JP2003085220A - 3D CAD system - Google Patents

Abstract

(57) [Summary] [PROBLEMS] To provide a three-dimensional CAD system in which the amount of data is significantly reduced to reduce the processing load of a computer and the handling of surfaces is made consistent. In a three-dimensional CAD system according to the present invention, a graphic element is defined using Bezier parameters, and display / output data is generated using area coordinate parameters, and parent-child relationship data is set. By expressing all surfaces with curved surface patches, the handling of surfaces is made consistent, the amount of data for describing graphics is significantly reduced, and the load on computer processing is reduced.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a three-dimensional CAD.
(3 Dimentional-Computer Aided Design: 3D-CA
D) System, more specifically, a three-dimensional CAD system to which Bezier curved surface expression is applied, and a program therefor.

[0002]

2. Description of the Related Art Currently, a system called "three-dimensional CAD" for drawing a three-dimensional design drawing on a computer has been proposed. For example, in a solid CAD method that uses various surfaces and a conventional CAD method that uses a free-form surface defined by a complicated mathematical expression, finally, a surface element represented by the minimum degree of freedom, that is, Decompose into a minute plane [usually a fine triangular plane element] PT. In other words, all the curved surfaces of the solid are decomposed into minute planes PT, and the arithmetic processing is performed using a linear discretization processing that is approximated by a collection [called a “polyhedron”] PP. It will be approximated by a broken line.

[0003]

[Problems to be Solved by the Invention] Conventional solid CAD
In the method, (1) a figure is created by a Boolean operation for superimposing basic figures (primitives) such as cylinders, cones, and hexahedrons. (2) It is necessary to stretch a fillet surface in the portion where the surfaces overlap with each other, and this fillet processing is unreasonable and is not suitable for design design. (3) In the curved surface processing, it is necessary to define an almost square surface and perform trim processing to adjust the shape of the surface. (4) These calculation processes perform polygon approximation (linear discretization approximation) and apply linear algebra theory to perform approximation calculation. Although it has the advantage of reproducing the design process from the beginning, it has a large amount of data, the computational load of the computer is excessive, and the handling of the surface is not consistent. There was a problem. The present invention solves the above-mentioned problems of the prior art, significantly reduces the amount of data, reduces the load of computer arithmetic processing, and has a consistent three-dimensional CAD system for handling surfaces. The purpose is to provide.

[0004]

Three-dimensional CAD according to the present invention
The system includes point element setting means defined by coordinate information, line element setting means defined by the point elements and Bezier parameters, surface element setting means defined by a plurality of the line elements, and a plurality of the surfaces. It is characterized by comprising three-dimensional element setting means defined by elements, and three-dimensional generation means for connecting a plurality of the set elements to generate a desired three-dimensional figure.

According to the present invention, the surface element is a conventional CA.
Compared to the surface processing method in the D method, it is possible to express a wide area with one patch (one surface element). In addition, since all the surfaces are approximated by this patch, the handling of the surfaces can be made consistent. Therefore, the amount of data for describing a figure can be significantly reduced, and the load of computer arithmetic processing can be reduced. Further, according to the present invention, when the generated three-dimensional figure is defined by the point group having the spatial coordinates expressed in the cubic form, the tangents of the surface ends are continuously connected without increasing the number of operations more than necessary. The surfaces can be deformed while maintaining the relationship of mechanically joining, and a sufficiently practical three-dimensional graphic representation can be obtained. Further, according to the present invention, it is possible to easily define the parent-child relationship of the graphic elements, and it is possible to easily move the child graphic along the curved surface of the parent graphic, for example. Since each graphic element has reference counting data, when deleting a certain element, refer to the reference counting data to check whether the element is a constituent factor of other elements. Therefore, it is possible to effectively determine whether or not deletion is possible.

[0006]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described in detail below with reference to the drawings. FIG. 2 is a block diagram showing a hardware configuration example of the three-dimensional CAD system according to the present invention. In this example, the system includes a CPU (central processing unit) 1, a storage device 2, an input operation device 3 such as a keyboard and a mouse, and a display device 4 such as a display. These devices 1 to 4 are connected via a bus 5. Are connected to each other. The CPU 1 that controls the entire system performs various controls according to a predetermined program, and particularly performs the three-dimensional graphic processing according to the present invention centrally. The storage device 2 is
In addition to the basic program, various graphic processing programs, ROM (read-only memory) that stores fixed data / parameters, RAM (random access memory) that temporarily stores various data, hard disk drive (HDD) and CD
An external storage device such as a ROM drive / FD (floppy disk) drive, which stores various graphic processing programs of the present invention and various graphic data / parameters. Further, the input operation device 3 such as a keyboard or a mouse can perform three-dimensional graphic processing by visually operating various screens displayed on the display 4. In this example, an output device such as a printer 7 or a plotter 8 is connected to the bus 5 via an interface 6, and for example, a three-dimensional figure can be drawn by the plotter 8. The created CAD data is output to the outside through an external storage device such as FD or a communication line such as LAN (not shown). FIG. 1 is a functional block diagram showing the functional configuration of the three-dimensional CAD system of the present invention. The three-dimensional CAD system of the present invention includes at least operation analysis, processing execution means 10 and point element generation means 1.
1, line (curve) element generating means 12, surface element generating means 1
3, a three-dimensional element generating means 14, a point moving means 15, a vector changing means 16, a display (painting, rotation) means 17, and a data output means 18. The operation analysis / process execution means 10 detects / analyzes the operation of the keyboard or mouse of the user of this system, and according to the processing instruction, the following means 1
1 to 18 are used alone or in combination to execute the instructed processing, the result is displayed on the screen, and further output as a file or to a printer or a line.

The point element generating means 11 generates point data. FIG. 3 is a flowchart showing the contents of the point data generation processing of the present invention. In S10, it is determined whether or not the user's instruction is to create a child figure, and if affirmative, S12.
If it is negative, the process proceeds to S11. S1
In 1, the three-dimensional coordinate information is input from the mouse or keyboard. When inputting with a mouse, for example, first click a desired position on the XY coordinate plane to generate point data, and move the point in the Z-axis direction by a desired distance (offset). Enter 3D coordinate information. In S18, the input point data is registered in the point data list in the system. S1
In 2, for example, the parent figure (line, triangular surface or four screens) already created is selected by the mouse. S
In 13, although the details will be described later, a 3D cursor placed on the parent figure is displayed by a mapping operation of the area coordinate parameter of the cursor to the three-dimensional coordinates. This area coordinate parameter will be described later, but in the case of a line, the position on the parent figure,
In the case of a surface, it corresponds uniquely to any position in the surface.
Furthermore, the definition can be extended to a solid, and in the case of a line or a solid, the term "area" is not used, but the term "area coordinate" is used inclusively. In S14, it is determined whether or not the mouse has been moved, and in the negative case, S16
If it is affirmative, the process proceeds to S15. S1
In 5, the details will be described later, but the cursor coordinates on the area coordinates are moved based on the mouse movement information, and the process returns to S13. Therefore, since the 3D cursor on the parent figure moves according to the mouse operation, the user operates the mouse to perform 3D
Move the cursor to the desired position. In S16, it is determined whether or not the mouse is clicked. If the result is negative, the process returns to S14, but if the result is affirmative, the process proceeds to S17. In S17, the three-dimensional coordinate data of the point on the parent figure indicated by the 3D cursor is registered in the point data list in the system, and this data includes the area coordinate parameter on the parent figure.

The line (curve) element generating means 12 generates line data. FIG. 4 is a flow chart showing the contents of the line data generation processing of the present invention. In S20, two pre-created points that are the end points of the line are selected. S21
, It is determined whether or not the two points are children of the same figure, and if affirmative, the process proceeds to S22, but if negative, S23.
Move to. In S22, curve data to be placed on the parent figure is generated. Although details will be described later, in the present invention, the line data is expressed (defined) by Bezier parameters including the coordinates of both end points and the internal control point and the information of the tangent (control) vector at each point. In step S22, the parameters of the curve are determined based on the parent graphic information so that the curve will ride on the parent graphic. In addition, the reference coefficient (count) of the end point data
Increment the value by 1. In S23, straight line data connecting two points is generated. The line is expressed by the Bezier parameter similar to the case of the child figure, but is a straight line because the tangent control vector direction of the end point is set to face the other end point by default. Further, the reference count value of the end point data is incremented by one. In S24, the line data generated in S23 or S24 is registered in the line data list of the system. The line data has no parent / child setting, but if the point data of the end point referred to by the line data is a child figure, the line is also a child figure.

The surface element generating means 13 generates surface data. The surface data includes at least triangular surface data and four-screen data, each of which includes three or four line data and one or a plurality of internal control point data that form each side. The three-dimensional element generating means 14 generates three-dimensional data. It should be noted that the solid is a figure in which a plurality of surface data are joined, and the surface does not need to be closed. The point moving means 15 provides a function of moving point data. When a point that is a parent figure is selected, it can be moved independently and arbitrarily. When a line, a plane, or a solid is selected, a plurality of point data included in those figures move at the same time. When the point is a child figure, it is necessary to move on the parent figure or keep a predetermined distance (offset).
In the same method as the processing of S13 to S15, one or more selected points are moved / displayed instead of the 3D cursor based on the mouse operation. In this case, the offset coordinate value (m_Ab_Ref) of the point is updated with the movement.

The vector changing means 16 changes the direction and size of the tangent control vector of the end point or internal control point which is the Bezier parameter of the selected line or surface. For example, the direction of the tangent control vector at the endpoint of the line determines the direction of the line exiting the endpoint, and the magnitude of the vector affects the curvature.
Therefore, by changing the directions of the tangent control vectors of the two lines coming out from one end point to be opposite,
It is possible to connect the curves of a book continuously (without breaking, continuously differentiable). Even when connecting faces, two or three
Smooth connection can be achieved by changing the directions of the tangent vectors of two or three lines that come out from the end points shared by one surface so that they are in opposite directions or in the same plane. When the control vector of the line or face that is the child figure is selected and changed, the bias vector of the selected control vector is updated. Similar to the case of the position of the point, these bias vectors represent the deviation from the vector calculated so as to ride on the parent figure, and the value is held even if the parent figure is deformed. (M_Cnt_ref of each surface
field)

The display (filling and rotating) means 17 displays various graphic data on the screen. FIG. 5 is a flowchart showing the contents of the line drawing process of the present invention. Although the details will be described later, changing the area coordinate parameter β of the line from 0 to 1 corresponds to moving from one end point to the other end point on the curve in three-dimensional coordinates. In S30, the area coordinate parameter β of the line is set to the starting point (β = 0). In S31, a predetermined value is set as the distance d between the drawing points on the area coordinates (for example, 0.0 if the line is divided into 100).
1) is set. In S32, β is mapped to three-dimensional coordinates using the Bezier parameter of the line to obtain the three-dimensional coordinate value of the drawing point. In S33, the three-dimensional coordinate values are further mapped to screen coordinates. In S34, a line connecting to the drawing point processed immediately before on the screen coordinates is drawn. In S35, d is added to β. S
At 36, it is determined whether β exceeds 1 (end point), and if the determination result is negative, the process returns to S32 and the drawing is repeated.

FIG. 6 is a flowchart showing the contents of the surface drawing processing of the present invention. Although details will be described later, changing the area coordinate parameters α and β of the surface from 0 to 1 corresponds to moving the point to all positions on the surface in three-dimensional coordinates. In S40, the area coordinate parameter α of the surface is set to the starting point (α = 0). In S41, a predetermined value (for example, 0.01 if the surface is divided into 100 in two orthogonal directions) is set as the distance d between the drawing points on the area coordinates. In S42, the area area coordinate parameter β is set to the starting point (β = 0). In S43, α and β are mapped to three-dimensional coordinates by using the Bezier parameters of the line data forming the sides of the surface, and the three-dimensional coordinate values of the drawing points are obtained. In S44, the three-dimensional coordinate values are further mapped to screen coordinates. However, when the shadow is seen from the currently set direction (the drawing surface is in the foreground), it is not mapped. In step S45, a small triangular patch is set between the point mapped on the screen coordinates and a point near the point, and the brightness is determined in consideration of the brightness when light is shined from a specific direction, and the patch is determined. To fill. In S46, d is added to β, it is determined in S47 whether β exceeds 1, and if the result is negative, the process returns to S43. In S48, d is added to α, it is determined in S49 whether α exceeds 1, and if the result is negative, the process returns to S42. The data output means 18 is composed of a large number of points arranged at predetermined intervals on the entire surface of the object by the same processing method as the display means.
Dimensional coordinate data is calculated, and based on the data, for example, three-dimensional shape data (cutter path data) in a standard format that can be directly input to the NC machine is output. Hereinafter, the embodiment will be described in more detail.

<< Explanation of Data Structure and Mapping >><Structure of 3D model data of three-dimensional CAD><1. Model Shape Data> FIG. 7 is an explanatory diagram showing the data structure of the system. All data representing the 3D model shape are objects derived from one root class CMdl, and have a hierarchy as shown in FIG. Each data is a class of C ++ (Object Oriented Programming Language) and has each data (attribute) and method. <1.1. Common data (data common to all shape data)> Common information is stored in the base class from which all figure data is derived.

CMdl * m_pMdl; Object entity address: usually refers to the original when copying by itself.・ TpUINT32 m_nMdlType; Data type identifier (MDL Cl
ass ID): Combined with the subtype identifier (m_wSchemaNo), it identifies the class of this object and also identifies the data format.・ TpUINT16 m_wSchemaNo; Subtype identifier (Mdl cla
ss schema No.)-TpINT32 m_nCount; Reference count: Reference count value from the figure including this as a constituent element. (1) Point: reference count from line (end point of line segment), (2) line: reference count from face (face boundary line), (3) face: reference count from solid (solid boundary face) ・ TpUINT16 m_wDispAttr ; Display mode (16bit) ・ TpUINT16 m_wSelectStatus; Selection status (16bit) ・ TpUINT16 m_wAttrFlags; Various flag bits (16bi
t), (1) bit-0: Changeable (0 = changeable, 1 = change prohibited), (2) bit-1: copy for editing (0 = substance, 1 = copy), (3) bit-2 ..3: Negative data discrimination flag (00 =), used for rendering as a hole figure during rendering. -CCoordinate * m_pParentCoordinate; Coordinate system (local coordinate system) pointer: Points to the local coordinate system to which this figure belongs. However, if this object has a coordinate system, it points to its parent coordinate system. CMdl * m_pParentRelation; Parent figure (parent turtle) pointer: If the point is constrained by another figure, the address of that figure is stored. In this case, the coordinates are calculated by the coordinate system parameters of the parent figure. When the object is a line or a face, it indicates that the control vector should be set so as to ride on the parent figure.

(1) Coordinate system (local coordinate system) To know the coordinate system to which a figure belongs, coordinate system (local coordinate system)
Refer to the pointer m_pParentCoordinate. For example, in the case of a point, its position coordinate is set in the local coordinate system, so if you need to convert to the world coordinate system, refer to this field and trace to the top level coordinate system. While converting. (2) Parent figure (parent turtle) In the case of a figure bound to another figure, the address of the parent figure is set in the parent figure (parent turtle) pointer m_pParentRelation. A parent figure can be specified only for points, and as will be described later, area coordinate information that determines the position of the point in the parent figure is set at the same time. (3) Data type identifier, subtype identifier This value is used to determine the format of the data, and is used, for example, to determine the type of surface of the selected graphic and process each. This identification information is also used to read the graphic data from the external file and restore the previous state. For example, the processing image in this case is shown below by pseudo coding.

<1.2. Point data (1 in 3D space
Data that expresses points)> Unique attributes as data that represent points are as follows, and can be roughly classified into independent points and points that lie on a parent turtle figure.・ CPoint3d m_Xyz; local coordinates (x, y, z) ・ CPoint2d m_Ab; parent turtle figure parameters (A, B) Effective only when the parent turtle exists: If this point is bound on the parent turtle figure, its It shows the parameter coordinates in the parent turtle figure.・ CPoint3d m_Ab_Ref; Offset vector from parent turtle figure: Effective only when parent turtle is present. After the coordinates are calculated using the parent turtle graphic parameters, this offset is added to obtain the coordinate values of the points. The coordinate field m_Xyz is represented by three values (x, y, z) in the three-dimensional coordinates of this point. The value is a value in the local coordinate system to which this point belongs, and is converted to the world coordinate system as necessary for display processing of the point. The specific data format of the coordinate field m_Xyz is as follows and is a three-dimensional coordinate and vector format. -Double x; X coordinate-double y; Y coordinate-double z; Z coordinate In the case of independent points, the desired (x, y, z) value may be directly set in this coordinate field m_Xyz.

When a point has another figure as a parent turtle, the coordinate value cannot be directly specified. Instead, the area coordinate values (A, B) of this point on the parent turtle figure are stored in the parent turtle figure parameter field m_Ab. The area coordinate value (A, B) specified here is used to obtain the actual point coordinate value.
By using, the value mapped to the three-dimensional space is used according to the type of parent turtle figure. The specific data format of the area coordinate value (A, B) is as follows.
It is a vector format.・ Double x; parameter a ・ double y; parameter b

FIG. 9 is an explanatory diagram showing the setting of parent turtle graphic parameters. There are the following two types of dots that are the turtle shape, and the specification method is different for each. (1) Line segment (curve) When the parent turtle figure is a line segment (curve), the curve coordinate β of the parent turtle figure is stored in m_Ab.x. (M_Ab.y is not used) In this case, the point moves while being bound by the curve according to the change of β value. (2) Surface patch (triangle, square patch) When the parent turtle figure is a surface patch (curved surface patch), two parameter values that represent the area coordinates of the parent turtle figure are m_Ab.x.
And m_Ab.y. (Refer to the table of FIG. 9 for the specific value setting method.) In this case, the point is constrained and moves on the parent turtle curved surface according to the change of the parameter. Figure 8
It is explanatory drawing which shows offset from a turtle figure. The offset m_Ab_Ref from the parent turtle graphic is the position offset of the point from the position on the parent turtle graphic, as shown in FIG. In any of the above cases, the parent turtle graphic parameter field m_Ab
The point moves at a position separated by this offset vector from the position where the parent figure was completely ridden according to the change of. In FIG. 9, the area coordinates of the parent turtle figure are directly stored except for the square patch. As shown in the lower part of FIG. 9, in the case of a square patch, the area (α, β, area of four rectangular regions divided by (A, B) in a square having sides of length 1
γ, δ) are the area coordinates of the square patch.

<1.3. Line segment> A line segment is a straight line or curve connecting two points.・ CMdlDot * m_pDot [2]; Pointer of the two end points of the line segment ・ CPoint3d m_Vect [2]; End point control point vector ・ CPoint3d m_Cnt_ref [2]; End point control point vector bias ・ TpUINT16 m_nAttr_vsel [2]; End point control point vector selection State ・ TpUINT16 m_nDivDsp; Line segment parameter step division number (used for mesh division etc.) ・ TpUINT16 m_nDivGoku; Continuum analysis integration step accuracy (line segment parameter step division number) ・ bool m_nStFlag; Straight line flag (distinguishes true line) ) Point attributes such as the coordinate values of the two end points are not directly held in the line segment, but the pointers of the end points are stored in the field m_pDot. Therefore, the transformation operation of moving the end point changes the coordinate value of the point without changing the information of the line segment itself.
The endpoint control point vector m_Vect is a three-dimensional vector having a size of 1/3 of the tangent vector at each endpoint.
This vector is expressed in the local coordinate system of the line segment.

FIG. 10 is an explanatory diagram showing mapping of line segments. From the line segment parameters (α, β), the three-dimensional space coordinate P (α,
The mapping to β) is calculated by the following total cubic equation symmetric with respect to (α, β). (Basically the same as the cubic Bezier curve)

[Equation 1]

Here, Dot [0] and Dot [1] are m_pDot [0].
And a position vector indicating the coordinates of each of the end points pointed to by m_pDot [1]. Further, the expression of the equation 2 is established.

[0022]

[Equation 2]

Here, the relation with the Bezier curve expression will be examined and viewed below. The Bezier curve is expressed by the n-ary Bernstein polynomial of one variable, and is as shown in Equation 3.

[0024]

[Equation 3]

B (t) in the above equation is a function of the variable t given by the following equation. (Bernstein function)

[Equation 4]

Pi is a control point of the Bezier curve, and the number thereof is n + 1. In addition, according to the second formula above, Bezier
The curve is a convex combination of these control points. Here, the following replacement is performed for comparison with the CAD expression of the present invention.

[0027]

[Equation 5]

As a result, the CAD line segment (curve) of the present invention
It can be seen that there is a relation of Expression 6 with the expression.

[0029]

[Equation 6]

Therefore, the following relationship is derived.

[0031]

[Equation 7]

As described above, mutual conversion is possible between the expressions.

In the CAD expression of the present invention in the operation of transforming a line segment (curve), two line segments (curve) which are once connected in succession have coordinate values of their connecting points, as will be described in the following description. Continuity is not broken just by changing.
Specifically, the movement of the point, that is, the change of the coordinate value m_Xyz, is performed independently of the setting of the control vector once set to be continuous, so once these control vectors are adjacent to each other by another operation. If differential continuation is set in the line segment, the control vector setting is maintained even if the connection point is moved.

That is, continuity is maintained even if Dot [0] or Dot [1] is changed. In fact, as in the second and third equations above, the effect is that P1 or P2 in the Bezier curve representation is automatically calculated.

FIG. 11 is an explanatory diagram showing mapping of a line segment which is a child figure. When a straight line (curved surface) has a parent figure, in order to put the curve on the parent figure, the control vectors (m_Vect [0] and m_Vect [1]) of the curve are calculated by the equation (8).

[0036]

[Equation 8]

This calculation formula calculates the line segment coordinates of the point P1 as (2/3,
1/3), that is, β = 1/3, and the line segment coordinates of the point P2 are (1 /
3, 2/3), that is, β = 2/3, first 2 on the parent figure
After the points P1 and P2 are put, it is derived that the child's curve passes through these two points P1 and P2 and is applied to the above-described line segment mapping equation to solve for the control vector.

Here, Dot [k] is the coordinate of the end point k, and Dot [k] = m_pDot [k] → m_Xyz. Note that “→” indicates a pointer (same below). Similarly, Dot [k]. Ab_Ref is the control vector bias of the end point k. Line [k]. Ab_Ref = m_p Line [k] → m_Ab_Ref In order to calculate the control vector, the point P1 on the parent figure is calculated.
It is necessary to obtain the three-dimensional coordinates of P2 and P2. This includes line segment coordinates on the parent figure of each of the two end points of the line segment /
It is necessary to calculate the line segment coordinates / area coordinates on the parent figure of each of the points P1 and P2 from the area coordinates, but the parent turtle figure parameters (A, B) of each end point, that is, the field m_
When the value of Ab is V0 and V1, the one obtained by the calculation formula of Expression 9 is used.

[0039]

[Equation 9]

This equation is comparable to the equation for obtaining the three-divided points of a straight line on a two-dimensional plane. That is, it means that the line segment (curve) to be obtained exists as a straight line in the area coordinate system on the parent turtle figure. (In the above formula, the same symbols are used in the area coordinate system of the parent for the points P1 and P2 in question.) Vector biases such as m_Cnt_Ref and Ab_Ref appearing in the calculation formula of Eq. It will be a deformation from the shape of riding completely. For example, when the end points are separated from the master surface, it is calculated that the end points are completely on the master surface. The bias value m_Cnt_Ref is further added to the result of such calculation. The bias is omitted from the equations for the surface described later, but it is the same.

FIG. 12 is an explanatory diagram showing a process for making two surfaces continuous. The process of connecting the end point of two line segments line1 and the start point of line2 with C0 continuation (without disconnection) is as follows.・ Line1.m_pDot [1] → m_Xyz = line2.m_pDot [0] → m_Xyz
; Make the coordinates of the end points equal. In this case, if you want to share points: ・ line1.m_pDot [1] = line2.m_pDot [0]; Share points. It should be done. Also, similarly C1 continuous (without breaking)
When connecting with, only the direction of the end point vector is opposite.・ Line1.m_pDot [1] → m_Xyz = line2.m_pDot [0] → m_Xyz
; ・ VLength1 = line1.m_Vect [1] .length (); ・ vLength2 = line2.m_Vect [0] .length (); ・ line1.m_Vect [1] = − vLength1 * line2.m_Vect [0]
/ vLength2; If the endpoints are shared here, the first step is not necessary. Furthermore, when connecting to C2 continuity (curvature continuity), the end point vectors are made equal in magnitude and the directions are opposite.・ Line1.m_pDot [1] → m_Xyz = line2.m_pDot [0] → m_Xyz
• line1.m_Vect [1] = − line2.m_Vect [0]; Again, if the endpoints are shared, the first step is unnecessary. Note that if it is attempted to connect two surfaces smoothly as shown in FIG. 12, this processing is performed by a pair of line segments line1 and line2, which are the boundaries of each surface, and line3 and line4.
It is sufficient to carry out each group independently. The lower part of FIG. 12 shows an image of the result of smoothly connecting the surfaces. The control vector at the end point D of the line segment line1 is the line segment l
The control vector at the end point C of the line segment line3 is changed to the state in which the control vector at the end point D of ine2 is copied in the reverse direction. There is. These are the only two changes in the data. In the above example, the two faces are the boundary line line5.
, The continuity between the faces is maintained even if the vertexes A to E of the faces are arbitrarily moved. When not shared, it is necessary to reflect the movement result of the points belonging to one surface at the points D and C to the other point.

<1.4. Triangular surface> This is a triangular curved surface patch having three line segments (curves) connecting three points in a three-dimensional space as surface boundary lines. As in the case of the line segment, the vertex and boundary line segment attribute information is not directly held in the surface patch, but a pointer to them is held.・ CMdlDot * m_pDot [3]; surface vertex pointer ・ CMdlLine * m_pLine [3]; surface boundary line pointer: 3 line segments (curves) that are the boundaries of this surface ・ CPoint3d m_Vect; in-plane control point vector: surface Controlling bulge ・ CPoint3d m_Cnt_ref; In-plane control point vector bias: In-plane control point vector = m_Vect + m_Cnt_ref ・ TpUINT16 m_nAttr_vsel; In-plane control point selection state ・ TpUINT16 m_nDivDsp; Number of plane coordinate parameter division (geometric calculation, For mesh division) ・ TpUINT16 m_nDivGoku; Number of plane coordinate parameter divisions (for continuum analysis) ・ TpMdlColor m_nColorPaletteNo; Display color RGBA ・ float m_fMin, m_fMax; Depth of front and back surface for minus patch.

In the surface vertex pointer m_pDot, the pointer of the point which becomes the vertex of this triangular surface is stored. These vertices are also the endpoints of the boundaries of the face and are shared between adjacent boundaries. Further, it may be shared by a plurality of surfaces, and in that case, when the position of the shared point is changed, the plurality of related surfaces are simultaneously deformed. Similarly, the surface boundary pointer m_pLine stores the pointer of the line segment that becomes the boundary of this triangular surface. Further, it may be shared by a plurality of surfaces, and in this case, when the shared line segment is changed, the plurality of related surfaces are simultaneously deformed. In-plane control point vector m_Ve
In ct, a vector for controlling the unevenness of the surface at the area coordinates (1 / 3,1 / 3,1 / 3) of the triangular surface is stored. If this vector is increased, larger unevenness will be created near the center.
This is set to 0 vector by default (in the case of a small turtle figure that rides on the parent turtle figure, the initial value is calculated so as to ride on it). FIG. 13 is an explanatory diagram showing the mapping of the triangular surface. The mapping from the area coordinates (α, β, γ) of the triangular surface to the three-dimensional space coordinates P (α, β, γ) is similar to the line segment and is expressed by the symmetric number 10 for (α, β, γ).
It is calculated by the total cubic equation of.

[0044]

[Equation 10]

Coefficient vectors C [0] to C [9] in this equation
Is expressed by a combination of the vertex coordinates and the boundary line control vector and the in-plane control point vector as shown in Expression 11.

[0046]

[Equation 11]

Here, Dot [k] is the coordinate of the vertex k.・ Dot [k] = m_pDot [k] → m_Xyz Similarly, Line [k]. Vect [0] and Line [k]. Vect [1]
Is the control vector of the boundary segment k.・ Line [k]. Vect [0] = m_p Line [k] → m_Vect [0] ・ Line [k]. Vect [1] = m_p Line [k] → m_Vect [1] On the area coordinate system When the value of any one of the components of the coordinates (α, β, γ) is fixed to 0, one of the boundary line segments of the triangular surface is naturally expressed. For example, when γ = 0,

[Equation 12]

Since α + β = 1, the above 1.
3. Comparing with the mapping equation from the line segment coordinate to the three-dimensional space coordinate described in Section 2, the line segment coordinate is exactly (α, β), and Dot [0] and Dot [0]
It is a line segment itself with [1] as the end point. α =
It can be seen that even when 0 and β = 0, the boundary line segment corresponding to each is expressed. On the contrary, if there are three closed line segments (curves), a triangular surface stretched by them can be created naturally. The area coordinate system (α, β, γ) of the triangular surface is shown in FIG.
The vertices of the plane triangle are (1,0,0), (0,
Points (α, β, γ) with coordinate values (1,0) and (0,0,1)
And the coordinate system is such that the area ratio of a triangle formed by dividing these three points into three is exactly the coordinates (α, β, γ). Since one of the coordinate values (α, β, γ) is 0 on the boundary line of the plane triangle, the mapping destination is the actual boundary line of the triangular surface as described above. In-plane control point vector of triangular surface m_Vec
t can be calculated as follows from the coordinates of the point in the three-dimensional space corresponding to the area coordinates (1 / 3,1 / 3,1 / 3). P = P (1 / 3,1 / 3,
1/3), the equations 13 and 14 are derived from the above mapping equation.

[0049]

[Equation 13]

Therefore,

[Equation 14]

This calculation is also used when a triangular surface is used as a Kogame figure on another surface. In other words, if the area coordinates of the in-plane control points of this triangular surface on the parent turtle figure are calculated, then the three-dimensional coordinates of the in-plane control points are calculated, and the obtained coordinate values are applied to P above. , Triangular surface attached to the parent turtle figure is obtained.

[Generation of Triangular Surface Riding on Parent Turtle] FIG. 14
FIG. 6 is an explanatory diagram showing a mapping of a triangular surface which is a child figure. First, it is necessary that the three vertices of the triangular surface be created as the small turtle figure of the parent turtle figure. At this time, the following description will be made assuming that the parent turtle graphic parameters (A, B) of each vertex, that is, the value of the field m_Ab is predetermined as follows. V0: (A0, B0) V1: (A1, B1) V2: (A2, B2) First, the coordinates of each in-plane control point of the child face in the area coordinate system of the parent figure must be obtained. In order to explain this, the same symbols as the corresponding points will be used in the parent area coordinate shape. (The same symbol is a two-dimensional point in the area coordinate system of the parent.) FIG. 15 is an explanatory diagram (2) showing the mapping of the triangular surface which is the child figure. Here, if V0 to V2 and P are considered as two-dimensional position vectors, the following two-dimensional vector formula is derived because the in-plane control point is located at the center of gravity of the triangle.

[0053]

[Equation 15]

The method of setting the parent turtle graphic parameters (A, B) is as shown in FIG. If the parent turtle graphic parameters of the four vertices V0 to V2 of the child surface are given as coordinate values to this vector formula, the coordinates of the in-plane control point P of the child surface in the parent area coordinate system can be calculated. The vector formula itself for calculating the area coordinate value of the in-plane control point is the same whether the surface to be the parent-game figure is a triangular surface or a square surface. As described above, if the area coordinates on the parent plane of each in-plane control point of the child plane (Kogame) are obtained,
Next, this area coordinate is used to obtain the three-dimensional coordinate of the in-plane control point by using the mapping formula of the master surface. In this way, the three-dimensional coordinate values of the in-plane control points of the triangular surface, which is the child plane in the end, can be obtained, and thus the in-plane control point vector calculation formula (Equation 14) described above is used to determine the parent plane. You can get a sticky triangular surface. The relationship with the Bezie triangular patch expression will be examined and viewed below. The Bezier triangular patch is expressed by a 2-variable nth-order Bernstein polynomial and is as follows.

[0055]

[Equation 16]

Here, B (u, v) is a Bernstein function of variables u and v given by the following equation.

[0057]

[Equation 17]

Pij is a control point of the patch, the number of which is (n + 1) (n + 2) / 2. In addition, according to the above second formula, Bezi
The er triangular patch is a convex combination of these control points. Here, the following replacement is performed for comparison with the CAD expression of the present invention.

[0059]

[Equation 18]

From this, it is understood that the CAD triangular patch expression of the present invention has the following relationship.

[0061]

[Formula 19]

Therefore, the following relationship is derived.

[0063]

[Equation 20]

<1.5. Square surface> This is a square curved surface patch in which a closed four line segment (curve) connecting four points in a three-dimensional space is used as a surface boundary line. As in the case of the line segment, the vertex and boundary line segment attribute information is not directly held in the surface patch, but a pointer to them is held. The above idea is exactly the same as the above-mentioned triangular surface.・ CMdlDot * m_pDot [4]; surface vertex pointer ・ CMdlLine * m_pLine [4]; surface boundary line pointer: 4 line segments (curves) that are the boundaries of this surface ・ CPoint3d m_Vect [4]; in-plane control point vector : Controls the expansion of the surface ・ CPoint3d m_Cnt_ref [4]; In-plane control point vector bias: In-plane control point vector = m_Vect + m_Cnt_ref ・ TpUINT16 m_nAttr_vsel [4]; In-plane control point selection state ・ TpUINT16 m_nDivDsp [ 2]; Surface coordinate parameter division number (for geometric calculation, mesh division) ・ TpUINT16 m_nDivGoku [2]; Surface coordinate parameter division number (for continuum analysis) ・ TpMdlColor m_nColorPaletteNo; Face display color RGBA ・ float m_fMin, m_fMax; Minus Range for patch Front and back depth

In the surface vertex pointer m_pDot, a pointer for the point that becomes the vertex of this square surface is stored. These vertices are also the endpoints of the boundaries of the face and are shared between adjacent boundaries. Also, it may be shared by a plurality of surfaces, and in that case, when the position of a shared point is changed, a plurality of surfaces referencing it are simultaneously deformed. Similarly, the surface boundary pointer m_pLine stores the pointer of the line segment that becomes the boundary of this square surface. This may also be shared by a plurality of faces, and in this case, when a shared line segment is transformed, a plurality of faces that refer to it are transformed at the same time. The in-plane control point vector m_Vect contains the area coordinates (4/9, 2/9, 1/9, 2/9), (2 /
9, 4/9, 2/9, 1/9), (1/9, 2/9, 4/9, 2/9), and (
2/9, 1/9, 2/9, 4/9) The vector which controls the unevenness of the square surface is stored. Although there are differences in the numbers, they work the same as the triangular surface described above. These are set to 0 vector by default. (In the case of a small turtle figure that rides on the parent turtle figure, the initial value is calculated so that it rides.) The area coordinates (α, β, γ, δ) of the square surface are, in fact, two-dimensional because the surface is essentially two-dimensional. It can be calculated from two parameters (u, v), so let's assume that these relationships are defined by the following equation.

[0066]

[Equation 21]

The positions of the above-mentioned four in-plane control points in the area coordinate system are represented by the following symbols: P0: (4/9, 2/9, 1/9, 2/9) P1: (2/9 , 4/9, 2/9, 1/9) P2: (1/9, 2/9, 4/9, 2/9) P3: (2/9, 1/9, 2/9, 4/9 ) FIG. 16 is an explanatory diagram showing in-plane control points of a square surface. When viewed on a normal (U, V) coordinate system, each corresponds to a position as shown in FIG. FIG. 17 is an explanatory diagram (2) showing in-plane control points of a square surface. The area coordinates (α, β, γ, δ) of the square surface are
Considering the comparison with a normal (U, V) coordinate system, when a unit square is divided into four rectangles with coordinates (u, v) as shown in FIG. 17, the area of the divided rectangles is obtained. In order to interpret this from another point of view, divide it into four triangles as shown in the lower part of FIG. When viewed in this way, for example (α,
Considering the set of β), it can be seen from the simple area calculation that the following relation holds.

[0068]

[Equation 22]

Here, Sab is the area of ΔAPB. Similarly, the same relationship is derived for the other three sets.

[0070]

[Equation 23]

From this relationship, for example, when Sab is 0,

[Equation 24]

However, in this case, since P is on the side AB, it indicates that the line segment coordinates of the side AB are simultaneously obtained. The same applies to the other groups. That is, it can be seen that the line segment coordinates of the boundary line are naturally derived from the surface area coordinates. This can be directly confirmed from the surface mapping formula shown in the next section, as in the case of the triangular surface described above. Similarly, it is confirmed that the following relation holds for the above-mentioned triangular surface, and the line segment coordinates about the boundary line are naturally derived from the area coordinates.

[0073]

[Equation 25]

The mapping from the area coordinates (α, β, γ, δ) of the quadrangular surface to the three-dimensional space coordinates P (α, β, γ, δ) is the same as the above-mentioned triangular surface (α, β, γ, δ) is calculated by the total cubic equation of Eq.

[0075]

[Equation 26]

Coefficient vectors C [0] to C [15] in this equation
Is represented by a combination of vertex coordinates and boundary line control vectors and in-plane control point vectors as shown below.

[0077]

[Equation 27]

Here, Dot [k] is the coordinate of the vertex k.・ Dot [k] = m_pDot [k] → m_Xyz Similarly, Line [k]. Vect [0] and Line [k]. Vect [1]
Is the control vector of the boundary segment k.・ Line [k]. Vect [0] = m_p Line [k] → m_Vect [0] ・ Line [k]. Vect [1] = m_p Line [k] → m_Vect [1] Square in-plane control point vector m_Vect is the area coordinates (4/9, 2/9, 1/9, 2/9), as in the case of the triangular surface described above.
(2/9, 4/9, 2/9, 1/9), (1/9, 2/9, 4/9, 2/9) and (2/9, 1/9, 2/9, 4 / 9) can be calculated as follows from the coordinates of the point in the three-dimensional space corresponding to.

[0079]

[Equation 28]

Here, P0, P1, P2 and P3 correspond to the mapping formulas of the quadrangular surface as follows.

[0081]

[Equation 29]

If a mapping formula for a quadrangular surface is applied to this to solve for the in-plane control vector, the above-mentioned calculation formula for the in-plane control vector is obtained. This calculation is also used when making a square surface a Kogame figure of another surface. That is, the area coordinates of the four in-plane control points of this square surface on the parent turtle figure were obtained, and the three-dimensional coordinates of these in-plane control points were calculated using the mapping equation of the parent turtle plane. If the three-dimensional coordinate values are applied to the above P0 to P3, a square surface attached to the parent turtle figure can be obtained.

[Generation of a square plane riding on a parent turtle] FIG.
FIG. 6 is an explanatory diagram showing a square surface of a child figure. First, it is necessary that the four vertices of the square surface be created as the small turtle figure of the parent turtle figure. At this time, the following description will be made assuming that the parent turtle graphic parameters (A, B) of each vertex, that is, the value of the field m_Ab is predetermined as follows. V0: (A0, B0) V1: (A1, B1) V2: (A2, B2) V3: (A3, B3) FIG. 19 is an explanatory diagram showing internal control points on the square surface of the child figure. First, the coordinates of each in-plane control point of the child plane in the area coordinate system of the parent figure must be obtained. In order to explain this, the same symbols as the corresponding points will be used in the parent area coordinate shape. (The same symbol is a two-dimensional point in the area coordinate system of the parent.) Considering V0 to V3 and P0 to P3 as two-dimensional position vectors, the following two-dimensional vector formula is derived.

[0084]

[Equation 30]

The method of setting the parent turtle graphic parameters (A, B) is as shown in FIG. If the parent turtle figure parameters of the four vertices V0 to V3 of the child surface are given as coordinate values to this vector expression, the coordinate values of the in-plane control points P0 to P3 of the child surface in the parent area coordinate system can be obtained. The vector formula itself for calculating the area coordinate value of the in-plane control point is the same whether the surface to be the parent-game figure is a triangular surface or a square surface. As described above, assuming that the area coordinates on the parent plane of each in-plane control point of the child plane (Kogame) are obtained, the next step is to use this area coordinate and use the mapping formula of the parent plane. To obtain the three-dimensional coordinates of the in-plane control point. In this way, the three-dimensional coordinate values of the four in-plane control points of the quadrangular surface, which is the child plane in the end, are obtained, so that the in-plane control point vector calculation formula described above is used to stick to the parent plane. You can get a square surface. The relationship with the Bezier square patch expression will be examined and viewed below. The Bezier square patch is expressed in a tensor product form of a 1-variable m-order Bernstein function and a 1-variable n-order Bernstein function, and is as shown in Formula 31.

[0086]

[Equation 31]

Here, B (u) and B (v) are Bernstein functions of variables u and v given by the following equations, respectively.

[0088]

[Equation 32]

Pij is the control point of the Bezie square patch, and the number thereof is (m + 1) (n + 1). Note that the Bezie square patch is a convex combination of these control points according to the third expression of Expression 32. Here, the following replacement is performed for comparison with the CAD expression of the present invention.

[0090]

[Expression 33]

Rewriting the patch expression with m = n = 3 gives the following.

[0092]

[Equation 34]

When this is specifically developed,

[Equation 35]

It becomes By executing the replacement described above, the following equation is obtained.

[0095]

[Equation 36]

From this, it can be seen that the CAD square patch expression of the present invention has the following relationship.

[0097]

[Equation 37]

Therefore, the following relationship is derived.

[0099]

[Equation 38]

<< Detailed Description of Major Functions of CAD of the Present Invention >><< 1. Creating points >>><1.1. Creation of Point Bound to Parent Turtle Figure> The flow of selecting one of the created line segments (curves) or faces and creating a point to be bound on it is as shown in FIG. 3 when the point creation is instructed by the menu
The D cursor is initialized to be located at the origin (0,0,0) of the current coordinate system. Also, at this point, no parent figure is associated with this cursor. The current state of the 3D cursor is stored in the program as a point object as follows.・ CmdlDot * pCursor3D; In the initial state, the following attributes are set for this cursor.・ PCursor3D → m_pParentCoordinate = address of the current coordinate system object ・ pCursor3D → m_pParentRelation = Null (no parent figure) ・ pCursor3D → m_Xyz = (0,0,0) At the origin of the reduced coordinate system, select the point creation mode by selecting the initialization menu Even after the transition, the point coordinate specification is not started immediately, but nothing is actually done until the Tab key or'C 'key is pressed. If none of these keys are pressed,
A figure can be selected by left-clicking the mouse. The operator selects the parent figure at this timing. However, if you press the Tab key next time, a point that is not bound to the parent figure will be created, and the selection will be ignored.

(1) Selection of parent figure In response to the mouse left button Up event, all figures (line segments and planes) are sequentially examined, and the point indicated by the mouse coordinates (mx, my) is from the center point of the figure. Find a figure that fits within a certain distance. If such a figure is found, the figure is stored as a selected figure in the figure selection list, and the display is changed to indicate that the figure is being selected. [Additional explanation] 1. The three-dimensional coordinates of the line segment and the center point of the surface are calculated, and the coordinates converted into the screen coordinate system and the mouse coordinates (mx, my) are compared to check whether they are within a predetermined distance. If it is within the predetermined distance, it is determined that the figure is selected. 2. Selected state field of the selected figure (m_wSelectS
tatus) is set to a value indicating that the entire figure is being selected. The selected display is performed by referring to the value of this field.

(2) Position setting of point on parent figure Receive event of pressing'C 'key (operator'C'
When the key is pressed), the selected figure list at that time is examined, the first line or face is stored as the parent figure, and the cursor indicating the position of the point is positioned at the center of the parent figure. The figure selection list is cleared here.・ PCursor3D → m_pParentRelation = address of selected figure (address of parent turtle figure) ・ pCursor3D → m_Ab = (a, b) parent turtle figure parameter (a, b)
Is set to the center of the parent turtle graphic. • pCursor3D → m_Ab_Ref = (0,0,0) The offset vector is initialized to 0 vector. FIG. 20 is an explanatory diagram showing the setting of the parent turtle graphic parameter (a, b). After that, in response to the movement event of the mouse pointer, the parameter coordinates (curve coordinate parameter for line segment, area coordinate parameter for surface) are moved according to the movement of the mouse coordinate, and the parameter coordinate after movement is set. Use it to calculate the 3D coordinates of the cursor and display it on the screen. The update of the parent turtle figure parameters (a, b) according to the movement amount of the mouse pointer is as follows.

[0103]

[Formula 39]

The coefficient of change is a small value of about 0.01. Parent turtle figure parameters (a, b) to parent turtle figure line segment coordinate system (α, β), triangular surface area coordinates (α, β, γ)
Alternatively, the conversion into the square surface area coordinates (α, β, γ, δ) is as shown in the rightmost column of the table of FIG.

(3) Generation of point data When the right button Up event of the mouse pointer is received,
Point data having the coordinate value of the position of the 3D cursor at that time is generated.・ CmdlDot * pNewDot = new CmdlDot; Create point object Set point local coordinate system (copy local coordinate system of parent turtle shape) ・ pNewDot → m_pParentCoordinate = pCursor3D → m_pPar
entRelation → m_pParentCoordinate; Set address of parent turtle shape ・ pNewDot → m_pParentRelation = pCursor3D → m_pParen
tRelation; Set parent figure parameter (a, b) ・ pNewDot → m_ m_Ab = pCursor3D → m_Ab; Set offset vector (offset vector from parent figure) ・ pNewDot → m_Ab_Ref = pCursor3D → m_Ab_Ref

<< 2. Creation of line segment (curve) >><2.1. When selecting a point that has already been created and creating a line segment> If two point objects are selected when the line creation menu selection event is received (the operator selects the menu), immediately Create and display a line segment (straight line) with two points as end points, and clear the selected figure list. (In other cases, wait until the creation of the line segment is started by pressing the Tab key.) The line segment generation performed at this time can be roughly divided into two types. There are a case where the selected two points are independent points (an independent point having no parent turtle figure) and a case where the selected two points are child figures created on the same parent turtle figure. (1) Generation of line segment data when end points are independent points A straight line segment connecting two selected points is generated.・ CMdlLine * pNewLine = new CmdlLine; Setting the point local coordinate system that generates the line segment object ・ pNewLine → m_pParentCoordinate = pCursor3D → m_pPa
rentCoordinate; ・ pNewLine → m_pDot [0] = Address of the selected first point object ・ pNewLine → m_pDot [1] = Address of the selected second point object ・ pNewLine → m_Vect [0] = 1 point Vector of 1/3 of vector from eye to second point ・ pNewLine → m_Vect [1] = Vector of 1/3 of vector from 2nd point to 1st point (2) Created on parent turtle figure with the same end point Generation of line segment data in the case of a child graphic that has been created In this case, a line segment (curve) that rides on the parent graphic of the two end points is generated.・ CMdlLine * pNewLine = new CmdlLine; Setting the point local coordinate system that generates the line segment object ・ pNewLine → m_pParentCoordinate = pCursor3D → m_pPa
rentCoordinate; ・ pNewLine → m_pDot [0] = Address of the first point object selected ・ pNewLine → m_pDot [1] = Address of the second point object selected The line of the parent turtle graphic address of the end point Copy to parent turtle graphic address ・ pNewLine → m_pParentRelation = pNewLine → m_pDot [0]
→ m_pParentRelation; Calculate and set the control vector so that the line segment will be on the parent turtle shape ・ pNewLine → m_Vect [0] = Set the calculated value ・ pNewLine → m_Vect [1] = Set the calculated value In order to put the curve on the parent figure, the control vector (m_Vect [0], m_Vect [1]) of the curve is calculated by the following formula.

[0107]

[Formula 40]

In this calculation formula, the line segment coordinates of the point P1 are (2 /
3, 1/3), that is, β = 1/3, and the area coordinates of the point P2 are
(1/3, 2/3), that is, β = 2/3, first put two points P1 and P2 on the parent figure, and then the child curve draws these two points P1.
And P2, the mapping equation of the line segment is solved for the control vector (m_Vect [0], m_Vect [1]). FIG. 21 is an explanatory diagram showing the control points of the line segment of the child figure. The intermediate points P1 and P2 appearing in the calculation formula are points on the parent figure, which are obtained as follows. First, the case where the parent turtle figure is a triangular or quadrangular surface figure will be described. On the area coordinate system of the parent figure, the positions of the end points Dot [0] and Dot [1] are Pa and Pb, respectively, and the area coordinates are (αa, βa,
..) and (.alpha.b, .beta.b, .gamma.b, ...). FIG. 22 is an explanatory diagram (2) showing the control points of the line segment of the child figure. Also,
The area coordinates of the parent figure of P1 and P2 on the area coordinate system are (α
1, β1, γ1, ...) and (α2, β2, γ2, ...), these values can be calculated by the following equation.

[0109]

[Formula 41]

Using the area coordinates obtained here, P1 (α1,
β1, γ1, ...) and P2 (α2, β2, γ2, ...) are calculated and applied to the above control vector calculation formula.

<< 3. Creation of surface >>><3.1. When creating a surface with the created line segment as the boundary> It can be configured as a surface with the line segment as the boundary regardless of whether it is a triangular surface or a quadrangular surface. It is possible to select and newly generate a surface as a surface surrounded by those line segments. The process flow is the same as the above-mentioned “2.1. Creating a line segment by selecting already created points”. As in the case of line segment creation, when the surface creation menu is selected and the boundary line segment of the surface is selected, the surface creation process is immediately started. At this point, the number of line segments and the number of closed line segments connected to each other are checked. If there are three selected line segments, a triangular surface,
If there are four, a quadrangular surface is generated. As in the case of the line segment described in 2.1 above, when the selected boundary line segments are all child figures having the same parent, the faces are also generated as child figures that ride on the same parent figure. In the calculation of the in-plane control point vector in the generation of the plane to ride on the parent, paragraph numbers [0052] to [005
4] and the case of a square surface are as shown in [0083] to [0085].

<< Graphic Creation Example >><Flowchart of Creation Example> 1. ~ 4. Shows the rough processing procedure of the creation example. 1. Creating points that become surface vertices (independent points that do not have parents) (1) Select the point creation menu to enter the point creation mode. The cursor is initialized to the value converted from the mouse coordinates at this point into the current three-dimensional model coordinate system. (2) Move the mouse cursor and left-click. The mouse coordinates are converted from screen coordinates into three-dimensional coordinates, a point object is generated, and the above coordinate values are substituted. (3) Repeat (2) until an event occurs such as selection of ESC key or other operation menu (9 points are created in the embodiment).

2. It becomes the boundary of the surface from the created point cloud 4
Create a quadrilateral while selecting points (1) Select the quadrilateral creation menu to enter the quadrilateral creation mode. The cursor is the current 3 from the mouse coordinate at this point.
Initialized to the value converted to the dimensional model coordinate system. (2) Since it is created from an existing point, it is made selectable with the ESC key. (3) Select the four points that are the vertices of the surface to be created with the mouse cursor. (Hold down the Cntl key simultaneously for multiple selections) Left-click the mouse to search for a graphic in the vicinity at the coordinates on the screen, and add it to the graphic selection list, if any. (4) Press'M 'key with 4 points selected. Ignore if 4 points are not selected in the program. If the conditions are met, proceed to the next. (5) Generation of quadrangular surface ・ Generate four straight lines connecting selected points in the order of selection. If a line segment connecting two points has already been created, it will not be created as shared. -Generates a quadrangular surface with the generated line segment as a boundary. In-plane control vector and bias vector are all set to 0 vector. The vertex address is set to point to the selected point.
The boundary line segment address is set to point to the line segment that was created or shared. (6) Repeat from (3) until an event such as ESC key or other operation menu selection occurs (six sides are created in the embodiment).

3. Create 8 points as child figures on the upper left surface (to be referred to as surface 3) (1) Select the menu for starting point creation to enter the point creation mode. The cursor is initialized to the value converted from the mouse coordinates at this point into the current three-dimensional model coordinate system. (2) Move to the figure selectable state to select the master surface.
The ESC key is used to temporarily suspend and shift to the figure selectable state. (3) Move to the center of mouse cursor surface 3 and left-click. This event causes surface 3 to be stored in the selected figure list. (4) Select the child figure creation menu to switch to the child figure creation mode. The program initializes the cursor in the center of the selected shape. When the square is the parent, (α, β, γ, δ) = (1
/ 4,1 / 4,1 / 4,1 / 4) is converted into three-dimensional coordinates using the surface mapping formula, and the cursor is displayed there. When the triangular surface is the parent, (α, β, γ) = (1 / 3,1 / 3,1 / 3). At the same time, this value is stored in the area coordinate storage variable of the parent figure. (5) While detecting the movement event of the mouse cursor, updating the area coordinates (area coordinate storage variable) on the master surface by the amount of mouse movement, and converting to the three-dimensional coordinates by the surface mapping formula and updating the cursor display position. To do. (6) When a left click event is detected, a point is generated using the area coordinate (area coordinate storage variable) value on the parent surface at that time. Point generation Parent turtle figure parameter <-Area coordinate on parent plane (area coordinate storage variable) Set offset vector <-(0,0,0) Parent turtle figure <-Address pointing to selected parent plane (7) The process is repeated from (5) until an event such as the ESC key or other operation menu selection occurs (eight points are created in the embodiment).

4. Creating a Child Face as a Child Graphic of the Parent Face (Face 3) Five child faces are created from the 8 points created in 3 above. (Procedure is exactly the same as 2). (1) Select the menu to start creating a square surface and enter the square creation mode. The cursor is initialized to the value converted from the mouse coordinates at this point into the current three-dimensional model coordinate system. (2) Since it is created from an existing point, it is made selectable with the ESC key. (3) Select the four points that are the vertices of the surface to be created with the mouse cursor. (Hold down the Cntl key simultaneously for multiple selections) Left-click the mouse to search for a graphic in the vicinity at the coordinates on the screen, and add it to the graphic selection list, if any. (4) Press the specified key with four points selected. Ignore if 4 points are not selected in the program. If the conditions are met, proceed to the next. (5) Generation of a square surface-Generation of four line segments that connect selected points in the order of selection If a line segment that connects two points has already been created, do not create it as shared. In this case, since the two points are on the common parent figure, the control vector of the line segment is calculated so as to be on the parent figure. Set the pointers to the selected 2 points at the end point address. For the control vector, set the vector value calculated to ride on the master surface. The control vector bias is set to 0 vector (0,0,0). Set a pointer to the parent figure address that points to the same parent figure as the point. The reference counts of 2 points are each incremented by 1. -Generate a quadrangular surface with the generated line segment as a boundary. The in-plane control vector of the quadrangular surface is calculated and set so as to ride on the parent figure of the vertex and the boundary line, and the bias vector is set to all 0 vectors. . Set a pointer to the selected 4 points at the vertex address. The boundary line address is
Set a pointer to the created or shared 4 line segment. Set a pointer to the parent figure address that points to the same parent figure as the point. The reference counts of the four surface boundary line segments are each incremented by one. (6) Repeat from (3) until an event occurs such as ESC key or other operation menu selection. (8 in the embodiment
5 faces are created from points).

The details of the creation example will be described below. (1) Creation of points that become the surface vertices of the base surface In the embodiment, nine points are created at the position of Z = 0 as shown in FIG. (These points are independent points that do not have parents.) In order to create points, it is necessary to first instruct the menu to start point creation. When the menu is selected, the 3D cursor is positioned at the origin of the current coordinate system as shown in FIG. This cursor moves in the three-dimensional space according to the movement of the mouse pointer. The position of the 3D cursor is stored in a variable for holding 3D cursor information. The display of the 3D cursor is performed based on the latest information of this variable. As will be described later, this 3D cursor is also used to generate a point as a child figure.・ CMdlDot pt3DCursor; Variable for saving the current 3D cursor position. This variable is initialized as follows when the point creation menu is selected. Initialize coordinates to (0,0,0) ・ pt3DCursor.m_Xyz.x = 0; ・ pt3DCursor.m_Xyz.y = 0; ・ pt3DCursor.m_Xyz.z = 0; Clear parent figure information ・ pt3DCursor.m_pParentRelation = Null ; Pointer pointing to parent turtle shape ・ pt3DCursor.m_Ab.x = 0; pt3DCursor.m_Ab.x = 0; Parent turtle coordinate parameters ・ pt3DCursor.m_Ab_Ref.x = 0; Offset vector from parent ・ pt3DCursor.m_Ab_Ref.y = 0; -pt3DCursor.m_Ab_Ref.z = 0; This cursor information is always maintained and is used to copy the necessary information at the point generation when the mouse left button down (press) event is received. The process of receiving a mouse left button down (press) event and generating a point is exactly the same as the point generation as a child figure described later in (3) at the coding level. In the example, since the figures are created in the world coordinate system, all the figures are in the same coordinate system, but if the model is created in multiple coordinate systems, that is, in multiple parts,
The current coordinate system is pt3DCursor.m_pPar of 3D cursor.
It is set every time the pointer indicating the coordinate system is switched to entCoordinate. The initial value is set to the world coordinate system.

(2) Creating a quadrangular surface while selecting four points that are the boundaries of the surface from the created point group. First, select the four points in the upper left from the above-mentioned nine points in sequence clockwise or counterclockwise. Create one square face. Figure 2
5 is an explanatory diagram showing the selection of vertices of a surface. The selected figure is held in the figure selection list and is referred to when the surface is generated later. When a predetermined key press event is received, the selected figure list is checked to check that the figure selected is four points. If OK, a straight line connecting these four points in sequence is generated. However, when a line segment connecting two points for which a line is to be generated already exists, it is shared without being newly created.
(In the case of FIG. 26, such a line segment does not exist.) It is premised that the square plane creation menu is selected to enter the square plane creation mode before the plane is created. (When selecting a point, it is not necessary to be in the quadrangular surface creation mode.) Similarly, the same thing is repeated for each set of four points at the lower left, lower right and upper right. In this case, line sharing occurs at the boundary of the faces. The surface creation ends when the ESC key is pressed or another graphic creation menu is selected.

The process of generating a square surface is as follows.・ CMdlDot * pDots [4]; Array holding 4 selected points ・ CMdlLine * pLines [4]; Array holding 4 face boundary lines Check that 4 points are held in the figure selection list, If OK, the elements of the list are sequentially fetched and stored in pDots. Create four closed border lines from the selected four points. However, if a line segment is already connected between two points, that line segment is reused.・ Repeat the following process from i = 0 to 3. {If pDots [i] .m_nCount is greater than 0 and pDots [(i +
1) If% 4] .m_nCount is greater than 0, execute the following {pLines [i] =
SerchLine (pDots [i], pDots [i + 1% 4]); if pLines [i]
If is not null, continue; ie, from the previously created line group
Find the line segment connecting pDots [i] and pDots [(i + 1)% 4]} pLines [i] = new CMdlLine; pLines [i] → m_pParentCoordinate = pt3DCursor. m_pPa
rentCoordinate; pLines [i] → m_pDot [0] = pDots [i]; Store endpoint pointers pLines [i] → m_pDot [1] = pDots [i + 1% 4]; Increment point reference count pLines [i] → m_pDot [0] → m_nCount ++; pLines [i] → m_pDot [1] → m_nCount ++; Calculate and set the control vector so that it becomes a straight line pLines [i] → m_Vect [0] = calculated vector; pLines [i] → m_Vect [1] = Calculated vector; Initialize control vector bias to 0 vector pLines [i] → m_Cnt_ref [0] .x = 0; pLines [i] → m_Cnt_ref [0] .y = 0; pLines [i ] → m_Cnt_ref [0] .z = 0; pLines [i] → m_Cnt_ref [1] .x = 0; pLines [i] → m_Cnt_ref [1] .y = 0; pLines [i] → m_Cnt_ref [1] .z = 0;}

Hereinafter, one quadrangular surface whose boundary is the four line segments created above is generated.・ CMdl4patch * pNewPatch = new CMdl4patch; ・ pNewPatch → m_pDot = pDots; Stores the vertex pointer ・ pNewPatch → m_pLine = pLines; Stores the boundary pointer ・ pNewPatch → m_pParentCoordinate = pt3DCursor. M_p
ParentCoordinate; Set in-plane control point vector and bias to 0 vector ・ for i = 0 to 3 do begin pNewPatch → m_Vect [i] .x = 0; pNewPatch → m_Vect [i] .y = 0; pNewPatch → m_Vect [i ] .z = 0; pNewPatch → m_Cnt_ref [i] .x = 0; pNewPatch → m_Cnt_ref [i] .y = 0; pNewPatch → m_Cnt_ref [i] .z = 0; Increment boundary reference count pNewPatch → m_pLine [ i] .m_nCount ++; end; In FIG. 27, the four points at the upper right are selected to generate a surface. When a predetermined key is pressed here, a surface is created in the upper right as shown in FIG. The next figure 29 is a view of the four surfaces that were finally made from diagonally above.

(3) Upper left surface (to be called surface 3)
8 points are created as child figures on the top First, as shown in FIG. 30, the upper left face (face 3) is selected. This is the surface that will become the figure of the parent turtle of the point that will be created from now.
(If the mouse pointer is near the center of the surface when the mouse is left-clicked, that surface is selected.) When the child figure creation menu is selected in this state, the cursor is moved to the center of the selected surface as shown in Fig. 31. Is moved and displayed. After that, as the mouse cursor is moved up, down, left, and right, the area coordinates on the parent figure are updated each time the move event is received. Along with this, the coordinate value of the three-dimensional coordinate system is calculated from the area coordinate system by the mapping formula of the surface, converted into screen coordinates, and the cursor is displayed at a new position. (When the OpenGL library is used, the conversion from the three-dimensional coordinate system to the screen coordinates is performed by OpenGL.) FIG. 32 shows a state in which the mouse cursor is moved diagonally to the upper left.

The area coordinates of the parent figure are updated in the following procedure. First, in order to hold the area coordinates on the parent figure, the following area coordinate storage variables (actually used as CAD points of the present invention for later use in point generation) are prepared.・ CMdlDot pt3DCursor; Current three-dimensional cursor position storage variable In this case, the parent turtle figure is a quadrilateral, so first of all, in the center of the quadrilateral, the area coordinates are (αβγδ) = (1 / 4,1 / 4, The initial setting is 1/4, 1/4). Actually, the area coordinates are uniquely determined by two independent variables, so if this is set to (u, v), this is updated while holding it in the variable ptParentCoorParam.・ U = v = 1/2; ・ pt3DCursor.m_pParentRelation = Pointer pointing to the selected parent shape ・ pt3DCursor.m_Ab.x = u; pt3DCursor.m_Ab.x = v; ・ pt3DCursor.m_Ab_Ref.x = 0; From parent The offset of is set to 0 vector. ・ Pt3DCursor.m_Ab_Ref.y = 0; ・ pt3DCursor.m_Ab_Ref.z = 0; When the child figure creation menu is selected, it is first initialized in this way. The relationship between the actual area coordinates and (u, v) is as follows for a square surface. α = 1-u-v + γ β = u-γ γ = u * v δ = v-γ With this relation, the area coordinate system can be obtained at any time.

Since the amount of movement of the mouse pointer is too large from the scale of area coordinates, the value obtained by multiplying the amount of movement of the mouse pointer by a small coefficient is (u,
v) is being updated. Each time the mouse pointer change event is received from the window system, the parameters (u, v) are updated as follows.・ U = ptParentCoorParam.x; v = ptParentCoorPara
mx; ・ u = u + 0.001 * Δmx; v = v + 0.001 * Δmy; ・ ptParentCoorParam.x = u; ptParentCoorParam.x =
v; where Δmx and Δmy are the movement amounts of the mouse in the x and y directions. (The sign may be reversed depending on the coordinate system of the device.) In this way, the area coordinates on the parent turtle figure change sequentially. The cursor is updated by (u,
After calculating the area coordinates (αβγδ) from v), it is mapped to the three-dimensional space using the mapping formula of the quadrangular surface and then converted to the screen coordinate system to update the display position. When the OpenGL library is used, the process of converting to the final screen coordinate system and displaying it is left to OpenGL. As an application, it will be an image in which a crosshair cursor is directly drawn in the three-dimensional space.

When the event of the left button down (press) of the mouse is received, as shown by the white dot in the upper left of FIG. 33,
A point as a child figure is generated at the area coordinate position determined by the parent turtle figure coordinate parameter at that time. At this point, a new point is created on the parent turtle figure by copying the current 3D cursor information as follows.・ CmdlDot * pNewDot = new CMdlDot; ・ pNewDot → m_Ab = pt3DCursor.m_Ab; ・ pNewDot → m_AbRef = pt3DCursor.m_AbRef; ・ pNewDot → m_pParentReration = pt3DCursor.
ntReration; ・ pNewDot → m_pParentCoordinate = pt3DCursor.m_pPa
rentCoordinate; The point generated in this way is registered as a member of the current part (active part) and also displayed in the drawing figure list. In the embodiment, 8 points are finally created as shown in FIG. FIG. 35 is a view of the completed state from oblique information. As shown in FIG. 36, since the offset vector of each point from the parent plane is a 0 vector, it can be seen that it sticks to the parent plane.

(4) Eight points (child figure) created on the surface 3
The following describes the procedure for creating five square faces whose vertexes are the points created in (3) above. The operation of the operator is exactly the same as that described in (2) above. (Refer to FIG. 37) When a predetermined key is pressed in this state, a surface is created as shown in FIG. This is exactly the same as (2) above,
The only difference is that the resulting surface is a child surface of the same parent as the selected vertex. In other words, the in-plane control point vector is calculated and set so as to ride on the same plane as the boundary line. Figure 3 shows the result of creating the other four sides in the same procedure.
It is 9. FIG. 40 is viewed from diagonally above.

A procedure for generating a face as a child face of the same figure when the four vertices are children of the same figure (square surface in this case) will be described below.・ CMdlDot * pDots [4]; Array holding 4 selected points ・ CMdlLine * pLines [4]; Array holding 4 face boundary lines Check that 4 points are held in the figure selection list, If OK, the elements of the list are sequentially fetched and stored in pDots. At this time, it is checked whether all points have the same parent, and if they are different parents, the same processing as the above (2) is performed.
If you have the same parent, follow the steps below to create a new face as a child face of the figure. Create four closed border lines from the selected four points. However, if a line segment is already connected between two points, that line segment is reused. In this case, the completed line segment is set by calculating the control vector so as to ride on the parent figure.・ Repeat the following process from i = 0 to 3. {If pDots [i] .m_nCount is greater than 0 and pDots [i + 1%
4]. If m_nCount is greater than 0, execute the following process {pLines
[i] = SerchLine (pDots [i], pDots [i + 1% 4], pDots [i] → m_
pParentRelation); If pLines [i] is not null, continue; that is, pDots [i] and pDots [(i
+1)% 4] is connected and the line segment that rides on the same parent figure is searched} pLines [i] = new CMdlLine; pLines [i] → m_pParentCoordinate = pt3DCursor. M_pPa
rentCoordinate; pLines [i] → m_pParentRelation = pDots [0] → m_pParen
tRelation; pLines [i] → m_pDot [0] = pDots [i]; Store endpoint pointers pLines [i] → m_pDot [1] = pDots [i + 1% 4]; Increment point reference count pLines [i] → m_pDot [0] → m_nCount ++; pLines [i] → m_pDot [1] → m_nCount ++; Calculate and set the control vector so that it becomes a curve that rides on the parent turtle pLines [i] → m_Vect [0] = calculated vector; pLines [i] → m_Vect [1] = Calculated vector; Initialize control vector bias to 0 vector pLines [i] → m_Cnt_ref [0] .x = 0; pLines [i] → m_Cnt_ref [0] .y = 0 ; pLines [i] → m_Cnt_ref [0] .z = 0; pLines [i] → m_Cnt_ref [1] .x = 0; pLines [i] → m_Cnt_ref [1] .y = 0; pLines [i] → m_Cnt_ref [ 1] .z = 0;}

Hereinafter, using the four line segments created above as boundaries, one square surface riding on the same parent is generated.・ CMdl4patch * pNewPatch = new CMdl4patch; ・ pNewPatch → m_pDot = pDots; Stores vertex pointers ・ pNewPatch → m_pLine = pLines; Stores boundary pointers ・ pNewPatch → m_pParentCoordinate = pt3DCursor. M_p
ParentCoordinate; ・ pLines [i] → m_pParentRelation = pDots [0] → m_pPar
entRelation; Calculate in-plane control point vector so as to ride on the parent plane.・ For i = 0 to 3 do begin Set the in-plane control point vector to the calculated value pNewPatch → m_Vect [i] = Calculated vector of in-plane control point i; end; ・ for i = 0 to 3 do begin : In-plane control point bias is set to 0 vector pNewPatch → m_Cnt_ref [i] .x = 0; pNewPatch → m_Cnt_ref [i] .y = 0; pNewPatch → m_Cnt_ref [i] .z = 0; Boundary line reference count Increment pNewPatch → m_pLine [i] .m_nCount ++; end; As a flow, the difference from (2) above is that the control vectors of the boundary line and the surface itself are calculated so as to ride on the parent surface, and the parent turtle shape Is to set a pointer to.
FIG. 41 is a rendering of the finished state.

(5) Lifting of the child surface (center surface of the five child surfaces) Next, processing for selecting one child surface in the center of the child surfaces created in (4) above and lifting in the Z direction Will be described.
FIG. 42 shows a display in which a point to be lifted is selected. In FIG. 42, the four vertices of the child face in the middle are selected. Although the vertices are selected in FIG. 43, the same is true when the entire center plane is selected. Here, when the move menu is selected or a predetermined key is pressed, the selected point or vertex of the surface is moved by an amount determined by moving the mouse. (It is also possible to specify the offset by key input). Figure 4
4 is a creation example, which is a result of dragging the mouse pointer while pressing the Shift key and the left mouse button. If the mouse is dragged while the Shift key is pressed, it is treated as movement in the Z-axis direction of the current coordinate system.

In this case, the information of the surface itself, that is, the in-plane control point vector and the in-plane control point vector bias are not changed at all, and only the offset vector for the vertex parent is changed. In addition, the boundary information, that is, the control vector and the control vector bias are not changed at all. This is a result of not deforming the riding parent, and when the parent surface is deformed by some influence as in (5) described below, the control vector of the child figure is changed. For the selected point, only the offset vector from the parent figure is changed. Specifically, when pPoint is a pointer variable that points to one of the selected points: pPoint → m_Ab_Ref = pPoint → m_Ab_Ref + delta; This operation should be performed on all selected points. Here, delta is a vector representing the movement amount. In the case of mouse operation, it is a vector parallel to the XY plane or Z axis of the current coordinate system. (However, the former can be switched to the XZ plane or the YZ plane from the menu.) If a face is selected as described above, it is the same as if all the vertices of the face were selected. Is processed. FIG. 45 shows a rendering display of the result of the child surface Z-direction lift in the creation example. By the way, 3 when the point is a child figure of another figure
Regarding the mapping to the three-dimensional space, the coordinates in the three-dimensional space are calculated by the following calculation formula. First, the parent turtle graphic parameter of the point is taken out and set to (u, v).・ From u = pPoint → m_Ab.x; v = pPoint → m_Ab.y; (u, v), the line segment coordinates / area coordinates of the parent figure are calculated from the table in FIG. When the line segment coordinates / area coordinates obtained here are applied to the mapping equation of the parent figure, the coordinates when the obset vector is 0 are first obtained. When this position vector is P, it is finally mapped to three-dimensional coordinates by pPoint → m_Xyz = P + pPoint → m_Ab_Ref;

(6) Lifting of Surface 1 (Bottom Left Surface) in Z Direction Next, an operation of lifting one of the base surfaces first created after the previous item (5) in the Z axis direction will be described. In order to lift the surface, the surface to be lifted first or all the vertices of the surface is selected as in (5) of the previous section. FIG. 46 has been selected to lift the lower left surface. As described above, the selected figure is registered in the selected figure list. You can select multiple figures at the same time by holding down the Cntl key and selecting with the mouse. In this state, as in the case of (5) above, when the move menu is selected or a predetermined key is pressed at this timing, the selected point or the vertex of the surface is moved by the amount determined by the mouse movement. (It is also possible to specify the offset by key input).

FIG. 47 shows an example of creation and shows the result when the mouse pointer is dragged while the Shift key and the left mouse button are pressed. If the mouse is dragged while the Shift key is pressed, it is treated as movement in the Z-axis direction of the current coordinate system. In this case, the coordinate values of the vertices of the lifted surface are only changed. Specifically, when pPoint is a pointer variable pointing to one of the selected points, then: pPoint → m_Xyz = pPoint → m_Xyz + delta; This operation should be performed on all selected points. Here, delta is a vector representing the movement amount. In the case of mouse operation, it is a vector parallel to the XY plane or Z axis of the current coordinate system. (However, the former can be switched to the XZ plane or the YZ plane from the menu.) If a face is selected as described above, it is the same as if all the vertices of the face were selected. Is processed. In this case, since one surface is lifted, the coordinate value of the vertex or the end point of the line segment is only changed for the surface or line segment (curve) that is not a child of another figure. For the line segment or surface that is the child figure created in step 1, the control vector of the line segment and the in-plane control point vector of the child surface are recalculated and updated so as to follow the deformation of the parent surface. However, regarding the point, even if it is a child figure, the parameters (parent turtle figure parameter and offset vector) for the parent figure are not changed and remain the same. (Even in this case, the three-dimensional coordinate values calculated from the parameters are changed.) FIG. 48 shows the final shape obtained by the above operation by rendering.

(7) Control Vector Resizing of Boundary Line of Surface 2 (Bottom Right Surface) Next, in addition to the modification of (6) above, control of two boundary lines of the surface adjacent to the right of the lifted surface. Apply a transformation that increases the length of the vector and loosens the gradient of the sleeve. Since it is a vector change here, the control vector of the line segment should be selected. In this system, the mouse pointer is moved to around 1/3 of the line segment on the desired vector side and the left button is pressed to select. FIG. 49 shows the case where two vectors are selected at the same time. (Multiple selection is done while pressing the Cntl key) Two selected control vectors are displayed. In the created example, the vector is extended in the X-axis direction, but it can be changed in any direction. Also, the value can be changed directly by key input.

The vector can be changed in the movement menu as in the case of moving the point, but in this system, the deformation operation restricted to the X-axis direction deformation (resizing) is used as shown in FIG. 51 shows the result of expanding the vector in the X-axis direction (-direction), and FIG. 52 shows the result of rendering. The vector deformation amount is set in exactly the same manner as the point movement described above. Programmatically, the following processing is applied to the selected line segment vector. • pLine → m_Vect [?] = PLine → m_Vect [?] + Delta; This operation may be performed on the selected vector of the selected line segment. Here, delta is a vector representing the amount of movement (change amount), and pLine is a pointer that points to a line segment having the selected vector. When a vector is selected, a line segment having the vector is registered in the selected figure list, and a bit flag indicating which vector is selected is set in the control vector selection flag of the line segment. (Line segment m_nAttr_
(vsel field) In the creation example, only the selected vector of the line segment having the selected vector is changed by the attribute of the model data. In this case, since the surface having the child figure (surface 3) is not deformed at all, no change occurs in the child figure. However, when the control vector of the boundary line of the parent figure is selected and changed, the attribute value of the child figure is also changed as described above in (6).
In the case of FIG. 51, since the line segment concerned is an independent line segment having no parent, the control vector is directly updated like pLine → m_Vect [?] = PLine → m_Vect [?] + Delta; When minute is a child figure of another figure, ・ pLine → m_Cnt_ref [?] = PLine → m_Cnt_ref [?] + De
The bias vector is updated like lta ;, and the control vector is recalculated and set by the control vector calculation formula (Equation 8) [0036] when riding on the parent.

(8) Lifting of Boundary Line of Surface 3 (Parent Surface) in Z Direction Now, an operation of lifting one of the boundary lines of a surface (surface 3) having a child figure in the Z-axis direction will be described. . Figure 5
3 is a state in which the boundary line to be lifted is selected. As described above, also in this case, selecting two end points of the line segment at the same time has the same effect. When the move menu is selected at this timing, the operation for changing the coordinates of the two end points of the selected line segment is then started. Of course, since there is a movement menu by key input, it is possible to select it and perform offset movement. In the created example, the mouse pointer was dragged while pressing the Siht key to lift in the Z-axis direction. (FIG. 54) In this case, since the coordinate values of the two end points are updated and the shape of the parent surface is changed, the control vector of the child figure follows the deformation of the surface as described in (6). And will be updated. In this example, the two endpoints that move are independent points that have no parent, so the coordinate values of m_Xyz are updated directly. By the way, even with the modification so far, the control vector (in-plane control point vector and bias) of the parent surface itself is not changed as it is. Since this surface itself is not a child of other figures, it is not updated unless these control vectors are changed by directly specifying it. FIG. 55 is a rendering display of the transformation result up to this point.

<< Volume Holding Deformation Function >> As an option, the following volume holding deformation function may be provided. 1. Operation procedure 1-1. Designation of figure for volume retention deformation (volume leader drawing) (1) When a solid (tetrahedron, pentahedron, hexahedron) is targeted: -Create and select a solid. (If it has already been created, select it.) ・ Create a volume leader that points to the figure selected in the "Auxiliary" → "Volume leader" → "Create" menu. (2) When a solid surrounded by a plurality of faces is targeted: -Connecting faces to create a closed solid. (Not required if already created) ・ Select all the surface groups created above and create one group. -Create a volume leader line that points to the group created by "Auxiliary" → "Volume leader line" → "Create". The volume leader created here plays a role of indicating the entire figure that is deformed with a constant volume, and is used to display the volume at the same time. 1-2. Figure selection cancellation In the next 1-3, perform the operation in 1-1 to select the part (active element) that moves according to the operator's instruction and the driven element that moves by convergence calculation so as to keep the volume constant. Cancel the selected figure. 1-3. After selecting the driven element from the constituent elements of the figure indicated by the volume leader created in Specifying the driven element 1-1, "Volume holding deformation" →
Specify the driven element from the "Driven element"->"Create" menu. The "active element" is a point, line, or plane that the operator specifies and moves, and the "driven element" is
Points, lines and planes that move to cancel the volume change associated with the movement of the "active element". The "driven element" moves so as to expand and contract around the expansion / contraction origin specified in 1-6 below. 1-4. Canceling the figure selection In the next 1-5, the figure selection made by the operation 1-3 to select the active element is canceled. 1-5. Volume retention Select the volume leader of the figure you want to transform and then select the active element. At this time, if the constituent element of the active element is also the constituent element of the driven element, no processing is performed. 1-6. Designation of the origin of expansion / contraction of the driven element The location of the origin of expansion / contraction referred to when the driven element is moved is specified inside the solid body targeted for volume retention deformation specified in 1-1. 1-7. Volume retention deformation → Parallel (Resize) → [Arbitrary deformation direction] Transform with mouse, or Volume retention deformation → Parallel (Resize)
→ Use key input to transform by key input.

2. Internal operation 2-1. The volume of the figure to be subjected to volume retention deformation is calculated and stored in a predetermined variable.

2-2. The volume is calculated by moving the active element by the movement amount specified in 1-7. If the volume calculated in 2-3-2-2 is larger than the volume stored in 2-1, the driven element is moved by the reduction amount toward the expansion / contraction origin. On the contrary, if the volume is smaller than the volume stored in 2-1, the driven element is moved from the expansion / contraction origin in the opposite direction by the reduction amount. At this time, the volume is calculated for the target solid by the same method as in 2-1 and the difference with the volume stored in 2-1 is calculated, and the minute movement of the driven element is continued until the error falls below a predetermined allowable value. repeat. 2-4. If the ESC key is pressed or no other menu is selected, the process returns to 2-2 and waits for the designation of movement of the active element.

[0137]

As described above, according to the present invention, the surface element represents a wide area with one patch (one surface element) as compared with the surface processing method in the conventional CAD method. Will be possible. In addition, since all the surfaces are approximated by this patch, the handling of the surfaces can be made consistent. Therefore, the amount of data for describing a figure can be significantly reduced, and the load of computer arithmetic processing can be reduced. Further, according to the present invention, when the generated three-dimensional figure is defined by the point group having the spatial coordinates expressed in the cubic form, the tangents of the surface ends are continuously connected without increasing the number of operations more than necessary. The surfaces can be deformed while maintaining the relationship of mechanically joining, and a sufficiently practical three-dimensional graphic representation can be obtained. The effect is that the vector for controlling the differential continuity is retained without being affected by the movement of the points, so that the processing for deforming a curve or surface while maintaining the once set differential continuity is a simple point movement. Is reduced to processing. For example, it is possible to easily obtain the shape in the intermediate process from the final shape of the mold to the intermediate shape by moving the points from the original figure, without the need to make fine adjustments by simply moving the vertices of the surface or curve. Demonstrate power. Further, according to the present invention, it is possible to easily define the parent-child relationship of the graphic elements, and it is possible to easily move the child graphic along the curved surface of the parent graphic, for example. Since each graphic element has reference counting data, when deleting a certain element, refer to the reference counting data to check whether the element is a constituent factor of other elements. Therefore, it is possible to effectively determine whether or not deletion is possible. Furthermore, in an application example such as volume retention deformation, the point to be the driven element is moved by convergence calculation so that the volume becomes constant, but at this time also the differential continuity of the surface is maintained, and the die design for forging is maintained. Etc. are effective.

[Brief description of drawings]

FIG. 1 is a block diagram showing functions of a three-dimensional CAD system of the present invention.

FIG. 2 is a block diagram showing a hardware configuration of a CAD system of the present invention.

FIG. 3 is a flowchart showing the contents of point data generation processing of the present invention.

FIG. 4 is a flowchart showing the contents of line data generation processing of the present invention.

FIG. 5 is a flowchart showing the contents of line drawing processing of the present invention.

FIG. 6 is a flowchart showing the contents of surface drawing processing of the present invention.

FIG. 7 is an explanatory diagram showing a data structure of the system.

FIG. 8 is an explanatory diagram showing offsets from a parent turtle figure.

FIG. 9 is an explanatory diagram showing setting of parent turtle graphic parameters.

FIG. 10 is an explanatory diagram showing mapping of line segments.

FIG. 11 is an explanatory diagram showing a mapping of a line segment that is a child figure.

FIG. 12 is an explanatory diagram showing a process of making two surfaces continuous.

FIG. 13 is an explanatory diagram showing mapping of a triangular surface.

FIG. 14 is an explanatory diagram showing mapping of a triangular surface which is a child figure.

FIG. 15 is an explanatory diagram (2) showing a mapping of a triangular surface which is a child figure.

FIG. 16 is an explanatory diagram showing in-plane control points of a square surface.

FIG. 17 is an explanatory diagram (2) showing in-plane control points of a square surface.

FIG. 18 is an explanatory diagram showing a square surface of a child figure.

FIG. 19 is an explanatory diagram showing internal control points on a square surface of a child figure.

FIG. 20 is an explanatory diagram showing setting of parent turtle graphic parameters (a, b).

FIG. 21 is an explanatory diagram showing control points of a line segment of a child figure.

FIG. 22 is an explanatory diagram (2) showing a control point of a line segment of a child figure.

FIG. 23 is an explanatory diagram (1) showing a processing screen of a creation example.

FIG. 24 is an explanatory diagram (2) showing a processing screen of a creation example.

FIG. 25 is an explanatory diagram (3) illustrating a processing screen of a creation example.

FIG. 26 is an explanatory diagram (4) showing a processing screen of a creation example.

FIG. 27 is an explanatory diagram (5) showing a processing screen of a creation example.

FIG. 28 is an explanatory diagram (6) illustrating a processing screen of a creation example.

FIG. 29 is an explanatory diagram (7) showing a processing screen of a creation example.

FIG. 30 is an explanatory diagram (8) showing a processing screen of a creation example.

FIG. 31 is an explanatory diagram (9) showing a processing screen of a creation example.

FIG. 32 is an explanatory diagram (10) showing a processing screen of a creation example.

FIG. 33 is an explanatory diagram (11) showing a processing screen of a creation example.

FIG. 34 is an explanatory diagram (12) showing a processing screen of a creation example.

FIG. 35 is an explanatory diagram (13) showing a processing screen of a creation example.

FIG. 36 is an explanatory diagram (14) illustrating a processing screen of a creation example.

FIG. 37 is an explanatory diagram (15) showing a processing screen of a creation example.

FIG. 38 is an explanatory diagram (16) showing a processing screen of a creation example.

FIG. 39 is an explanatory diagram (17) showing a processing screen of a creation example.

FIG. 40 is an explanatory diagram (18) showing a processing screen of a creation example.

FIG. 41 is an explanatory diagram (19) showing a processing screen of a creation example.

FIG. 42 is an explanatory diagram (20) showing a processing screen of a creation example.

FIG. 43 is an explanatory diagram (21) showing a processing screen of a creation example.

FIG. 44 is an explanatory diagram (22) showing a processing screen of a creation example.

FIG. 45 is an explanatory diagram (23) showing a processing screen of a creation example.

FIG. 46 is an explanatory diagram (24) showing a processing screen of a creation example.

FIG. 47 is an explanatory diagram (25) showing a processing screen of a creation example.

FIG. 48 is an explanatory diagram (26) showing a processing screen of a creation example.

FIG. 49 is an explanatory diagram (27) showing a processing screen of a creation example.

FIG. 50 is an explanatory diagram (28) showing a processing screen of a creation example.

FIG. 51 is an explanatory diagram (29) showing a processing screen of a creation example.

FIG. 52 is an explanatory diagram (30) showing a processing screen of a creation example.

FIG. 53 is an explanatory diagram (31) showing a processing screen of a creation example.

FIG. 54 is an explanatory diagram (32) showing a processing screen of a creation example.

FIG. 55 is an explanatory diagram (33) showing a processing screen of a creation example.

FIG. 56 is an explanatory diagram showing area coordinate calculation of a parent figure.

[Explanation of symbols]

10 ... Operation analysis and processing execution means, 11 ... Point element generation means, 12 ... Line element generation means, 13 ... Surface element generation means, 1
4 ... 3D element generating means, 15 ... Point moving means, 16 ... Vector changing means, 17 ... Displaying means, 18 ... Data outputting means

   ─────────────────────────────────────────────────── ─── Continued front page    F term (reference) 5B046 AA05 BA01 CA04 DA08 FA12                       FA18 GA01 GA02 HA07                 5B050 AA04 BA09 BA18 CA07 EA28                       FA02 FA03 FA15                 5B080 AA06 AA14 AA15 BA08

Claims (5)

[Claims] 1. A point element setting means defined by coordinate information, a line element setting means defined by the point element and a Bezier parameter, and a surface element setting means defined by at least a plurality of the line elements. 3. A three-dimensional element setting means defined by the surface element, and three-dimensional generation means for connecting a plurality of the set elements to generate a desired three-dimensional figure.
Dimensional CAD system. 2. The three-dimensional CA according to claim 1, wherein the surface element is expressed by a total cubic form of area coordinate parameters whose coefficients are expressed by Bezier parameters.
D system. 3. The three-dimensional CAD system according to claim 1, wherein the element has reference counting data indicating how many other elements refer to the element. 4. The three-dimensional CAD system according to claim 1, further comprising a volume-constant deforming means for deforming a created figure having a constant volume. 5. A point element setting means defined by coordinate information, a line element setting means defined by the point element and a Bezier parameter, and a surface element setting means defined by at least a plurality of the line elements. A program of a three-dimensional CAD system for realizing the functions of the three-dimensional element setting unit defined by the surface element and the three-dimensional generation unit that connects a plurality of the set elements to generate a desired three-dimensional figure.