JP2000076489A - Curve deformation processing method and device therefor, storage medium storing curve deformation processing program, curved surface deformation processing method and device therefor and storage medium storing curved surface deformation processing program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To attain a smooth deformation processing by multiplying an original curve component element by coordinate conversion matrix, based on a calculated moved amount, to obtain a converted curve. SOLUTION: A mobile point P5 and a mobile vector A are defined and a curve R, the point P5 and the vector A (dx, dy, dz) are used for the deformation processing. The curve R is converted into the least number of component elements at the passing point P5. The converted segments S1 and S2 are moved at the point P5 in the direction and by a distance which are defined by the vector A for every tangent, and the segments S1 and S2 are deformed like the segments S11 and S22. The information on each control point o converted segments S1 and S2 and segments S11 and S22 is generated from a coordinate conversion matrix. The information on the moved control points are reflected on the control points of segments R1 to R10 forming an original curve R by means of the coordinate conversion matrix. Thus, a new curve R' is generated while the connection state of the original curve is preserved.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a curve deformation processing method suitable for an information processing apparatus utilizing a CAD / CAM system. Furthermore, the present invention relates to a curved surface deformation processing method and the like. More specifically, after transforming a curve or surface composed of multiple elements into multiple elements and transforming the whole by changing only one pass point, the result of the transformation operation is converted to the original curve or surface. Thus, a curved surface or curve deformed in a natural manner can be obtained while maintaining the original connection state of the curve or curved surface.

[0002]

2. Description of the Related Art In an information processing apparatus using a CAD (computer aided drawing) system or a CAM (computer aided manufacturing) system, Bezier (Bezier) is used as an expression method for creating a free curve or a free-form surface.
zier) Curves and Bezier surfaces are often used.

A curve created by giving (n + 1) control points is called an nth-order Bezier curve. A surface created by giving (n + 1) × (n + 1) control points is called an nth-order Bezier surface. Of these, a cubic Bezier curve is often used as the Bezier curve because of its easy control. For the same reason, a cubic Bezier surface represented by 4 × 4 control points is frequently used for the Bezier surface.

A cubic Bezier curve expressing a free curve using four control points is represented by four control points CP0 as shown in FIG.
When CP3 is given, the Bezier curve R is uniquely determined by giving a parameter (influence parameter) t (0 ≦ t ≦ 1). The cubic Bezier curve is represented by the following equation.

R (t) = (1-t) ³ P0 + 3t (1-t) ²
P1 + 3t ² here (1-t) P2 + t 3 P3, the control point P0~P3 is both position vector has a component of (x, y, z).

[0006] Of the control points CP0 to CP3, the point through which the curve passes may be called an end point (passing point). Therefore, as shown in FIG. 17, an end point composed of a plurality of control points, for example, P
By giving 0 to P6, a smooth free curve as shown in the figure can be created.

The minimum component curve formed by the two end points is called a segment, and is represented by (n + 1) × (n +
1) A curved surface (rectangle) of the minimum component created by giving control points is called a patch.

[0008]

When a free curve or a curved surface is created by using a cubic Bezier curve or a cubic Bezier surface, the created curve or curved surface may be deformed. For example, there is a case where the user wants to move the passing point P2 of the original curve toward the arrow as shown in FIG. 18 and deform the curve as shown by the broken line.

However, in most cases, the conventional minimum unit for performing curve deformation is a single segment. Therefore, as shown in FIG. 19, among the curves composed of a plurality of passing points P0 to P6, the passing points P1 and P4 are respectively set to P1 'and P1.
If you move it by 4 ', the curve may break,
Curve discontinuities may occur.

For example, since the passing point P1 is both an end point on the side of the end point P0 and a starting point on the side of the passing point P2, when the end point on the side of the passing point P2 is moved to the side of P1 ', as shown in FIG. Only the end point on the P2 side moves, and the curve is cut.

When the respective passing points of the passing points P3 and P5 are simultaneously moved, the segment R, which is the smallest component, is moved.
Since only 3 and R4 are affected, a discontinuity of the curve occurs.

As described above, in the related art, since local deformation is performed in units of segments, conventionally, the same amount of deformation is performed, or each passing point is manually deformed little by little to obtain the most natural deformation curve. I'm trying to get. Therefore, considerable skill and processing time are spent in this deformation processing.
Needless to say, since the deformation operation is manually performed according to an empirical rule, when the shape after the deformation is evaluated by an equal luminance line or the like, it is often not determined that the shape is satisfactory, in other words, a beautiful shape deformation.

[0013] A similar situation occurs for a Bezier surface. Of the Bezier surfaces described above, the cubic Bezier surface is
As shown in FIG. 20, a free-form surface (Bézier surface) is formed by connecting a large number of patches (minimum components) each including 16 control points CP0 to CP15.

Therefore, if the flat surface as shown in FIG. 21 is moved in the directions shown by arrows a and b by the amount shown by the arrows, the movement can be made by using a single passing point or by using two or more points. Depending on whether or not to move using a passing point, FIG.
It becomes a deformation like.

In the case of FIG. 22, since the left deformation can only perform local deformation of only the surrounding four patches including the passing point, how much influence is exerted on the other curved surfaces. Or I can't figure out if it should. In other words, not only the surrounding local patches including the pass point where the arrow a is placed but also the peripheral patches cannot be affected, in other words, smooth global deformation cannot be performed. Similarly, the deformation on the right side is the movement like the arrow b,
Only the end point moves, resulting in a discontinuous curved surface deformation.

As described above, conventionally, it takes a certain processing time to deform the entire curve or the entire curved surface (global deformation), and it is difficult to smoothly deform the target curve or curved surface easily. was there.

Accordingly, the present invention has been made to solve such a conventional problem, and provides a method of processing a curve or a curved surface, which enables smooth deformation processing, and a processing apparatus for them.

[0018]

According to a first aspect of the present invention, there is provided a curve deformation processing method for converting a plurality of curve elements constituting a curve into a minimum number of conversion elements. While transforming the minimum conversion element, the corresponding point on the modified minimum conversion element corresponding to the passing point through which the curve component passes is obtained, the moving amount of the passing point at the corresponding point is calculated, and the calculated By multiplying the movement amount by the coordinate transformation matrix of the original curve component, a curve after conversion is obtained.

In the curve deformation processing device according to the present invention, a conversion means for converting a plurality of curve components constituting a curve into a minimum conversion element, and a deformation means for deforming the converted minimum conversion element Calculating means for obtaining a corresponding point on the deformation minimal conversion element corresponding to a passing point through which the curve component passes, and calculating a moving amount of the passing point at the corresponding point; And a generation means for generating a converted curve by multiplying the curve component by a coordinate conversion matrix.

In the storage medium according to the present invention, a plurality of curve components forming a curve are converted into a minimum conversion element, and the converted minimum conversion element is deformed. A corresponding point on the minimum transformation element corresponding to the passing point to be passed is obtained, a movement amount and a rotation amount of the passing point at the corresponding point are calculated, and the calculated movement amount is coordinate-transformed to the original curve component. A program for curve transformation processing for obtaining a curve after conversion by multiplying by a matrix is stored.

[0021] In the curved surface deformation processing method according to the present invention, a plurality of curved surface constituent elements constituting a curved surface are converted into a minimum converted element, and the converted minimum converted element is deformed. A corresponding point on the transformation minimum transformation element corresponding to the passing point through which the element passes is calculated, a movement amount of the passing point at the corresponding point is calculated, and the calculated movement amount is converted to the original curved surface component by a coordinate conversion matrix. Is obtained by multiplying by .times..times..times..times..times..times.

According to a nineteenth aspect of the present invention, there is provided a curved surface transformation processing apparatus for converting a plurality of curved surface components constituting a curved surface into a minimum transformed element, and a transforming unit for transforming the converted minimal transformed element. Calculating means for obtaining a corresponding point on the minimum transformation element corresponding to the passing point through which the curved surface component passes, and calculating a moving amount of the passing point at the corresponding point; And a generating means for generating a converted curved surface by multiplying the curved surface component by a coordinate transformation matrix.

In the storage medium according to the present invention, a plurality of curved surface components constituting a curved surface are converted into a minimum transform element, and the converted minimum transform element is deformed. A corresponding point on the transformation minimum transformation element corresponding to the passing point to be passed is obtained, a movement amount and a rotation amount of the passage point at the corresponding point are calculated, and the calculated movement amount is coordinate-transformed to the original curved surface component. A curved surface deformation processing program for obtaining a converted curved surface by multiplying by a matrix is stored.

In the present invention, a curve and a plurality of constituent elements constituting the curve are converted into a minimum number of constituent elements and are associated with the original curve or surface while being deformed. In order to preserve the connection state, the movement amount at each passing point is added to all the passing points of the original curve or curved surface.

Since the transformation process is performed after converting a plurality of components into the minimum number of components, the calculation time can be reduced.
Since a new curve or curved surface is formed while associating with the original curve or curved surface, the connection state of the original curve or curved surface is deformed while being saved. As a result, the deformed curve or curved surface shape changes very naturally. That is, since the deformation processing can be performed smoothly, the global deformation can be processed in an extremely natural form.

Since these processes only need to provide a moving point and a moving vector and can be automatically processed thereafter, an excellent CA
A D system or a CAM system can be constructed, and a storage medium storing such processing program contents can be provided.

[0027]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, an embodiment of a method for deforming a curve or a curved surface according to the present invention, a deforming apparatus and a storage medium storing the contents of a process (1) will be described in detail with reference to the drawings. .

In the present invention, an nth-order Bezier curve and an nth-order Bezier curved surface can be applied as described above. However, in the following embodiment, smooth curves and curved surfaces can be created despite the easiest processing. A description will be given by taking a second-order Bezier curve and a third-order Bezier surface as examples.

FIG. 1 is a conceptual diagram of an essential part showing an embodiment in which the apparatus for processing curves and curved surfaces according to the present invention is applied to a CAD / CAM system. In other words, if this deformation processing device can be applied to curve deformation processing, it can also be applied to curved surface deformation processing, and it is a system that can be naturally applied to both types of deformation processing.

The CAD / CAM system 10 shown in FIG. 1 has a curve / curved surface deformation processing device 12. In the curve / curved surface deformation processing device 12, shape data representing a curve or a curved surface subjected to a deformation process in a state where the connection state of the original curve or the curved surface is stored is created, and the created shape data is used as a tool path creating device. At 14, it is converted into machining data for cutting.

The processing data is downloaded to, for example, a floppy disk (FD) 16, and the downloaded floppy disk 16 is set in the NC milling machine 18. The NC milling machine 18 drives an NC milling machine (not shown) or the like based on the processing data, and creates a product die represented by the shape data.

The curve / curved surface deformation processing device 12 has a curved / curved surface creation unit 20 having a central processing unit (CPU).
Therefore, the curve / curved surface creation unit 20 includes a CPU 22 and other memory means (ROM) for storing programs.
24, and a working memory means (RAM or hard disk device) 26 used when generating a curve or a curved surface. The memory means 24 stores various control programs such as a curve generation control program, a curved surface generation control program, and the like necessary for smoothly globally deforming a curve or a curved surface.

The curve / curved surface creating section 20 is provided with an input means for giving an instruction for performing a deformation process on a curve or a curved surface. In this example, dial input means 30, mouse input means 32, and numerical input means 34 using a keyboard.
Can be used arbitrarily.

Here, when a free curve or the like is generated, it is known that a natural connection can be realized by using a part (segment) of a parabola as a newly generated curve. As is well known, the parabola skillfully utilizes the property that the curvature changes smoothly and the curvature monotonously decreases as the distance from the vertex of the parabola increases.

For forming a curve using a part of such a parabola, for example, a standard parabola (default parabola) displayed in advance on the screen may be used. As parameters for performing a transformation operation on the parabola, four parameters are provided: a start point and an end point for determining a segment of a part of the parabola, and a tangential contraction and a parabolic contraction for determining the shape of the parabola. An arbitrary curve is generated by controlling these parameters independently.

Therefore, the dial input means 30 has four dials 30a to 30d for controlling respective parameters.
30d are provided. When the mouse input unit 32 is used, parameter control is performed using auxiliary points (markers) for controlling each parameter displayed on a parabola of the screen. When the keyboard 34 is used, a numerical value is directly input for each parameter.

A display unit 36 for monitoring is connected to the curve / curved surface generation unit 20, and a curve or a curved surface is generated using the curve or parabola displayed on the display unit 36.
As the display unit 36, a CRT, a liquid crystal display element, or the like can be used.

The shape data created by the curve / surface generator 20 is supplied to the tool path generator 14 described above and converted into machining data. The curve / surface generator 20 further includes a disk drive 38. In addition to being able to download to a connected and mounted disk (magnetic disk, optical disk, etc.), a program for creating a curve or a program for creating a curved surface stored in the memory means 24 can be downloaded. ing. Thus, the control program can be installed in another CAD / CAM system or the like using the downloaded floppy disk.

Now, an embodiment of a procedure for generating a free curve or the like using the curve / curved surface deformation processing apparatus 12 configured as described above will be described in detail with reference to the flowchart of FIG. 2 and FIGS. 3 and 4, respectively. explain.

FIG. 2 is a flowchart used in the curve deformation processing. A curve R to be deformed is displayed on the screen as shown in FIG. 3A. The curve R is generated by a cubic Bezier curve. In this example, the curve R is an example composed of ten segments R1 to R10.

On the other hand, as shown in FIG. 3B, a point to be moved among a plurality of passing points P0 to P10 and a moving direction and a moving distance, that is, a moving vector are designated. In the example of the figure, P5 is given as a moving point, and A is given as a moving vector. Therefore, first, the curve R, the moving point P5, and the moving vector A (dx, dy, dz) are given for the deformation processing (step 42 in FIG. 2).

The above is the information given. After this,
This is a deformation processing method according to the present invention. First, the curve R is converted into the minimum number of components at the passing point P5 (step 4).
4). In this example, it is divided into two parts with the passing point P5 being the moving point therebetween, and between the passing points P0 and P5 and the passing points P5 and P10.
Each segment is one segment (approximate segment) S
1 and S2 (see FIG. 4A).

The following three conversion methods are conceivable. α. A straight line connecting two points. β. A curve that preserves the tangent directions of two points. γ. A curve that approximates the shape of a segment.

In this embodiment, the conversion method of (β) is adopted for reasons such as the naturalness of the shape after deformation and the high calculation speed. Two internal control points for approximating with a cubic Bezier curve are determined based on the respective tangent directions and lengths at the start point P0 and the end point P10 in the curve R. This determines the degree of bending of the segments S1 and S2. Therefore, for example, the segment S as shown in FIG.
1, S2 are generated.

The degree of bending of the segments S1 and S2 is determined by the length of the tangent line. In this example, the length of the tangent is selected to be 1/3 of the distance between the start point and the end point.

Subsequently, the converted segments S1 and S2 are moved by the direction and the distance given by the vector A together with the tangent at the moving point P5 to transform the two segments S1 and S2 into segments S11 and S22 ( Step 46). FIG. 4B shows the deformed segments S11 and S22.

Next, the two converted segments S1,
From S2 and S11, S22, information on each control point is generated from the coordinate transformation matrix (step 48).
Using this coordinate transformation matrix, information on the moved control point is reflected on the control points of the segments R1 to R10 constituting the original curve R. As a result, the curve R is deformed while maintaining the connection state of the original curve, and a new curve R '(segments R0' to R10 ') as shown by the broken line in FIG. 4B can be generated (step 50).

As described above, at each passing point of the curve R ',
By adding the information (difference information) of the control points of the conversion segments S1, S2 and S11, S22, the entire curve R can be deformed.

Two segments S1, S2 and S1
1, the conversion method to S22 gives only the tangent direction at each passing point, so the length of the tangent is free. It goes without saying that the shape of the entire curve R '(the shape of global deformation) changes depending on the length of the tangent line. The data generated in this way is used as curve shape data.

When a deformation operation is performed while converting a plurality of constituent elements into the minimum number of constituent elements, global deformation processing for simultaneously deforming the entire curve, instead of local deformation processing, can be automatically realized. .

Next, FIGS. 3 and 4 will be described in detail with reference to FIGS. For convenience of explanation, the curve to be handled is a simple single-peak curve C as shown in FIG.
This curve C has four cubic Bezier curves (segments) R
1, R2, R3, and R4. A method of generating a new curve when the passing point P2 of the curve C is moved to the vector A will be described.

This new curve is generated as follows, approximating the minimum number of segments.

First, control points constituting the segments R1 to R4 are represented as shown in FIG. Where CP0 (R1) -C
P3 (R1) is a control point when the segment R1 is generated, and similarly, CP0 (R2) to CP3 (R2) are control points of the segment R2, and CP0 (R3) to CP3
(R3) and CP0 (R4) to CP3 (R4) represent control points for the segments R3 and R4, respectively.

The cubic Bezier curve of each of the segments R1 to R4 can be expressed as follows. R1 (t) = (1-t) ³・ CP0 (R1) +3 (1-t) ² t ・ CP1 (R1) +3 (1-t) t ²・ CP2 (R1) + t ³・ CP3 ( R1) R2 (t) = (1-t) ³・ CP0 (R2) +3 (1-t) ² t ・ CP1 (R2) +3 (1-t) t ²・ CP2 (R2) + t ³・CP3 (R2) R3 (t) = (1-t) ³・ CP0 (R3) +3 (1-t) ² t ・ CP1 (R3) +3 (1-t) t ²・ CP2 (R3) + t ³・ CP3 (R3) R4 (t) = (1-t) ³・ CP0 (R4) +3 (1-t) ² t ・ CP1 (R4) +3 (1-t) t ²・ CP2 (R4) + t ³・ CP3 (R4)

The moving point is the control point P2. The approximate segments S1 and S2 (shown by broken lines) passing through the control point P2 as shown in FIG. 5 are generated. That is, a first approximate segment S1 having a start point P0 and an end point P2 is generated, and a second approximate segment S2 having a start point P2 and an end point P4 is similarly generated.

To explain the first approximate segment S1, as shown in FIG. 6, the tangent vector at the same point P0 of the curve C is used as the tangent vector passing through the control point P0, and the tangent vector of the curve C is used as the tangent vector passing through the control point P2. By using the tangent vectors at P2 respectively, new control points CP0 (S1) to CP3 (S1) as follows:
Is obtained.

CP0 (S1) = P0 CP1 (S1) = {CP1 (R1) −CP0 (R1)} · n + P0 CP2 (S1) = {CP3 (R2) −CP2 (R2)} · m + P2 CP3 (S1) = P2 Parameters n and m are 0 ≦ n, m ≦ 1

The curve shapes of the approximate segments S1 and S2 to be deformed change depending on how to take the values of the parameters n and m, and are used as parameters affecting the segments. In this example, n = 0.33 and m = 0.33. This is only an example.

These four new control points CP0 (S1)
ＣＰCP3 (S1) is used to generate a first approximate segment S1. In a similar manner, using the control points P2 and P4 as shown in FIG. 6, four new control points CP0 (S2)
= CP3 (S1) = P2, CP1 (S2), CP2 (S
2) From CP3 (S2) = P4, a second approximate segment S2 is generated.

With respect to the approximate segments S1 and S2 generated in this way, the control point P2 is moved by the vector A, and the segments S1 and S2 are changed to S1 'and S1 as shown in FIG.
Deformation (global deformation) as in 2 '.

A new control point moved by the vector A is defined as P
Assuming that the approximate segment S1 is the control point P0, P
Deform to pass through 2 '. Therefore, first, the control point P0 used when generating the approximate segment S1 is used as it is as the first control point P0 (= CP0 (S1 ′), and the second control point CP1 (S1 ′) is used as the first control point CP1 (S1 ′). Control point CP
1 (S1), only the length is different.

As the third control point CP2 (S1 '), a point obtained by translating the control point CP2 (S1) in the same direction as the vector A by the same length is used. The fourth control point is P2 '
It is. These new control points P0, CP1 (S1 '),
A third approximate segment S1 'is generated using CP2 (S1') and P2 '(see the solid line in FIG. 7). Therefore, the control points of the third approximate segment S1 'can be expressed as follows.

P2 ′ = P2 + A CP1 (S1 ′) = CP1 (S1) CP2 (S1 ′) = CP2 (S1) + A CP3 (S1 ′) = CP3 (S1) + A

Similarly, when the second approximate segment S2 is moved by the vector A, the fourth approximate segment S2 '
Are as follows. CP0 (S2 ') = CP0 (S2) + A = P2' CP1 (S2 ') = CP1 (S2) + A CP2 (S2') = CP2 (S2) CP3 (S2 ') = P4

Next, the first and second approximate segments S1,
Using S2 and the original four segments R1 to R4, position parameters t1 and t2 of these approximate segments S1 and S2 are obtained as shown in FIG. The position parameter t1 is a value at a point where a perpendicular is dropped from the control point P1 to the segment S1, and the position parameter t2 is a value at a point where a perpendicular is dropped from the control point P3 to the approximate segment S2. In the case of FIG. 8, t1 ≒ 0.48 (0 ≦ t1 ≦ 1) t2 ≒ 0.48 (0 ≦ t2 ≦ 1).

Using the position parameters t1 and t2, the approximate segments S1 and S2 are divided into two by De Castello's theorem (division theorem). Therefore, the first approximate segment S1 is composed of the first and second divided segments S11,
It is divided into S12.

Here, the first divided segment S11 is
As shown in FIG. 9, four control points CP0 (S11) = P0, C
P1 (S11), CP2 (S11), CP3 (S11)
= T1. Second divided segment S1
2 is CP0 (S12) = CP0 (S11), CP1
(S12), CP2 (S12), CP3 (S12) = P
Approximation by 2.

Similarly, the second approximate segment S2 is also divided into third and fourth segment segments S21 and S22 by the position parameter t2. The control point of the third segment S21 is “CP0 (S21) = P2, CP1 (S21), CP2 (S21), CP3 (S21) = t2”, and the control point of the fourth segment S22 is "CP0 (S22) = t2, CP1 (S22), CP2 (S22), CP3 (S22) = P4".

Similarly, for the third and fourth approximate segments S1 'and S2', the position parameter t
1 and t2, and split into two using de Castello's theorem. Therefore, the fifth, sixth, seventh, and eighth divided segments S11 ', S12', S21 ', S22' are respectively constituted by the following control points.

S11 ′: CP0 (S11 ′) = P0, CP1 (S11 ′) = CP1 (S11 ′), CP2 (S11 ′), CP3 (S11 ′) S12 ′: CP0 (S12 ′), CP1 (S12 ′) ), CP2 (S12 '), CP3 (S12') = P2 'S21': CP0 (S21 ') = P2', CP1 (S21 '), CP2 (S21'), CP3 (S21 ') S22': CP0 ( S22 '), CP1 (S22'), CP2 (S22 '), CP3 (S22') = P4

As described above, the eight divided segments (S1
1, S12, S21, S22) and (S11 ', S1
2 ′, S21 ′, S22 ′) are obtained by using the original curve C
This is for accurately obtaining the movement amounts of the four segments R1, R2, R3, and R4 constituting the above.

Next, each control point {CP} in the original curve C
0 (R1) to CP3 (R1)}, {CP0 (R2) to C
P3 (R2)}, {CP0 (R3) -CP3 (R3)}
And {CP0 (R4) to CP3 (R4)},
When reflecting the movement amounts of the corresponding control points of the divided segments S11 to S22 and S11 'to S22' by a calculation formula described later, when the original segment R1 is moved to the final segment R1 'as shown in FIG. The amount of movement is
The adjacent segment segments S11 and S11 shown in FIG.
The calculation is performed with reference to the control points 11 '.

Similarly, the new segment R2 'refers to the control points of the divided segments S12 and S12', the new segment R3 'refers to the control points of the divided segments S21 and S21', and the new segment R4 ' Reference is made to the control points of the divided segments S22 and S22 '.

Here, the amount of movement of each control point is the amount of rotation, expansion and contraction around the unit vector N at each control point, and the coordinate axis of the control point for calculation is returned to the final coordinate axis of the control point. It can be expressed by the amount of translation. Describing the segment R1, the movement amount of each control point is as follows.

CP0 (R1 ′) = M1a · CP0 (R1) CP1 (R1 ′) = M1a · M2a · M3a · CP1 (R1) CP2 (R1 ′) = M1b · M2b · M3b · CP2 (R1) CP3 (R1 ') = M1b · CP3 (R1) where M1a, M1b: a coordinate transformation matrix for translating a passing point (end point of a segment) M2a, M2b: a coordinate transformation matrix for giving a rotation around the control point P0 M3a, M3b is a coordinate transformation matrix that gives the amount of expansion (contraction) at the control point P0.

Here, assuming that the respective translation amounts with respect to the x, y, and z axes are 1, m, and n, the coordinate transformation matrices M1a and M1b for the translation are as follows.

[0077]

(Equation 1)

Further, unit vectors Na (u, v, w),
The coordinate transformation matrices M2a and M2b when rotated by θ about a straight line having the direction of Nb (u, v, w) as an axis can be expressed by the following equation (2).

[0079]

(Equation 2)

Then, a coordinate conversion matrix M representing expansion and contraction
3a and M3b are as follows.

[0081]

(Equation 3)

The movement amount of each control point with respect to the other segments R2, R3, R4 can be calculated in the same manner, and the final segments R2 ', R2 referred to in this manner can be calculated.
3 'and R4' are as shown in FIG. A curve R 'composed of segments R1' to R4 'shown in FIG.

In each of the above-described embodiments, the global deformation due to the rotation of the control tangent at the passing point has been described. However, the present invention is not limited to this. It is possible.

For the curved surface deformation, the entire curved surface can be deformed in the same manner as the curve deformation.

FIG. 11 is a flowchart used in the curve deformation processing. A curved surface Q to be deformed is displayed on the screen as shown in FIG. The curved surface Q is generated by a cubic Bezier curved surface, and the curved surface Q is configured by a plurality of continuous patches constituting the curved surface.

A movement point Px and a movement vector A are designated for this curved surface Q (step 62 in FIG. 11). The curved surface Q is converted into the minimum number of components at the moving point (passing point) Px (step 64). In this example, since the minimum number of components is four, the components are divided into four with the moving point Px interposed therebetween and converted into four approximate patches PB0 to PB3 (see FIG. 13).

In this conversion method, as in the case of the curve deformation, the conversion is performed using a cubic Bezier surface so as to be a surface in which the tangential directions of adjacent patches are preserved. The shape of the curved surface is determined by the parameter t of the cubic Bezier surface.

Next, by moving each patch by the direction and distance given by the vector A, the four approximate patches PB0 to PB0
B3 is deformed (step 66). FIG. 14 shows the deformed approximate patches PB0 'to PB3'.

Next, the converted four approximate patches PB
Information of each patch is generated from the coordinate transformation matrix from 0 'to PB3' (step 68). Using the coordinate transformation matrix, information on the moved control point is reflected on the control point of the patch PB constituting the original curved surface Q. As a result, the surface Q can be deformed while maintaining the connection state of the original surface, and a new surface Q ′ as shown in FIG. 15 can be generated (step 70).

Thus, at each passing point of the curved surface Q ',
By multiplying the information of the control points of the approximate patches PB0 'to PB3' (the coordinate transformation matrix indicating the difference information), the deformation operation of the entire curved surface Q can be performed at once.

The shape of the entire curved surface Q '(the shape of global deformation) changes according to the length of the tangent line, as in the case of the curve generation. The data generated in this way is used as curved surface shape data.

As described above, when a transformation operation is performed while converting a plurality of constituent elements into the minimum number of constituent elements, global deformation processing for simultaneously deforming the entire curved surface, instead of local deformation processing, can be automatically realized. .

As the type of deformation, in addition to the movement of the passing point, a deformation such as rotation, expansion and contraction of a tangent at the position of the passing point is also possible. This is similarly converted into two segments, the control side is rotated, expanded and contracted, and the like, and the difference is obtained and mapped.

[0094]

As described above, according to the present invention, a curve or a plurality of constituent elements constituting a curve is converted into a minimum number of constituent elements and is associated with an original curve or curved surface while being deformed. In addition, the amount of movement at each pass point is added to all the pass points of the original curve or surface in order to preserve the connection state of the original curve or surface.

According to this, since the transformation process is performed after converting a plurality of components into the minimum number of components, the calculation time can be reduced. Since a new curve or curved surface is formed while associating with the original curve or curved surface, the connection state of the original curve or curved surface is deformed while being saved. As a result, the deformed curve or curved surface shape changes very naturally. That is, since the deformation processing can be performed smoothly, the global deformation can be processed in an extremely natural form.

Since these processes only need to provide a moving point and a moving vector and can be automatically processed thereafter, an excellent CA
A D system or a CAM system can be constructed, and a storage medium storing such processing program contents can be provided.

[Brief description of the drawings]

FIG. 1 shows a curve / curved surface generating apparatus according to the present invention which is CAD / C.
1 is a system diagram of a main part showing an embodiment when applied to an AM system.

FIG. 2 is a flowchart showing an embodiment for describing an algorithm of a curve deformation process according to the present invention.

FIG. 3 is an explanatory diagram for a curve deformation process (part 1);

FIG. 4 is an explanatory diagram for a curve deformation process (part 1).

FIG. 5 is an explanatory diagram approximating two segments.

FIG. 6 is an explanatory diagram showing a relationship between approximate segments and control points at that time.

FIG. 7 is an explanatory diagram when an approximate segment is deformed.

FIG. 8 is a diagram illustrating a calculation example of a position parameter.

FIG. 9 is a diagram showing a relationship between a deformed approximate segment and a control point at that time.

FIG. 10 is a diagram showing a relationship between an original curve and a deformed curve.

FIG. 11 is a flowchart illustrating an embodiment of a curved surface deformation process according to the present invention.

FIG. 12 is a diagram illustrating a relationship between a plane configuration for curved surface deformation and a movement vector.

FIG. 13 is a diagram illustrating an example of conversion into an approximate patch.

FIG. 14 is a configuration diagram of a curved surface when an approximate patch is deformed.

FIG. 15 is a diagram showing a newly deformed curved surface.

FIG. 16 is an explanatory diagram of a cubic Bezier curve (part 1).

FIG. 17 is an explanatory diagram of a cubic Bezier curve (part 2).

FIG. 18 is a diagram illustrating a relationship between a cubic Bezier curve and a movement vector.

FIG. 19 is an explanatory diagram of deformation and cutting.

FIG. 20 is an explanatory diagram of a cubic Bezier surface.

FIG. 21 is a diagram illustrating an example of creating a curved surface using a patch.

FIG. 22 is a diagram showing an example of deformation and cutting of a conventional curved surface.

[Explanation of symbols]

10 ... system, 12 ... curve / curved surface generation device,
20: Curve / curved surface creation unit, 30: Dial input means, 32: Mouse input means, 34: Keyboard for numerical value input, 36: Display unit, 38: Disk drive device,

Claims (22)

[Claims] 1. A plurality of curve components constituting a curve are converted into a minimum conversion element, and the converted minimum conversion element is deformed, and the transformed minimum conversion element corresponding to a passing point through which the curve component passes. The corresponding point above is obtained, the moving amount of the passing point at the corresponding point is calculated, and the calculated moving amount is multiplied by the coordinate transformation matrix on the original curve component to obtain a converted curve. A curve deformation processing method characterized in that: 2. The curve deformation processing method according to claim 1, wherein said curve is created by an nth-order (n ≧ 2) Bezier curve. 3. A curve deformation processing method according to claim 1, wherein said n is a cubic Bezier curve in which n = 3. 4. The curve deformation processing method according to claim 1, wherein the curve component is a segment having a curve passing point as an end point. 5. In a global transformation process in which an end point of a plurality of curve components is set as a passing point and an arbitrary passing point is moved, a plurality of curves before and after being divided with the passing point interposed therebetween. 2. The curve deformation processing according to claim 1, wherein each of the constituent elements is converted into one minimum conversion element, and a deformation processing is performed on these two minimum conversion elements to obtain a curve after global deformation. Method. 6. The curve deformation processing method according to claim 1, wherein the moving amount of the passing point before and after the deformation is represented by a rotation amount, an expansion amount and a parallel movement amount at each of the passing points. 7. In converting into the minimum component,
2. The curve deformation processing method according to claim 1, wherein the degree of deformation of the curve of the minimum component can be adjusted by changing a value of a parameter for determining a control point used as the minimum component. . 8. A conversion means for converting a plurality of curve components constituting a curve into a minimum conversion element, a deformation means for deforming the converted minimum conversion element, and a conversion point corresponding to a passing point through which the curve component passes. Calculating means for calculating a corresponding point on the transformation minimum transformation element and calculating a movement amount of a passing point at the corresponding point; and converting the calculated movement amount by multiplying the original curve component by a coordinate transformation matrix. And a generating means for generating a subsequent curve. 9. It has a central processing unit, memory means for storing a curve deformation processing program and the like, and working memory means for deforming a curve and performing arithmetic processing on a curve component. 9. The curve deformation processing device according to claim 8, wherein: 10. A plurality of curve components forming a curve are converted into a minimum conversion component, the converted minimum conversion component is deformed, and the transformed minimum conversion component corresponding to a passing point through which the curve component passes. Curve deformation processing for obtaining the corresponding curve above, calculating the amount of movement of the passing point at the corresponding point, and multiplying the calculated amount of movement by the coordinate transformation matrix on the original curve component to obtain a converted curve. A storage medium characterized by storing an application program. 11. The storage medium according to claim 10, wherein said storage medium is a tape storage medium or a disk storage medium such as a magnetic disk or an optical disk. 12. Converting a plurality of curved surface components constituting a curved surface into a minimum transformed element, transforming the converted minimal transformed element, and modifying the transformed minimal transformed element corresponding to a passing point through which the curved surface component passes. The corresponding point above is obtained, the moving amount of the passing point at the corresponding point is calculated, and the calculated moving amount is multiplied by the coordinate transformation matrix on the original curved surface component to obtain a converted surface. A curved surface deformation processing method characterized by the above-mentioned. 13. The curved surface deformation processing method according to claim 12, wherein the curved surface is created by an nth-order (n ≧ 2) Bezier curved surface. 14. The curved surface deformation processing method according to claim 12, wherein said n is a cubic Bezier surface where n = 3. 15. The curved surface component is a segment having a curved surface passing point as an end point.
The curved surface deformation processing method described. 16. In a global deformation process performed by using end points of a plurality of curved surface components as passing points and moving any one of the passing points, a plurality of curved surfaces before and after being divided with the passing point therebetween. 13. The surface deformation processing according to claim 12, wherein each of the components is converted into one minimum conversion element, and the two minimum conversion elements are subjected to deformation processing to obtain a curved surface after global deformation. Method. 17. The curved surface deformation processing method according to claim 12, wherein the amount of movement of the passing point before and after the deformation is represented by the amount of rotation, the amount of expansion and contraction, and the amount of translation at each of the passing points. 18. The degree of deformation of a curved surface of the minimum component may be adjusted by changing a value of a parameter for determining a control point used as the minimum component in converting the minimum component into the minimum component. 13. The curved surface deformation processing method according to claim 12, wherein: 19. A conversion means for converting a plurality of curved surface components forming a curved surface into a minimum conversion element, a deformation means for deforming the converted minimum conversion element, and a passing point corresponding to a passing point through which the curved surface component passes. Calculating means for calculating a corresponding position on the transformation minimum transformation element and calculating a movement amount of a passing point at the corresponding position; and converting the calculated movement amount by multiplying the original curved surface component by a coordinate transformation matrix. And a generating means for generating a subsequent curved surface. 20. A computer having a central processing unit, memory means for storing a curved surface deformation processing program and the like, and working memory means for deforming a curved surface and performing arithmetic processing on a curved surface component. Claim 19
The curved surface deformation processing apparatus according to the above. 21. A plurality of curved surface components constituting a curved surface are converted into a minimally transformed component, the transformed minimally transformed component is transformed, and the transformed minimally transformed component corresponding to a passing point through which the curved surface component passes. The corresponding surface above is obtained, the movement amount and the rotation amount of the passing point at this corresponding position are calculated, and the calculated movement amount is multiplied by the coordinate transformation matrix on the original surface component to obtain a converted surface. A storage medium storing a curved surface deformation processing program. 22. The storage medium according to claim 21, wherein the storage medium is a tape storage medium or a disk storage medium such as a magnetic disk or an optical disk.