JPH10240326A - Free-form surface machining method, free-form surface machining device and recording medium therefor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To deform a curved surface while maintaining the smooth connection state of a patch inside a specified area by instructing the prescribed area of a free-form surface and dividing the free-form surface based on a specified area. SOLUTION: In this free-form surface machining method, the free-form surface SALL is re-divided corresponding to the specified area AR and the four patches S(u ,v)1 C, S(u ,v)2 D, S(u ,v)3 A and S(u ,v)4 B after re-division are just fitted inside the specified area AR. Thus, by moving only an end point group GP 10 inside the specified area AR, without generating an incompatible feeling in the connection state with the curved surface adjacent to the specified area AR, the deformation work of the curved surface desired by a designer is performed only inside the specified area AR. By the constitution, by newly allocating a control point to the respective re-divided patches, only a specified part desired by the designer is deformed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[Table of Contents] The present invention will be described in the following order.

BACKGROUND OF THE INVENTION Problems to be Solved by the Invention (FIG. 16) Means for Solving the Problems Embodiments of the Invention (1) Principle of Quadrilateral Patch Connection (FIGS. 1 and 2) (2) Group movement of control points (FIGS. 3 and 4) (3) Free-form surface processing (FIGS. 5 to 9) (4) Operation and effects of the embodiment (5) Other embodiments (FIGS. 10 to 10) 15) Effects of the invention

[0003]

TECHNICAL FIELD The present invention relates to a free-form surface processing method,
Regarding a free-form surface processing apparatus and its recording medium, for example, CA
D (computer aided design) or CAM (computer aided design)
It is suitable to be applied when processing a shape having a free-form surface in aided manufacturing).

[0004]

2. Description of the Related Art For example, when designing the shape of an object having a free-form surface using a CAD method (geometric mode)
In general, a designer specifies a plurality of points in a three-dimensional space through which a curved surface passes (this is called a node), and generates a boundary curve network connecting the specified nodes using a predetermined vector function. Thus, a curved surface represented by a so-called wire frame is created. Thus, a large number of framework spaces surrounded by boundary curves can be formed (such processing is hereinafter referred to as framework processing).

[0005] The boundary curve network formed by the framework processing itself represents a rough shape to be designed by the designer, and is formed by a predetermined vector function using the boundary curve surrounding each framework space. If a surface that can be represented can be interpolated, a free-form surface (which cannot be defined by a quadratic function) designed by the designer can be generated as a whole. Here, the curved surface formed in each frame space forms a basic element constituting the entire curved surface,
This is called a patch.

Conventionally, in this kind of CAD system,
As a vector function expressing a boundary curve network, for example, a Bezier equation, a B-spline (B-Spli)
The third-order tensor product of ne) is used, and is considered to be optimal for expressing a free-form surface having no special feature in shape, for example.

That is, in a free-form surface having no special feature in shape, when points given in space are projected on an xy plane, the projected points may be regularly arranged in a matrix. In many cases, when the number of projection points is represented by m × n, it is known that the framework space can be easily extended by using a quadrilateral patch represented by a cubic Bezier equation.

However, when the conventional mathematical expression is applied to a curved surface having a characteristic shape (for example, a curved surface having a greatly distorted shape), there is a difficulty in a method of connecting patches, and a high mathematical expression is required. Because it is necessary to perform arithmetic processing,
There has been a problem that the computation processing by the computer becomes complicated and enormous, and the computation time becomes long.

As a method of solving this problem, an internal control point that satisfies the condition of continuation of a tangent plane is obtained for a shared boundary of adjacent framework spaces, and a free-form surface determined by the internal control point is expressed. There has been proposed a method of forming a patch consisting of a free-form surface using a vector function (Japanese Patent Application Laid-Open No.
JP-A-62-135965, JP-A-62-151978, JP-A-62
-157968, JP-A-62-173569, JP-A-62-1
90564, JP-A-62-216076, JP-A-62-221
No. 073, JP-A-62-224863, JP-A-62-22628
No. 1).

[0010]

[Problems that the Invention is to Solve Yotsute this type of connection, for example, as shown in FIG. 16, the node P ₁₁ to P _{14,
P 21 ~P 24, P 31 ~P} 34, P 41 by the connexion framework to framework space to P _44, quadrilateral Patsuchi S _{(u, v) 1A} ~S
_{(u, v) 1c} , S _{(u, v) 2A to} S _{(u, v) 2c} , S _{(u, v) 3A to} S
_When it is intended to form a free-form surface as a whole by extending _{(u, v) 3c} , a vector function capable of designating coordinates by parameters u and v defined in a predetermined range for each patch is used. . Here, the characters “P” and “S” represent vectors, and hereinafter “vector P”, “vector S”, “vector n”, “vector a”, “vector b”, “vector c”, "Vector H" is simply expressed as "P", "S", "n", "a", "b",
They are described as “c” and “H”.

For example, the quadrangular patches S _{(u, v) 1A to} S
_{As (u, v) 3c} ,

(Equation 1) , A vector function S represented by a cubic Bezier equation
_{When (u, v)} is used, the definition area of each quadrilateral patch is defined by parameters u and v as

(Equation 2)

(Equation 3) A technique of limiting the area to 0 to 1 is used as shown in FIG.
_{As shown by (u, v) 2B} , the parameters are u = 0, u = 1,
In the boundary curve represented by v = 0 and v = 1, by determining an internal control point that satisfies the condition of continuation of a tangent plane with an adjacent patch, the adjacent patches are smoothly connected to each other. can go.

However, when the designer tries to form a free-form surface by executing a framework process using such a method, a plurality of quadrilateral patches S _{(u, v) 1A to} S _{(u, v) 1c} , S
Extremely deforming any part of the free-form surface consisting of _{(u, v) 2A to} S _{(u, v) 2c} and S _{(u, v) 3A to} S _{(u, v) 3c} from the original curved surface shape Without moving it in a predetermined direction by a small amount,
In addition, there are cases where it is desired to correct or confirm the shape by returning to the original shape.

In such a case, in the above-described free-form surface forming method, each of the quadrangular patches S _{(u, v) 1A to} S
_{(u, v) 1c} , S _{(u, v) 2A to} S _{(u, v) 2c} , S _{(u, v) 3A to} S
_{(u, v)} for _3c, node _{P 11 ~P 14, P 21 ~P} 24, P 31
ＰP ₃₄ , P ₄₁内部 P ₄₄ and the internal control points are moved in any direction to deform the curved surface shape for each patch, and again satisfy the condition of tangential plane continuity with the adjacent patch. By re-determining the internal control points, the adjacent patches must be smoothly connected to form a new curved surface, which requires an extremely complicated design work for the designer.

The present invention has been made in view of the above points, and provides a free-form surface processing method capable of smoothly changing an arbitrary area of the free-form surface while maintaining the atmosphere of the original shape by a simple operation. An object of the present invention is to propose a free-form surface processing apparatus and its recording medium.

[0015]

According to the present invention, a predetermined area of a free-form surface is designated, and the free-form surface is divided based on the designated area. A patch is formed, a node shared by a plurality of patches in the area and a control point around the node are moved in the same direction and by the same amount of movement, and a new plurality of patches are maintained while substantially maintaining the connection state of the plurality of patches. Form.

By forming a plurality of patches in the designated area, if a node shared by the plurality of patches and a control point around the node are moved in the same direction and by the same amount of movement, the patches in the designated area will be reciprocated. The connection state is kept smooth. In addition, by dividing and forming a plurality of patches so that a plurality of patches are exactly included in the designated area, moving only a node shared by the plurality of patches and a control point around the node causes a curved surface due to the movement. The deformation almost falls within the specified area.

[0017]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below in detail with reference to the drawings.

(1) Principle of Quadrilateral Patch Connection In this embodiment, the boundary curve representing the boundary of the quadrilateral frame space subjected to the frame processing, and the patch applied to each quadrilateral frame space are expressed by the following equations.

(Equation 4) A vector function S _{(u, v)} consisting of a cubic Bezier equation
Is expressed using. In equation (4), P ₍₀₀₎ is, as shown in FIG. 1, a curved surface formed between two adjacent frame spaces,
That is, a position representing the position of one end of a boundary (this is called a shared boundary) held by both the first quadrilateral patch S _{(u, v) 1} and the second quadrilateral patch S _{(u, v) 2.} And a position vector P _{(03) of} the other end, position vectors P _{(30) 1} , P _{(33) 1 of} the first patch S _{(u, v) 1} and a second patch S _{(u, v) 1.}
Together with the position vectors P _{(30) 2} and P _{(33) 2 of (u, v) 2} , they constitute a node specified in the framework processing.

Thus, the first and second patches S _{(u, v) 1}
And S _{(u, v) 2} are nodes P ₍₀₀₎ −P _{(30) 1} −P
_{(33) 1} -P ₍₀₃₎ -P ₍₀₀₎ and P ₍₀₀₎ -P _{(30) 2} -P
It can be seen that it is surrounded by four boundary curves of _{(33) 2} -P ₍₀₃₎ -P ₍₀₀₎ .

Of these boundary curves, nodes P ₍₀₀₎ and P
The boundary curve between ₍₀₃₎ constitutes a shared boundary COM, and defines a third-order Bezier equation by two control points P ₍₀₁₎ and P ₍₀₂₎ .

On the other hand, the boundary curves between the nodes P ₍₀₀₎ and P _{(30) 1 of} the first patch S _{(u, v) 1} , P _{(30) 1} and P _{(30) 1}
The boundary curve between _{(33) 1} and the boundary curve between P _{(33) 1} and P ₍₀₃₎ are two control points (P _{(10) 1} , P _{(20) 1} ), respectively.
(P _{(31) 1} , P _{(32) 1} ) and (P _{(23) 1} , P _{(13) 1} ). A boundary curve between the nodes P ₍₀₀₎ and P _{(30) 2 of} the second patch S _{(u, v) 2} , P _{(30) 2} and P
The boundary curve between _{(33) 2} and the boundary curve between P _{(33) 2} and P ₍₀₃₎ are two control points (P _{(10) 2} , P _{(20) 2} ), respectively.
(P _{(31) 2} , P _{(32) 2} ) and (P _{(23) 2} , P _{(13) 2} ).

In addition to this, the first and second patches S
The internal shapes of _{(u, v) 1} and S _{(u, v) 2} are represented by internal control points (P
_{(11) 1} , P _{(21) 1} , P _{(22) 1} , P _{(12) 1} ) and (P
_{(11) 2} , P _{(21) 2} , P _{(22) 2} , P _{(12) 2} ). These internal control points P _{(11) 1 to} P _{(12) 1} and P _{(11) 2 to} P _{(12) 2} are formed by quadrangular patches S _{(u, v) 1} and S _{(u, v) 1.}
It has the feature of controlling the internal shape of _{(u, v)} 2.Therefore, these internal control points represent the characteristics of the patch curved surface shape, and changing its position changes the patch curved surface shape. be able to.

In equation (4), E and F are shift operators in the u and v directions, and patches S _{(u, v) 1} and S
_For a control point P _{(i, j)} represented by a position vector on _{(u, v) 2} ,

(Equation 5)

(Equation 6) With the relationship

Here, u and v are parameters in the u and v directions, respectively.

(Equation 7) Varies between 0 and 1, as represented by. Thus, as shown in FIG. 1, the first and second patches S _{(u, v) 1} and S
_{For (u, v) 2} , a patch S _{(u, v)} using coordinates (u, v) taking the u-axis in the horizontal direction from the node P ₍₀₀₎ and the v-axis in the vertical direction. The coordinates on a free-form surface in ₁ and S _{(u, v) 2} can be represented.

Thus, the following equation obtained by expanding equation (4)

(Equation 8) A vector function that can be expressed by a mathematical expression of the product sum of 16 control points including 4 nodes and 12 control points (which are collectively called control points) and parameters u and v as shown in Thus, all the vector positions on the patches S _{(u, v) 1} and S _{(u, v) 2} and thus their shapes can be defined.

When the free-form surface is defined in this way, the _u of the first patch S _{(u, v) 1} is set at each point on the common boundary COM.
The tangent vector taken in the direction (ie, the direction traversing the shared boundary COM) is expressed by the equation (4) as 1 for the parameter u.
By performing partial partial differentiation,

(Equation 9) It is represented by Here, a ₀ is from the node P ₍₀₀₎ to the control point P
_{(10) The} control edge vector heading for ₁ is shown, and the shift operator F
And for the first patch S _{(u, v) 1} ,

(Equation 10) Can be used to represent the control edge vector a _j (j = 0, 1, 2, 3). Here, a ₁ is a control point P ₍₀₁₎ from the control point P ₍₀₁₎ of the shared boundary COM inside the _first patch S _{(u, v) 1.
(11)} shows the control side vector directed to _1, also, a ₂ denotes a control edge vector directed into the interior of the control points P _{(12) 1} from the control point P ₍₀₂₎ in the same manner.

Similarly, on the shared boundary COM, the tangent vector of the second patch S _{(u, v) 2 in} the u direction is:
By performing the first partial differentiation of the equation (4) with respect to the parameter u, the following equation is obtained.

[Equation 11] It is represented by Here, c ₀ indicates a control edge vector directed from the node P ₍₀₀₎ to the control point P _{(10) 2} of the second patch S _{(u, v) 2} , and together with the shift operator F, the second patch S _{( u, v) 2} ,

(Equation 12) Can be used to represent the control edge vector c _j (j = 0, 1, 2, 3). Here, c ₁ is a control point P ₍₀₁₎ from the control point P ₍₀₁₎ of the shared boundary COM inside the _second patch S _{(u, v) 2.
(11)} shows the control side vector directed to _2, c ₂ denotes a control edge vector directed into the interior of the control points P _{(12) 2} from the control point P in the same manner as _(02).

Further, the tangent vector in the v direction on the _first patch S _{(u, v) 1} side at each point on the shared boundary COM is:
By performing the first partial differentiation of the equation (4) with respect to the parameter v, the following equation is obtained.

(Equation 13) It is represented by Here, b ₁ is from the node P ₍₀₀₎ to the control point P
₍₀₁₎ indicates the control edge vector toward _(01), and for the shared boundary COM together with the shift operator E,

[Equation 14] Can be used to represent the control edge vector b _j (j = 1, 2, 3). Here, b ₂ indicates a control edge vector from the control point P ₍₀₁₎ to P ₍₀₂₎ , and b ₃ indicates a control edge vector from the control point P ₍₀₂₎ to the node P ₍₀₃₎ .

By the way, quadrilateral patches S _{(u, v) 1} and S _{(u, v) 1 are} placed in two adjacent frame spaces formed by the frame processing.
_{When (u, v) 2} is applied, the curved surface at the common boundary COM is not generally smooth. Therefore, two patches S _{(u, v) 1} and S _{(u, v) 2} having a shared boundary COM are defined as shared boundaries C
Each patch S so that the connection is smooth at the OM
Control points P _{(11) 1} and P _{(12) 1} inside _{(u, v) 1} and S _{(u, v) 2}
, P _{(11) 2} , and P _{(12) 2} are set again, and the free-form surface to be patched is interpolated again using these internal control points. By doing so, all patches can be smoothly connected over the entire curved surface framed by the boundary curve network, so that the external shapes of many objects can be expressed without becoming unnatural.

The smooth connection at the shared boundary COM is based on the control edge vector a that satisfies the condition of continuation of the tangent plane.
₀ ~a _3, is realized by determining the _{b 1 ~b 3, c 0 ~c} 3.

In order for the condition of continuation of the tangent plane to be satisfied at all points on the shared boundary COM, the first patch S
_{For (u, v) 1} , the connection vector in the u direction (represented by equation (9)) and _{u in} the second patch S _{(u, v) 2}
Directional tangent vector (represented by equation (11))
And the tangent vector of the first patch S _{(u, v) 1 in} the v direction (represented by equation (13)) needs to be on the same plane. Where

(Equation 15) The parameters may be reset so as to satisfy the condition (1).

Where λ (v), μ (v), ν (v) are
This is a scalar function,

(Equation 16)

[Equation 17]

(Equation 18) To be selected.

Therefore, the expressions (16) to (18) are replaced by (15)
At the same time, the equations (9), (11), and (13) are substituted into the equation (15). As a result, the unknowns κ ₁ , κ ₂ and η ₁ , η are set so that the equation (15) is established. If you select ₂ ,
Two patches S while satisfying the condition of tangent plane continuity
_{(u, v) 1} and S _{(u, v) 2} can be connected.

In practice, the expressions (9), (11) and (13) and the expressions (16) to (18) have a term of (1-v) and a term of v. (15) of the left and right ^{side, (1-v) 4,} v (1-v) 3, v 2 (1-
v) It can be expanded and arranged in the form of the sum of terms of ² , v ³ (1-v) and v ⁴ . Therefore, if the condition that the coefficient parts are equal to each other in each term of the expansion equation is established, the following equation is obtained.

[Equation 19]

(Equation 20)

(Equation 21)

(Equation 22)

(Equation 23) Is obtained, and the four unknowns κ ₁ , κ ₂ and η ₁ , η ₂ can be solved.

Here, the tangent plane refers to a plane formed by tangent vectors in the u direction and the v direction at each point of the common boundary COM, and accordingly, at each point of the common boundary COM, a patch S _(u, When the tangent planes of _{v) 1} and S _{(u, v) 2} are the same, the condition of continuation of the tangent plane is satisfied.

That is, an arbitrary point P on the shared boundary COM
The condition of continuation of the tangent plane for _(0v) is determined as shown in FIG. That Patsuchi S _{(u, v)} for _1, tangent vector H _a, and the direction along the shared boundary COM (i.e. v in a direction crossing the shared boundary COM (i.e. u direction)
Direction), the normal vector n ₁ of the tangent vector H _b is

(Equation 24) And for patch S _{(u, v) 2} , the shared boundary CO
The tangent vector H _c in the direction transverse to M and the shared boundary CO
Normal vector n of tangent vector _Hb along direction M
₂ is

(Equation 25) It is represented by

[0037] Under such conditions, in order that the tangent plane continuous, tangent vector H _a, H _b and H _c, H _b must be present on the same plane, so that the normal vector n ₁ and n ₂ will be in the same direction.

Where:

(Equation 26)

[Equation 27]

[Equation 28] It is.

(2) Group Movement of Control Points A part of a free-form surface composed of a plurality of patches connected smoothly so as to satisfy the condition of continuation of the tangent plane described above with reference to FIGS. Alternatively, a case of performing a concave process will be described.

FIG. 3 shows four patches S _{(u, v) 1} ,
S _{(u, v) 2} , S _{(u, v) 3,} and S _{(u, v) 4} are connected to each other smoothly to satisfy the condition of continuation of a tangent plane. Indicates _ALL . In such a smooth free-form surface, the node P _{(03) serving as} the center of the connection is 4
Two patches S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4}
Is shared by

Further, the first patch S _{(u, v) 1} and the second patch S _{(u, v) 2} are connected by a shared boundary COM1, whereby two controls for defining the shared boundary COM1 are provided. The points P ₍₀₁₎ and P ₍₀₂₎ are shared by the first patch S _{(u, v) 1} and the second patch S _{(u, v) 2} . Also, the second patch S _{(u, v) 2}
And the third patch S _{(u, v) 3} are connected by a shared boundary COM2, whereby two control points P _{(13) 23} and P _{(23) 23} defining the shared boundary COM2 are connected to the second boundary. Patch S
_{(u, v) 2} and the third patch S _{(u, v) 3} are shared. Further, the third patch S _{(u, v) 3} and the fourth patch S _{(u, v) 4} are connected by a shared boundary COM3, whereby two control points P _{( 04)} and P ₍₀₅₎ are shared by the third patch S _{(u, v) 3} and the fourth patch S _{(u, v) 4} . Also, the fourth patch S _{(u, v) 4} and the first patch S
_{(u, v) 1} are connected by a shared boundary COM4, and thus two control points P that define the shared boundary COM4.
_{(13) 14} and P _{(23) 14} are shared by the fourth patch S _{(u, v) 4} and the first patch S _{(u, v) 1} .

Here, in the first patch S _{(u, v) 1} , a shared node P which is a connection point with the other three patches is used.
₍₀₃₎ and three control points P ₍₀₂₎ , P _{(12) 1} and P
₍₁₃₎ It can be seen that it has ₁₄ . These four control points P ₍₀₃₎ , P ₍₀₂₎ , P _{(12) 1} and P _{(13) 14} are connected to the other three patches S _{(u, v) 2} , S _{(u, v) 3} and It is called an end point group element of the first patch S _{(u, v) 1} relating to connection with S _{(u, v) 4} .

In the second patch S _{(u, v) 2} ,
It can be seen that it has three control points P ₍₀₂₎ , P _{(12) 2} and P _{(13) 23} together with a shared node P ₍₀₃₎ which is a connection point with the other three patches. These four control points P
₍₀₃₎ , P ₍₀₂₎ , P _{(12) 2} and P _{(13) 23} are replaced by the other three patches S _{(u, v) 1} , S _{(u, v) 3} and S _{(u, v) 4} Is referred to as an end point group element of the second patch S _{(u, v) 2} relating to the connection with.

In the third patch S _{(u, v) 3} ,
It can be seen that it has _three control points P ₍₀₄₎ , P _{(14) 3} and P _{(13) 23} along with a shared node P ₍₀₃₎ which is a connection point with the other three patches. These four control points P
₍₀₃₎ , P ₍₀₄₎ , P _{(14) 3} and P _{(13) 23} are replaced by the other three patches S _{(u, v) 1} , S _{(u, v) 2} and S _{(u, v) 4} Is referred to as an end point group element of the third patch S _{(u, v) 3} relating to the connection with.

In the fourth patch S _{(u, v) 4} ,
It can be seen that it has three control points P ₍₀₄₎ , P _{(14) 4} and P _{(13) 14} together with a shared node P ₍₀₃₎ which is a connection point with the other three patches. These four control points P
₍₀₃₎ , P ₍₀₄₎ , P _{(14) 4} and P _{(13) 14} are replaced by the other three patches S _{(u, v) 1} , S _{(u, v) 2} and S _{(u, v) 3} Is referred to as an end point group element of the fourth patch S _{(u, v) 3} relating to the connection with.

Each of the patches S _{(u, v) 1} ,
All of the end point group elements of S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} (control points P ₍₀₃₎ , P ₍₀₂₎ , P _{(12) 2} , P _{( 13) 23} ,
P _{(14) 3} , P ₍₀₄₎ , P _{(14) 4} , P _{(13) 14} and P _{(12) 1} )
To the four patches S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S
_It is called an end point group GP1 relating to the connection of _{(u, v) 4} .

Here, the free-form surface S _ALL is viewed obliquely from FIG.
As shown in the figure, four patches S _{(u, v) 1} , S _{(u, v) 2} , S
_{Since (u, v) 3} and S _{(u, v) 4} are connected smoothly under the condition of continuation of the tangent plane, each patch at the node P ₍₀₃₎ shared by the four patches is used. S _{(u, v) 1} ,
The tangent planes of S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} form the same plane. That is, each normal vector n ₀₃ of the four patches S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4 at} the node P ₍₀₃₎ Will match. This normal vector n ₀₃ is the connection center (node P _{(03) of the} four patches S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4.} ) Represents the direction of the normal, which is the direction of the four patches S _{(u, v) 1} ,
S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} represent the features of the concavo-convex shape.

The four patches S _{(u, v) 1} , S _{(u, v) 2} , S
Let the portion where _{(u, v) 3} and S _{(u, v) 4} are connected (the area AR surrounded by the dashed line in FIG. 3) smoothly bulge upward while maintaining the atmosphere of the original shape. In this embodiment, all the control points P ₍₀₃₎ , P ₍₀₂₎ , P _{(12) 2} , P _{(13) 23} , P _{(14) 3} , P _(14)
(04) , P _{(14) 4} , P _{(13) 14} and P _{(12) 1} are moved by the same distance in the same direction as the normal vector n ₀₃ .

At this time, the patches S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S
Internal control point P on the connection center (node P ₍₀₃₎ ) side of _{(u, v) 4
(12) 1} , P _{(12) 2} , P _{(14) 3} and P _{(14) 4,} and control points P ₍₀₂₎ , P _{(13) 23} , and P ₍₁₃₎ defining common boundaries COM1, COM2, COM3, and COM4 _{By including (04)} and P _{(13) 14} and a node P ₍₀₃₎ serving as a connection center, a smooth connection state of each patch is maintained.

That is, in the first patch S _{(u, v) 1} , the node P ₍₀₃₎ , the control points P ₍₀₂₎ and P _{(13) 14} defining the shared boundaries COM1 and COM4, and the connection center ( Node P ₍₀₃₎ )
Connected to the other three patches S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} in the area AR by the internal control point P _{(12) 1} on the side Is defined, and in the second patch S _{(u, v) 2} , the node P ₍₀₃₎ and the shared boundaries COM1 and C
By the control points P ₍₀₂₎ and P _{(13) 23} defining the OM2 and the internal control point P _{(12) 2} on the connection vertex (node P ₍₀₃₎ ) side,
The other three patches S _{(u, v) 1} and S _{(u, v) 3} in the area AR
And the shape of the connecting portion with S _{(u, v) 4} is defined, and the third patch S _{(u, v) 3} defines the node P ₍₀₃₎ and the shared boundaries COM2 and COM3. The control points P _{(13) 23} and P ₍₀₄₎ and the internal control point P on the connection vertex (node P ₍₀₃₎ ) side
_{According to (14) 3} , the shape of the connection portion with the other three patches S _{(u, v) 1} , S _{(u, v) 2} and S _{(u, v) 4} in the area AR is defined. In addition, in the fourth patch S _{(u, v) 4} ,
A node P ₍₀₃₎ , control points P ₍₀₄₎ and P _{(13) 14} that define the shared boundaries COM3 and COM4, and an internal control point P _{(14) 4} on the connection vertex (node P ₍₀₃₎ ) side. Therefore, the area AR
The other three patches S _{(u, v) 1} , S _{(u, v) 2} and S
The shape of the connection part with _{(u, v) 3} is specified.

Therefore, all of these control points P ₍₀₃₎ , P ₍₀₂₎ , P _{(12) 2} , P
_{(13) 23} , P _{(14) 3} , P ₍₀₄₎ , P _{(14) 4} , P _{(13) 14} and P
_{(12) Even if 1} is moved by the same distance in the same direction (the direction of the normal vector n ₀₃ ), the connection portion maintains the continuation of the tangent plane.

Thus, each control point P ₍₀₃₎ , P ₍₀₂₎ , P _{(12) 2} , P _{(13) 23} , P _{(14) 3} , P ₍ point _{) of the} end point group GP1.
₍₀₄₎ , P _{(14) 4} , P _{(13) 14} and P _{(12) 1} are moved by the same distance in the direction of the normal vector n ₀₃ to form a new control point P
_{(03) NEW} , P _{(02) NEW} , P _{(12 ) 2NEW} , P _{(13) 23NEW} , P
_{(14) 3NEW} , P _{(04) NEW} , P _{(14) 4NEW} , P _{(13) 14NEW} and P _{(12) 1NEW} are generated, and a new patch S _{(u, v) 1NEW} is generated by the new control point. , S _{(u, v) 2NEW} , S _{(u, v) 3NEW} and S _{(u, v) 4NEW} to generate four patches S
_{(u, v) 1, S} (u, v) 2, S (u, v) 3 and S _{(u, v) 4,} the direction of the normal vector n ₀₃ while maintaining a smooth connection with each other,
That is, the four patches S _{(u, v) 1} , S _{(u, v) 2} , S
_{The (u, v) 3} and S _{(u, v) 4} are deformed so as to expand in a direction in which the shape characteristics in the connected area AR can be maintained.

(3) Free-Form Surface Processing In FIG. 5, reference numeral 10 denotes a free-form surface processing apparatus as a whole. When the designer operates the input device 14 including a mouse, a keyboard and the like to instruct the start of the free-form surface processing,
The CPU (central processing unit) 15 reads the free-form surface processing program and the free-form surface creation processing program used for this process from the hard disk 11 in accordance with the instruction, and stores them in the corresponding areas of the program storage memory 17. I do. Thus, the CPU 15 completes the start of the free-form surface processing. In addition, the designer reads various free-form surface data created by the free-form surface creation method from the hard disk 12 and writes the data to the memory 18 for storing the surface data.

In this state, the designer operates the input device 1
4 to start the free-form surface processing,
The PU 15 starts the free-form surface processing procedure shown in FIG. 6 based on the instruction. That is, the CPU 15 enters the free curved surface processing procedure from step SP0 in FIG. 6, reads out the curved surface data of the free curved surface to be processed in step SP1, and stores the curved surface data in the memory 16.

This curved surface data is stored in the graphics circuit 2
1 and is visually displayed on the monitor 22 via the display 1. In FIG. 3 described above,
At this time, the free-form surface selected by the designer and displayed on the display screen of the monitor 22 is shown. However, the control points P _{(00) to} P _{(36) 4} shown in FIG. 3 are only read from the memory 18 as data for controlling the curved surface, and the four patches S _(u) are displayed on the display screen of the monitor 22. _{, v) 1} ,
Only the free-form surface consisting of S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} is displayed.

The four patches S constituting the free-form surface
_{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} satisfy the condition of tangent plane continuity at the shared boundaries COM1, COM2, COM3 and COM4. Connected. The surface data representing the free-form surface is composed of three-dimensional data, and the surface image displayed on the monitor 22 can be rotated so as to be viewed from various angles. For example, as shown in FIG. 3, when the designer operates the input device 14 with the free-form surface viewed from the front, the display screen is displayed as if the free-form surface was viewed obliquely as shown in FIG. Can be rotated within.

In the state where the free-form surface is displayed as described above, the CPU 15 goes to step SP2 and waits for the designation of the processing area by the designer. Here, when the designer designates an area AR to be deformed in particular by operating the input device 14 while viewing the display image of the free-form surface, the CPU 15 determines the area AR based on the designated area data. A dividing line L representing AR is displayed on the display screen of the monitor 22. Thus, the designer can visually distinguish the designated area AR from other areas by the division line L.

As described above, when the area AR to be processed is specified, the CPU 15 proceeds to step SP3, and re-divides the patches constituting the free-form surface in accordance with the specified area AR. That is, when deforming only the designated area AR in the free-form surface (FIGS. 3 and 4) being processed at this time, the CPU 15 originally uses four patches S
_The free-form surface generated by connecting _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} is re-divided (hereinafter referred to as Subdivision). In this division method, division is performed such that patches after division are arranged in a matrix of m × n in a designated area AR, that is, an end point group (4) that forms a connection center of four patches as described above with reference to FIG. In the case of FIG. 3, division is performed such that at least one GP1) exists in the designated area AR. In the case of FIG. 3, the free-form surface before division (FIG. 3) has at least one end point group GP1 in the designated area AR, and thus the CPU 1
5 is a shared boundary COM1, COM in the designated area AR.
2. While using COM3 and COM4 as they are as the shared boundary, the outer shape of the area AR (partition line L) is divided so as to form the outer shapes of a plurality of patches in the area AR after the re-division.

As a result, as shown in FIG.
Are four patches S _{(u, v) 1C} , S in the designated area AR
_The division is performed so that _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B} exist. These four patches S _{(u, v) 1C} ,
The mutual boundaries of S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B} are the four patches S _{(u, v) 1} , S _{(u, v )} before subdivision. _{) 2} , S
The shared boundaries COM1, CO of _{(u, v) 3} and S _{(u, v) 4} (FIG. 3)
M2, COM3 and COM4, and the four patches S _{(u, v) 1C} , S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B} after subdivision. The outer shape is the shape of the specified area AR (partition line L)
Matches.

When the subdivision is performed in this manner, the CPU 1
In step SP4 (FIG. 6), the control point 5 re-assigns control points for each subdivided patch for the subdivided free-form surface. In this case, similar to the case described above with reference to FIG. 1, four internal control points for each patch,
Twelve control points (including four nodes) that define the outer shape of each patch are provided. When there are adjacent patches, the twelve control points that define the outer shape are shared control points that define a shared boundary with the adjacent patches, thereby keeping each patch connected. In this state, since the free-form surface before subdivision was originally generated by connecting patches so as to satisfy the condition of tangent plane continuity, the control points provided around each shared boundary are The assignment has been made so as to satisfy the continuous condition.

As shown in FIG. 7, four patches S _{(u, v) 1C} constituting the designated area AR in a state where control points are newly assigned to each patch of the subdivided free-form surface S _ALL. , S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B}
The end point group GP10 is formed around the node P ₍₀₃₎ which is the connection center of the end point GP. Also, four patches S _{(u, v) 1C} , S _{(u, v) 2D} , S _{(u, v) 3A} and S
_{(u, v) 4} patches S just to fit _{4B
Since (u, v) 1C} , S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B} are generated by subdivision, the four patches S _{(u, v) 1C} , S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B} define the curved shape of the designated area AR by all the control points that define the shape. Will be.

When a new control point is allocated as described above, the CPU 15 proceeds to step SP5 (FIG. 6) to deform the curved surface in the designated area AR in accordance with the instruction of the designer. In this case, as shown in FIG. 8, the CPU 15 displays the free-form surface S _ALL and the designated area AR on the display screen of the monitor 22.
Is displayed, and the end point group character L indicating the end point group GP10 in the designated area AR is displayed.
Display _GP1 . By operating the input device 14, the designer operates the end point group character L on the monitor 22.
_GP1 is designated, and the moving amount and moving direction of the end point group GP10 are input. As a result, as shown in FIG. 9 showing the free-form surface S _ALL as viewed from the side, the designated area AR is deformed so as to expand by the movement amount D designated by the designer.

When the deformation processing of the designated area AR is completed in this way, the CPU 15 proceeds to step SP6, and determines whether or not to deform another area based on the instruction input of the designer. If a positive result is obtained here, this means that the designer has instructed to deform another area. At this time, the CPU 15 moves to step SP7, and as a result of the deformation in step SP5 described above. Is input to the memory 16 as new surface data, and is replaced with the surface data before deformation. In this way, the memory 16 stores new deformed surface data, a surface based on this surface data is displayed on the monitor 22, and the processing of steps SP2 to SP5 is repeated again, so that the designer Similar deformation processing can be repeated for a new area.

On the other hand, if a negative result is obtained in step SP6, this means that the designer has input that the deformation processing of the curved surface is to be completed.
At this time, the CPU 15 moves to step SP8, stores the deformed surface data in the storage hard disk 13 according to the instruction of the designer, or prints it using the printer 23, and ends the free curved surface processing procedure in step SP9. .

(4) Operation and Effect of Embodiment In the above configuration, a plurality of patches S _{(u, v) 1} ,
A free-form surface S formed by connecting S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} (FIG. 3) so as to satisfy the condition of continuation of a tangent plane.
_ALL means that each patch S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S
_{(u, v) 4} are connected so as to share the node P ₍₀₃₎ . That is, on the free-form surface S _ALL , an end point group GP1 centering on the node P ₍₀₃₎ is formed.

In this state, the designer specifies an area AR to be deformed. As shown in FIG. 3, the dividing line L representing the area AR has four patches S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S _{( u). u, v) 4} , if the end point group GP1 existing in the area AR is moved as it is to deform the curved surface,
Two patches S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4}
Are maintained, but the internal control points P of each patch S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} are maintained. _With the movement of _{(12) 1} , P _{(12) 2} , P _{(14) 3,} and P _{(14) 4} , the curved surface may be deformed outside the designated area AR.

Therefore, in the free-form surface processing method, the free-form surface S _ALL is subdivided according to the designated area AR.
As shown in FIG. 7, four patches S _{(u, v) 1C} , S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 3} after the subdivision in the designated area AR.
Make sure that _{(u, v) 4B} fits exactly. If you do this,
Since the four patches S _{(u, v) 1C} , S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B} directly become the free-form surface of the designated area AR, Patch S _{(u, v) 1C} , S _{(u, v) 2D} , S
All the control points that define the respective curved surface shapes of _{(u, v) 3A} and S _{(u, v) 4B} define the shape of the free-form surface of the designated area AR.

In this case, the end point group GP10 exists in the designated area AR, and the patches (S _{(u, v) 1A} , S _{(u, v) 1B} , S _{(u, v) 1B} , S ₎ adjacent to the designated area AR and the periphery thereof.
_{(u, v) 2A} , S _{(u, v) 2B} , S _{(u, v) 2C} , S _{(u, v) 3B} , S
_{(u, v) 3C} , S _{(u, v) 3D} , S _{(u, v) 4C} , S _{(u, v) 4D} , S
The boundary between _{(u, v) 4A} and S _{(u, v) 1D} ) is the designated area AR
And shared endpoint groups (GP11, GP12, GP13, GP14, GP14)
15, GP16, GP17, GP18).

In this case, the shared endpoint group (GP11,
GP12, GP13, GP14, GP15, GP16,
GP17, GP18) include a peripheral portion of the designated area AR and patches (S _{(u, v) 1A} , S _{(u, v) 1B} ,
S _{(u, v) 2A} , S _{(u, v) 2B} , S _{(u, v) 2C} , S _{(u, v) 3B} , S
_{(u, v) 3C} , S _{(u, v) 3D} , S _{(u, v) 4C} , S _{(u, v) 4D} , S
_{(u, v) 4A} and S _{(u, v) 1D} ), and satisfies the condition of continuation of the tangent plane. By fixing these common end point groups, substantially the designated area AR Even if the end point group GP11 existing in the central part is moved, the designated area A
The connection between the peripheral edge of the R and the patch adjacent to the peripheral edge maintains a smooth enough connection for practical use.

Further, four patches S are assigned to the designated area AR.
_{Since (u, v) 1C} , S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B} are subdivided so as to just fit, the end points in the designated area AR Even if the group GP10 is moved, the deformation of the curved surface accompanying the movement of the end point group 10 remains in the designated area AR unless the control point of the patch outside the designated area AR is moved.

In this way, by moving only the end point group GP10 in the designated area AR, the designer does not feel uncomfortable with the connection state with the curved surface adjacent to the designated area AR. Can be deformed.

According to the above configuration, the free-form surface is re-created so that the patches are arranged in a matrix of m × n in the area AR specified by the designer (ie, so that there are nodes shared by a plurality of patches). By dividing and reassigning control points to each of the subdivided patches, it is possible to deform only a specific part desired by the designer.

Therefore, the designer can arbitrarily deform only a desired portion of the free-form surface in the initial stage of the design or the final stage of the design by using the free-form surface processing method.

(5) Another embodiment

(5-1) In the above embodiment, FIG.
As shown in the figure, four patches S _{(u, v) 1} , S _{(u, v) 2} , S
_Although the case where a part of the free-form surface S _{ALL formed} by connecting _{(u, v) 3} and S _{(u, v) 4} is specified has been described, the number of patches constituting the free-form surface is not limited to this. For example, FIG.
As shown in the figure, twelve patches S _{(u, v) 11 to} S _{(u, v) 22}
May be designated as an area AR for partially processing a free-form surface _SALL . in this case,
Patches S _{(u, v) 12} , S _{(u, v) 13} , S including the designated area AR
By subdividing only _{(u, v) 14} , S _{(u, v) 16} and S _{(u, v) 17,} a patch arrangement as shown in FIG. 10B is obtained. In this way, the patches (S _{(u, v) 11} , S _{(u, v) 14} , S _{(u, v) 15} , S _{(u)
(u, v) 18} , S _{(u, v) 19} , S _{(u, v) 20} , S _{(u, v) 21} and S
Unnecessary increase in the number of patches can be prevented without dividing _{(u, v) 22} ).

(5-2) In the above embodiment, FIG.
As shown in the figure, the area AR specified by the designer is included in the four patches S _{(u, v) 1} , S _{(u, v) 2} , S _{(u, v) 3} and S _{(u, v) 4} ( That is, four patches S _{(u, v) 1} , S _{(u, v) 2} , S
_A common node P _{(03) that} is the connection center of _{(u, v) 3} and S _{(u, v) 4}
Has been described in the specified area AR), but the present invention is not limited to this. For example, as shown in FIG. 11A, the specified area AR has two patches S _{(u, v) 11} and S
_The present invention can be applied to the case where _{(u, v) 12} is included. In this case, as shown in FIG. 11B, four patches S _{(u, v) 21F} , S _{(u, v) 21G} ,
The free-form surface _SALL may be subdivided so that S _{(u, v) 22B} and S _{(u, v) 22C} just fit.

As shown in FIG. 12A, when the designated area AR is included in one patch S _{(u, v) 31} , FIG.
As shown in (B), four patches S are included in the designated area AR.
_{(u, v) 31F, S} (u, v) 31G, S (u, v) 31J and S _{(u, v) 31k} may be subdivided form surface S _ALL to fit exactly.

(5-3) In the above embodiment, FIG.
As shown in the figure, four patches S are included in the designated area AR.
_{Subdivision is performed so that (u, v) 1C} , S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B} exist, and one end point group GP10 is moved to convert the surface. Although the case of deformation has been described, the present invention is not limited to this. For example, the area AR is specified so as to straddle more than four patches, or the area AR is specified in the specified area AR at the time of subdivision. More than one patch may be present so that a plurality of end point groups may be formed and moved.

For example, as shown in FIG. 13A, a case is shown where 24 patches S _{(u, v) 41 to} S _{(u, v) 64} exist in the designated area AR. 15 in AR
There are end point groups GP41 to GP55. In this case, the designer can specify the deformation of the curved surface for each end point group by individually specifying the movement amount and the movement direction for each end point group displayed on the display screen of the monitor 22. FIG. 13B shows a case in which the same movement amount and movement direction are designated for each end point group, and the curved surface is deformed so as to bulge into a substantially trapezoidal shape in the designated area AR. On the other hand, FIG.
The case where the largest movement amount is designated for the end point group in the center portion of the designated area AR, and the movement amount is smaller as the end point group moves away from the center of the designated area AR, is shown. Deformed into a chevron shape.

(5-4) In the above-described embodiment, the case where the end point group GP10 (FIG. 7) in the designated area AR is moved in the normal direction has been described. It may be moved in the direction.

(5-5) In the above embodiment, FIG.
As shown in the figure, four patches S are included in the designated area AR.
_{If (u, v) 1C} , S _{(u, v) 2D} , S _{(u, v) 3A} and S _{(u, v) 4B} exist, the node P shared by these four patches
_Although the case of moving the end point group GP10 centered on ₍₀₃₎ has been described, the present invention is not limited to this.
As shown in FIG. 4, for a free-form surface S _ALL composed of two patches S _{(u, v) 1} and S _{(u, v) 2} ,
Control points P ₍₀₃₎ and P ₍₀₂₎ shared by _{(u, v) 1} and S _{(u, v) 2}
End point group GP60 (P _{(12) 1} , P ₍₀₂₎ , P
_{(12) 2} , P _{(13) 23} , P ₍₀₃₎ and P _{(13) 14} ) as the unit of movement, thereby connecting two patches S _{(u, v) 1} and S _{(u, v) 2} . A curved surface can be deformed while maintaining the condition of continuity of a plane.

By using this method, as shown in FIG. 15, when the designated area AR includes the patches S _{(u, v) 4A} and S _{(u, v) 1D} at the peripheral end of the free-form surface S _ALL . , the two Patsuchi S _{(u, v) 4A} and S _{(u, v) 1D} by moving an end point group GP61 that share, Patsuchi S _{(u, v)} in the designated area AR _4A and S _{(u, v)} Deformation of a curved surface desired by a designer can be performed while maintaining a smooth _1D connection state.

(5-6) In the above embodiment, the free-form surface S to be deformed on the display screen of the monitor 22
_ALL is displayed, and the division line L indicating the designated area AR and the end point group GP10 (FIG. 8) that can be instructed to move can be displayed. However, the present invention is not limited to this.
It is also possible to display all the control points distinguished by the color grouping and the like with the end point group GP10 in which movement can be instructed.

(5-7) In the above embodiment, the case where a quadrilateral patch represented by a cubic Bezier equation is set in the framework space has been described. However, the present invention is not limited to this, and a triangular patch is used. However, the order of the mathematical expression is not limited to this, and 4
It may be more than next.

(5-8) In the above embodiment, the case where the patch represented by the Bezier formula is stretched has been described. However, the present invention is not limited to this, and the spline type, Coons type, Other vector functions such as the Forgason equation may be used.

(5-9) In the above embodiment, the case where the curved surface data before machining, the free curved surface machining program and the curved surface data after machining are stored in the hard disks 12, 11 and 13, respectively, has been described. The present invention is not limited to this. For example, various other recording media such as a rewritable optical disk and a tape-shaped recording medium may be used.

[0087]

As described above, according to the present invention, the free-form surface is divided so that a plurality of patches exist in a designated area on the free-form surface, and the condition that the plurality of patches are connected to each other by a tangent plane is determined. The control point group to be shared is satisfactorily moved in the same direction and the same distance in units of the control point group, so that the curved surface is deformed while the patch is smoothly connected in the designated area. be able to.

[Brief description of the drawings]

FIG. 1 is a schematic plan view for explaining a free-form surface creation method.

FIG. 2 is a schematic diagram for explaining a condition of continuation of a tangent plane;

FIG. 3 is a schematic plan view showing a free-form surface formed by connecting four patches.

FIG. 4 is a schematic perspective view for explaining movement of an end point group;

FIG. 5 is a block diagram showing an embodiment of a free-form surface machining apparatus according to the present invention.

FIG. 6 is a flowchart showing a free curved surface processing procedure according to the present invention.

FIG. 7 is a schematic plan view for explaining the subdivision of the patch.

FIG. 8 is a schematic plan view showing a free-form surface displayed on a monitor and a processing region thereof.

FIG. 9 is a schematic cross-sectional view for explaining the deformation processing of the curved surface by moving the end point group.

FIG. 10 is a schematic plan view for explaining a patch subdivision according to another embodiment.

FIG. 11 is a schematic plan view for explaining subdivision of a patch according to another embodiment.

FIG. 12 is a schematic plan view for explaining a subdivision of a patch according to another embodiment.

13A and 13B are a schematic plan view and a schematic cross-sectional view illustrating a curved surface deformation processing by moving an end point group according to another embodiment.

FIG. 14 is a schematic plan view showing an end point group of a free-form surface formed by connecting two patches.

FIG. 15 is a schematic plan view showing a designated state of a processing area according to another embodiment.

FIG. 16 is a schematic plan view for explaining a method of connecting a quadrilateral patch.

[Explanation of symbols]

Reference numeral 10: free-form surface processing device, 11, 12: hard disk, 13: storage hard disk, 14: input device, 15: CPU (central processing unit), 16, 1
7, 18 ... memory, 21 ... graphics circuit, 2
2 ... monitor, S _ALL ... free-form surface, S _{(u, v) x} ... patch, AR ... designated area, GPx ... end point group, n _x
... Normal vector.

Claims (4)

[Claims] 1. A method for processing a free-form surface created by forming a large number of frame spaces surrounded by boundary curves by a frame process, and patching the frame space with a patch represented by a predetermined vector function. In the curved surface processing method, a plurality of patches are formed in the region by dividing the free curved surface based on the region designation step for designating a predetermined region of the free curved surface and the region designated by the region designation step. The dividing step to be formed and the nodes shared by the plurality of patches in the area and the control points around the nodes are moved in the same direction and by the same amount of movement, and a new plurality of patches are maintained while the connection state of the plurality of patches is substantially maintained. And a curved surface machining step for forming a patch. 2. The dividing step includes forming the plurality of patches such that a boundary of the designated area coincides with one side of each of the plurality of patches divided and formed in the area. The method for processing a free-form surface according to claim 1, wherein: 3. A process for forming a large number of frame spaces surrounded by boundary curves by a frame process, and processing a free-form surface created by stretching a patch represented by a predetermined vector function in the frame space. In the curved surface processing apparatus, a plurality of patches are formed in the region by dividing the free curved surface based on the region designated by the region designating step, and a region designation means for designating a predetermined region of the free curved surface. A dividing unit to be formed, and a node shared by a plurality of patches in the area and a control point around the node are moved in the same direction and by the same amount of movement, so that a new plurality of patches are maintained while substantially maintaining the connection state of the plurality of patches. And a curved surface processing means for forming a patch. 4. A process for forming a large number of frame spaces surrounded by boundary curves by a frame process, and processing a free-form surface created by stretching a patch represented by a predetermined vector function in the frame space. In the recording medium on which the curved surface processing program is recorded, the free curved surface processing program includes an area designating step for designating a predetermined area of the free curved surface, and the free form processing step based on the area designated by the area designating step. By dividing a curved surface, a dividing step for forming a plurality of patches in the region, and a node shared by a plurality of patches in the region and a control point around the node are moved in the same direction and by the same amount of movement. A curved surface processing step for forming a new plurality of patches while substantially maintaining the connection state of the plurality of patches. Medium.