacent detail surface shape, respectively; Be The position vector data of the internal control points within the triangular detail surface shape is such that the tangent plane formed by the torque and the third tangent vector pointing in the direction along the shared boundary is the same. A first means for setting, a second means for sequentially designating the first, second and third internal control points by sequentially designating the triangle detail surface shape; First, second and third adjacent to detail surface shape
By displaying, on a display means, a normal vector of a point on the shared boundary between the adjacent detailed surface shape and a contour line in the triangular detailed surface shape on the display means, the connection state at the shared boundary is smoothed. And a third means for correcting the first, second and third internal control points by confirming the first and second internal control points.