JP3534259B2 - Free-form surface creation method and free-form surface creation device - Google Patents

Description

Detailed Description of the Invention

[0001]

[Table of Contents] The present invention will be described in the following order. Industrial Application Conventional Technology (FIG. 14) Means for Solving Problems to be Solved by the Invention (FIGS. 4 to 11) Action (FIGS. 4 to 11) Working Example (1) CAD / CAM System (FIG. 1) (2) Principle of free curve (FIG. 2) (3) Free curved surface creation processing procedure between free curve and free curved surface (FIGS. 3 to 12) (4) Other embodiment (FIG. 13) ) The invention's effect

[0002]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a free-form surface forming method and a free-form surface forming apparatus, and more particularly to CAD / CAM (computer).
It can be applied to a design device using a method of aided design / computer aided manufacturing.

[0003]

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 model).
Generally, a designer specifies a plurality of points (called points of contact) in a three-dimensional space through which a curved surface should pass, and calculates a boundary curve network connecting the specified points of contact with a desired vector function. Creates a curved surface represented by a so-called wire frame. Thus, a large number of framework spaces surrounded by boundary curves can be formed (this processing is called framework processing).

The boundary curve network formed by such frame processing itself represents a rough shape which the designer intends to design, and a boundary vector surrounding each frame space is used to define a predetermined vector function. If the curved surface that can be expressed can be interpolated, the free curved surface (which cannot be defined by a quadratic function) designed by the designer can be generated as a whole. Here, the curved surface stretched in the frame space forms a basic element that constitutes the entire curved surface, and this is called a patch.

By the way, in order to give the generated free-form surface as a whole a more natural outer shape, two frame spaces adjacent to each other across the shared boundary are patched so as to satisfy the condition of tangential plane continuity at the shared boundary. As described above, a free-form surface creation method has been proposed in which the control edge vector around the shared boundary is reset (Japanese Patent Application No. 60-277448).
issue).

As shown in FIG. 14, this free-form surface forming method uses a cubic Bezier equation to convert a quadrilateral patch vector S _{(u, v) 1} and a vector S _{(u, v) 2} extended in a quadrilateral frame space. It is represented by the vector function vector S _{(u, v)} . Then, in order to smoothly connect the two patch vectors S _{(u, v) 1} and S _{(u, v) 2} , the node vector P ₍₀₀₎ and the vector P _{(30) 1} given by the frame processing are given. , Vector P
_{Based on (33) 1} , vector P ₍₀₃₎ , vector P _{(33) 2} , and vector P _{(30) 2} , adjacent quadrilateral patch vectors S
_At the shared boundary COM of _{(u, v) 1} and the vector S _{(u, v) 2} , the control side vector a ₁ , the vector a _{2, the} vector c ₁ , and the vector c ₂ are set so that the condition of continuous tangential plane is satisfied. Further, by using these control side vectors, control point vector P _{(11) 1} , vector P _{(12) 1} , vector P
_The principle is to reset _{(11) 2} and vector P _{(12) 2} .

If this method is applied to other shared boundaries as well, the patch vectors S _{(u, v) 1} and S _{(u, v) 2} will eventually be smoothed according to the condition of adjacent patches and tangential plane continuity. Can be connected to. Here, the vector function vector S _{(u, v)} consisting of a cubic Bezier equation is

[Equation 1] As in, u and v directions parameters u and v, are expressed using a shift operator E and F, the control point vector P _(ij), the following equation

[Equation 2]

[Equation 3]

[Equation 4]

[Equation 5] Have a relationship.

Further, the tangent plane means a plane formed by tangent vectors in the u direction and the v direction at each point of the shared boundary. For example, for the shared boundary COM in FIG. 14, the patch vector S _{(u, v)} When the tangent planes of ₁ and the vector S _{(u, v) 2} are the same, the condition of continuous tangent planes holds.

According to this method, the curved surface shape as a whole changes smoothly as intended by the designer.
It is possible to easily design an object shape that is difficult to design by the conventional design method.

[0010]

By the way, by using such a designing device, a so-called fillet curved surface, which is in contact with the free curved surface with the free curved surface as a boundary between the free curved surface and the free curved surface in a three-dimensional space, is called. If a free-form surface can be generated, it is considered possible to create a high-quality design that makes the most of the designer's sensitivity. in this case,
There is a method of generating a curved surface from a free curve and generating a fillet curved surface of a predetermined radius between this generated curved surface and the free curved surface. Even in this way, if the end of the free curved surface comes to the position of the free curve. There is a problem that is not always the case. Moreover, since the height and position of the generated curved surface of the cylinder are determined by the predetermined radius, there is a problem that the designer cannot arbitrarily specify it.

As a method of generating such a free curved surface, there is a method of generating a fillet curved surface by sweeping an arc along a free curve, and when the distance between the free curved surface and the free curved surface is constant, a smooth curve is created. It is possible to generate a curved surface, but if the distance between the free curved surface and the free curved surface is not constant, there is a problem that the generated fillet curved surface does not contact the free curved surface smoothly.

There is also a method of generating a tangential arc from a plurality of points on a free curve at each point corresponding to the free curved surface and approximating the plurality of arcs to generate a fillet curved surface. Since it is necessary to generate and approximate a contact arc, it takes a huge amount of time for processing and there is a problem in that it is not convenient to use.

The present invention has been made in consideration of the above points, and is a free-form surface having a constant curvature or a specified radius that smoothly comes into contact with a specified free-form surface from a free-form curve whose shape and position are defined. It is intended to propose a free curved surface creating method and a free curved surface creating apparatus capable of easily creating the following curved surface.

[0014]

In order to solve such a problem, in the present invention, a free curved surface representing the surface shape of an object is formed between a free curved surface and a free curved surface in a three-dimensional space by using a computer. In the free curved surface creating method for creating a curved surface, the free curved surface (A) is moved by a predetermined distance to generate a second free curved surface (AO), and the free curved surface (B) is generated.
Setting a plurality of reference points _{(Q i)} above, a plurality of planes containing the tangents _{(V i)} reference point as normal _{(Q i)} of free curve at each reference point _{(Q i) (B) (} PL _i) generates, it generates the radius of the circle of a predetermined distance around each reference point on the plurality of planes (PL _i) a _{(Q i)} (CI _i), a circle (CI _i) and the second free A plurality of intersections (R _1i , R _2i ) with the curved surface (AO) are obtained, and the second free-form surface (A
_{Perpendicular} to the free-form surface (A) from a plurality of intersections (R _1i , R _2i ) on the vertical line (P _1i , P).
_2i ), and a plurality of planes (PL _i )
A plurality of arcs (ARC _i ) having a predetermined distance and having the reference point (Q _i ) and the perpendicular foot (P _i ) as the end points are generated, and the free curve (B), the free curved surface (A), and the plurality of arcs are generated. Arc (ARC
generate a fillet surface based on _i ).

Further, a curved surface generating means for generating a second free curved surface (AO) by moving the free curved surface (A) by a predetermined distance, and a plurality of reference points (Q _i ) are set on the free curve (B). and, a planar generating means for generating a plurality of planes (PL _i) including the reference point tangent to _{(V i)} as the normal line of the free curved line (B) at the reference point _{(Q i)} a _{(Q i)} each, a plurality of A circle (CI _i ) having a predetermined radius centered on the reference point (Q _i ) is generated on the plane (PL _i ), and the intersection () of the circle (CI _i ) and the second free-form surface (AO) is generated. R _1i , R _2i ) are obtained, and a plurality of intersections (R) on the second free-form surface (AO) are obtained.
_1i , R _2i ) to the free-form surface (A), and obtain the feet (P _1i , P _2i ) of the perpendicular, respectively, on the plurality of planes (PL _i ) and the reference point (Q _i ) and the perpendicular. It is generated by an arc generating means for generating a plurality of arcs (ARC _i ) having a radius of a predetermined distance with the foot (P _i ) as both end points, and a free curve (B), a free curved surface (A) and an arc generating means. And curved surface generating means for generating a curved surface based on a plurality of arcs (ARC _i ).

[0016]

In order to solve such a problem, the present invention provides:
In a free-form surface creating method for creating a free-form surface, which is a free-form surface representing the surface shape of an object, between a free-form curve and a free-form surface in a three-dimensional space using a computer, move the free-form surface (A) by a predetermined distance. The generated second free curved surface (AO) is generated, a plurality of reference points (Q _i ) are set on the free curve (B), and the tangent line (V) of the free curve (B) at each reference point (Q _i ) is set. _i ) is a normal line, a plurality of planes (PL _i ) including a reference point (Q _i ) are generated, and a plurality of planes (PL _i ) each have a radius of a predetermined distance centered on the reference point (Q _i ). Generate a circle (CI _i ),
I _i ) and the intersection (R _1i , R) of the second free-form surface (AO)
_2i ) is obtained, a perpendicular is drawn from each of a plurality of intersections (R _1i , R _2i ) on the second free-form surface (AO) to the free-form surface (A), and feet (P _1i , P _2i ) of the perpendicular are drawn. Then, a plurality of arcs (ARC _i ) each having a predetermined distance and having a reference point (Q _i ) and a perpendicular foot (P _i ) as end points on a plurality of planes (PL _i ) are generated, and a free curve ( B), a free-form surface (A) and a plurality of arcs (ARC _i ) are used to generate a fillet-surface, so that a free-form curve whose shape or position is defined can be smoothly contacted with a designated free-form surface. It is possible to easily generate a free-form curved surface having a constant curvature or a designated radius.

[0017]

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

(1) Overall Structure of CAD / CAM System In FIG. 1, 10 indicates a CAD / CAM system as a whole, and after the shape data DT _S representing the free curved surface is created by the free curved surface creating device 12, the tool path is created. The device 13 creates processing data DT _CL for cutting.

That is, the free-form surface forming device 12 has a central processing unit (CPU), and operates the input device 17 in response to the display of the display device 16 so that the wireframe model designated by the designer is cubically input. After the patch is stretched using the Bézier equation, the shape data DT _{S of the} object having the free curved surface is created by reconnecting the patch.

On the other hand, the tool path creating device 13 creates the processing data DT _CL for roughing and finishing the die based on the shape data DT _S , and then, the processing data for the roughing and finishing. The DT _CL is output to the NC milling machine 14 via, for example, the floppy disk 15. The NC milling machine 14 uses the processed data DT
Based on _CL , for example, an NC milling machine is driven, and a mold for the product represented by the shape data DT _S is created by this.

(2) Principle of free curve As shown in FIG. 2, the Bezier curve is expressed by the following equation using the cubic Bezier equation:

[Equation 6] It is expressed by a parametric space curve vector R _(t) represented by. Here, t is expressed by the following equation from the one contact vector P ₀ to the other contact vector P ₃ in the direction along the curve segment vector K _SG.

[Equation 7] It is a parameter that changes from the value 0 to the value 1 as represented by.

In this way, the curve segment vector K _SG represented by the cubic Bezier equation is converted by the shift operator E into two control point vectors P ₁ and P between the contact vector P ₀ and the vector P _3. By designating ₂ each point on the curve segment vector K _SG

[Equation 8] Is expressed as a position vector R _(t) from the origin O in the xyz space. Here, the shift operator E is expressed by the following equation with respect to the control point vector P _i on the curve segment vector K _SG.

[Equation 9]

[Equation 10] Have a relationship of.

Therefore, by expanding the equation (6) and substituting the relationship of the equation (9), the following equation is obtained.

[Equation 11] Can be calculated as follows, and as a result, the equation (8) is obtained.

Thus, each of the curve segment vectors K _SG1 , vector K _SG2 , and vector K _SG3 represented by Bezier curves respectively has two nodes and control point vectors P _{(0) 1 to} P _{(0 )} based on the equation (8). _{) 3} , vector P _{(1) 1 to} P _{(1) 3} , vector P _{(2) 1 to} P
_{(2) 3} and the vectors P _{(3) 1 to} P _{(3) 3} . Further, the node vectors P _{(0) 1 to} P
Control point vector P between _{(0) 3} and vector P _{(3) 1
(1) 1 to} P _{(1) 3} and vector P _{(2) 1 to} P
₍₂₎ By setting ₃ , the node vector P
Control point vectors P _{(0) 1 to} P _{(0) 3} and vector P through _{(0) 1 to} P _{(0) 3} and vector P _{(3) 1
(1) 1 to} P _{(1) 3} , vector P _{(2) 1 to} P
_{(2) 3} and vectors P _{(3) 1 to} P _{(3) 3} can be set to a shape determined.

(3) Free-form surface creation processing procedure between free-form curve and free-form surface The free-form surface creation device 12 allows an operator to give a free-form curve and a free-form surface to a three-dimensional space so that the free-form surface is created between the free-form surface and the free-form surface. A free-form surface is generated from a movement trajectory obtained by moving a sphere so that the free-form curve serves as a boundary and is in contact with the free-form surface. That is, the free-form surface creating device 12 is shown in FIG.
The processing is started at step SP0 of the free curved surface creation processing procedure between the free curved surface and the free curved surface shown in FIG.
Move on to. Here, as shown in FIG. 4, when the operator designates and inputs the free-form surface vector A and the free-form curve vector B in the three-dimensional space, the data of the surface-surface vector A and the curve vector B are fetched.

In practice, the free-form surface vector A designated in this way is decomposed from the equation (1) to obtain the equations (2) and (3).
By substituting the relationship of the expression, the following expression

[Equation 12] It is represented by.

The free curve vector B is a nodal vector PB ₀ , a vector PB ₃ , an internal control point vector PB ₁ ,
The following equation, which is defined by the vector PB ₂ and is obtained by modifying the equation (11),

[Equation 13] It is represented by.

Next, the free-form surface forming device 12 uses the step SP.
2, 11 point vectors Q _i (i = 1 to 11) are obtained on the free curve vector B by parameter division. This point vector Q _i (i = 1 to 11) is the free curve vector B
An arbitrary point that can be moved over,

[Equation 14] It is represented by.

The free-form surface forming device 12 moves to step SP3, moves the free-form surface vector A by an arbitrary designated radius r amount, and each point on the free-form surface vector A is equidistant (radius amount) from each corresponding point. An offset curved surface vector AO is generated.

Then, in step SP4, the tangent line of the point vector Q _i on the free-form surface vector A is obtained. The tangent line of the point vector Q _i at this time is

[Equation 15] It is represented by. Since the plane is defined by one point and the normal, as shown in FIG. 5, the plane tangent vector V _i of the point vector Q _i from the point vector Q _i and the normal vector V _i as the normal vector Find PL _i .

The free-form surface forming device 12 obtains the plane vector PL _i in step SP4, and then proceeds to step SP5. Here, as shown in FIG. 6, the center point vector Q _i on the plane vector PL _i, to produce a circular vector CI _i for a specified radius r. To determine the arc center point necessary for generating a free-form surface where the intersection vector R _1i between the circle vector CI _i and offset curved vector AO in the plane vector PL _i, obtaining the vector R _2i.

After this, in step SP6, the end point of the circular arc is obtained, so that the offset curved surface vector A as shown in FIG.
A perpendicular line is drawn from the two-point vector R _1i and the vector R _2i on O onto the free-form surface vector A, respectively. At this time, the feet of the perpendiculars are set as point vectors P _1i and P _2i , respectively, and these are set as the end points of the arc.

Next, in step SP7, two arcs are generated. As shown in FIG. 8, the starting point of each arc is a point vector Q _i on the free curve vector B, and the ending point of each arc is a point vector P _1i and a vector P _2i on the free curved surface vector A. Further, with the point vector R _1i and the vector R _2i on the offset curved surface vector AO as the centers and the radius as an arbitrary designated radius r, the arc vector ARC _i1 and the vector ARC _i2 are respectively generated.

Two arc vectors ARC _i1 and vector A
After RC _i2 is generated, the free-form surface forming device 12 moves to step SP8, and the two arc vector ARC thus obtained are obtained.
_{From i1} and vector ARC _i2 , one arc is selected by the following selection method. First, for one arc vector ARC _i1 , the cross product of the tangent vector V _{i at} the point vector Q _i on the free curve vector B and the normal vector W _{1i at} the point vector P _1i on the free curved surface vector A is the vector X _i.
And Also, the starting point vector Q _i of the arc vector ARC _i1
From the end point vector P _1i to the vector Y _1i
And the angle between the outer product vector X _i and the direction vector Y _1i is θ _1i , these relationships are

[Equation 16]

[Equation 17]

[Equation 18] It is represented by.

Similarly, for the other circular arc vector ARC _i2 , the tangent vector V _{i at} the point vector Q _i on the free curve vector B and the normal vector W _{2i at} the point vector P _2i on the free curved surface vector A are similarly defined. Let the outer product be the vector X _i . The direction vector from the start point vector Q _i of the arc vector ARC _i2 to the end point vector P _2i and vector Y _2i, when the angle formed by the outer product vector X _i and the direction vector Y _2i and theta _2i, these relationships

[Formula 19]

[Equation 20]

[Equation 21] It is represented by.

Here, when selecting one of the two circular arcs, the tangent line is arranged so as to be aligned with the circular arc on the constant side of the two circular arcs generated from each point vector Q _i (i = 1 to 11) as a starting point. Select an arc whose vector is close to the cross product vector X _i . That is, in order to select the smaller one of the obtained two angles θ _1i and θ _2i , the angle θ is smaller than the angle θ _{1i.
When 2i} is small, arc vector ARC _i2 is selected. When angle θ _1i is smaller than angle θ _2i , arc vector AR is selected.
Select C _i1 .

At step SP9, the free curve vector B
It is determined whether or not the arc vector ARC _i (i = 1 to 11) has been obtained from each of the 11 point vectors Q _i (i = 1 to 11) above. If a negative result is obtained here, step S
Return to P4 and continue processing. When an affirmative result is obtained (FIG. 10), the process moves to step SP10 and each arc vector A
End point group vector P _i (i = 1 to 1) of RC _i (i = 1 to 11)
11) is obtained, and a curve vector C is generated by approximating these 11 points by least squares (Japanese Patent Application No. 3-311952).

After this, the free-form surface forming device 12 proceeds to step S.
Moving to P11, each arc vector ARC _i (i = 1 to 11)
On the other hand, the point group vector AR _ij on each arc is obtained by dividing by the parameter j (j = 1 to 11). Finally, the process proceeds to step SP12 and, as shown in FIG.
Curve vector C obtained in P11, free curve vector B,
Using the four boundary curves of the arc vector ARC ₁ and the arc vector ARC ₁₁ as a framework, the point cloud vector AR _ij inside the boundary curve
A surface patch is generated by least-squares approximation based on (i, j = 1 to 11) (Japanese Patent Application No. 3-311952), and the process is terminated at step SP13.

According to the above configuration, when the free curved surface is generated from the movement locus obtained by moving the sphere so as to be in contact with the free curved surface with the free curved surface as a boundary in the three-dimensional space, the radius of the free curved surface is generated. By using an offset plane that has been offset by a certain amount to generate an arc of a predetermined radius and create a curved surface based on the free curve, free curved surface and arc,
It is possible to easily generate a free-form curved surface having a constant curvature such that it smoothly contacts a designated free-form surface from a free-form curve whose shape and position are determined. Therefore, high quality design that makes the most of the designer's sensitivity can be made.

(4) Other Embodiments In the above-mentioned embodiment, the smaller one of the angles θ _1i and θ _2i is selected at the time of arc generation, and the arc having the tangent vector that generates this angle is selected. Although the selection has been described, the present invention is not limited to this, and the same applies even if the larger one of the angles θ _1i and θ _2i is selected and the arc having the tangent vector generating this angle is selected. The effect of can be obtained.

Further in the aforementioned embodiment, the intersection point vector R _1i between the circle vector CI _i and offset curved vector AO in the plane vector PL _i, obtains a vector R _2i, in contact with the free-form surface vector A from the free curve vector B Although the free-form surface is created by generating an arc, the present invention is not limited to this, and when the intersection of the circle on the plane and the offset curved surface cannot be obtained, that is, from the point on the free-form curve. When the arc contacting with can not be generated shorter than a predetermined radius, as shown in FIG. 13, a sweep curved surface or the like formed by dropping a perpendicular line from the free curved line to the free curved surface of an arbitrary length by the operator's designation is generated. A free-form surface may be generated between the two free-form surfaces.

Further, in the above-mentioned embodiment, the free-form surface is created between the free-form curve vector B and the free-form surface vector A, but the present invention is not limited to this.
It is also good for generating free-form surfaces that represent the shape of counterbore holes, convex button holes, and the like.

Further, in the above-described embodiment, a plurality of arc vectors ARC _i generated with a constant designated radius r.
Although the free-form surface is created based on (i = 1 to 11), the present invention is not limited to this, and a plurality of arcs having different radii are created and the free-form surface is created based on these arcs. You may do it.

Further, in the above-mentioned embodiment, the description has been given of the case where the free curved surface represented by the Bezier equation and the free curved surface formed between the free curved surfaces are created, but the present invention is not limited to this, and the B-spline is not limited thereto. The same effect can be obtained with a free curved surface represented by a formula other than the Bezier equation and a free curved surface formed between free curved surfaces such as a function.

[0045]

As described above, according to the present invention, a free curved surface and a free curved surface are given in a three-dimensional space by using a computer, and an offset curved surface obtained by offsetting the free curved surface by a radius amount is used to obtain a predetermined radius. By generating an arc and creating a free-form curve, a free-form surface based on the free-form surface, and an arc, a fixed curvature or designation that smoothly contacts the specified free-form surface from the free-form curve whose shape and position are determined It is possible to easily generate a fillet curved surface that is a free curved surface of a radius.

[Brief description of drawings]

FIG. 1 is a block diagram showing the overall configuration of an embodiment of a CAD / CAM system to which a free-form surface forming method and a free-form surface forming apparatus according to the present invention are applied.

FIG. 2 is a schematic diagram for explaining a free curve represented by a vector function.

FIG. 3 is a flow chart showing a free curved surface creation processing procedure in which a free curved surface is a boundary and is in contact with the free curved surface.

FIG. 4 is a schematic diagram showing a free curve and a free curved surface designated by an operator.

5 is a schematic diagram showing a plane generated with a tangent line from a point set on the free curve in FIG. 4 as a normal line.

FIG. 6 is a schematic diagram showing an intersection of an offset curved surface of a free curved surface and a circle generated on a plane.

7 is a schematic diagram showing a foot of a perpendicular line when a perpendicular line is drawn from the intersection on the offset curved surface of FIG. 6 to the free curved surface.

8 is a schematic diagram showing an arc centered on an intersection on the offset curved surface in FIG. 7 and having a point on the free curved surface and a foot of a perpendicular line on the free curved surface as an end point.

9 is a schematic diagram showing a vector connecting both end points of the arc of FIG. 8 and a normal line of a free-form surface on a foot of a perpendicular line.

FIG. 10 is a schematic diagram showing an arc group generated from a point group set on a free curve.

FIG. 11 is a schematic diagram showing a curved surface patch generated from the arc group, the free curve and the free curved surface of FIG.

FIG. 12 is a schematic diagram showing a free-form surface created from four curved-surface patches between the free-form curve and the free-form surface.

FIG. 13 is a schematic diagram showing a free-form surface created when a predetermined radius is shorter than the radius of an arc when creating the arc.

FIG. 14 is a schematic diagram for explaining a free-form surface.

[Explanation of symbols]

10 ... CAD / CAM system, 12 ... Free-form surface creation device, A ... Free-form surface, B, C ... Free-form curve, AO ...
… Offset curved surface, Q _{1 to} Q ₁₁ …… Reference point, ARC ₁
~ ARC ₁₁ ... Arc.

─────────────────────────────────────────────────── ─── Continuation of front page (58) Fields surveyed (Int.Cl. ⁷ , DB name) G06F 17/50

Claims (8)

(57) [Claims] 1. A computer in a three-dimensional space using a computer.
A free curve that expresses the surface shape of an object between a free curve and a free-form surface
In a free-form surface creating method for creating a fillet curved surface consisting of surfaces , a second free-form surface generated by moving the free-form surface by a predetermined distance is generated, a plurality of reference points are set on the free-form curve, and the reference points are respectively set. on the tangent of the free curve to generate a plurality of planes containing the reference point as normal, it centered on each of the above reference points on the plurality of planes in
A circle having a radius of a predetermined distance is generated, a plurality of intersections of the circle and the second free curved surface are obtained, and a perpendicular is drawn from each of the plurality of intersections on the second free curved surface to the free curved surface. Each of which is obtained, and a plurality of arcs having a radius of the predetermined distance with the reference point and the foot of the perpendicular as the end points on the plurality of planes are respectively generated, and the free curve, the free curved surface, and the plurality of the above A free-form surface creation method, characterized in that the above-mentioned fillet surface is created based on an arc. 2. The arcs are first and second arcs having a predetermined radius with the reference point on the free curve and the foot of the perpendicular line on the free curved surface as both end points, and the arc at the reference point is determined. The outer product of the tangent vector of the free curve and the normal vector of the free curved surface at the foot of the perpendicular is obtained, and the first and second lines from the reference point to the foot of the perpendicular are obtained based on the first and second arcs. The method for creating a free-form surface according to claim 1, wherein a direction vector is obtained and only the first or second arc having a first or second direction vector close to the outer product is generated. Wherein during the arc generation, when the arc of a predetermined radius on the plane can not be generated, Ren from the free curve
An object with a perpendicular to the free-form surface of the desired length
A sweep curved surface representing the surface shape of the body is generated, and a predetermined radius is provided between the sweep curved surface and the free curved surface, and the free curved surface is in contact with the free curved surface.
The free curved surface creating method according to claim 1 or 2, wherein the fillet curved surface is generated. 4. A second free-form curve is approximately generated by least-squares approximation based on a point group of feet of the perpendicular line which is one end point of the plurality of arcs generated on the free-form surface, and the second free-form curve is generated. Based on the free-form curve, the free-form curve, the plurality of arcs, and the point group on the arcs, the least-squares approximation described above
The free-form surface creation method according to claim 1 or 3, wherein a fillet surface is approximately generated. 5. Between a free curve and a free curved surface in a three-dimensional space
Free-form curved surface representing the surface shape of an object
In the free-form surface creating apparatus for creating a free-form surface, a free-form surface is generated by moving the free-form surface by a predetermined distance, and a plurality of reference points are set on the free-form curve. the plane generating means for generating a plurality of planes containing the reference point tangent of the free curve as normal, on the center of each said reference point on said plurality of planes
A circle having a radius of a predetermined distance is generated, a plurality of intersections of the circle and the second free curved surface are obtained, and a perpendicular is drawn from each of the plurality of intersections on the second free curved surface to the free curved surface. Of each of the predetermined points with the reference point and the foot of the perpendicular line as the end points on each of the plurality of planes.
Arc generating means for generating a plurality of arcs having a radius of distance; and the file based on the free curve, the free curved surface, and the plurality of arcs generated by the arc generating means.
And a curved surface generating means for generating a curved surface. 6. The arc generating means obtains first and second arcs having a predetermined radius with the reference point on the free curved line and the foot of the perpendicular line on the free curved surface as end points, and the reference point is obtained. Of the tangent vector of the free curve and the normal vector of the free curved surface of the foot of the perpendicular, the first and second feet from the reference point to the foot of the perpendicular based on the first and second arcs. The free-form surface creating apparatus according to claim 5, wherein the direction vector of 2 is obtained, and only the first or second circular arc having the first or second direction vector close to the outer product is generated. 7. The arc generating means, when the arc having a predetermined radius cannot be generated on the plane, drops from the free curve to the free curved surface of an arbitrary length.
A sweep curved surface representing the surface shape of the object is drawn, and a predetermined radius is provided between the sweep curved surface and the free curved surface, and the free curved surface is in contact with the free curved surface.
Sculptured surface generating device according to claim 5 or claim 6, wherein the generating the Fuiretsuto curved. 8. The curved surface generating means approximate-generates a second free-form curve by least-squares approximation based on a point group of feet of the perpendicular line which is one end point of the plurality of arcs generated on the free-form surface. and, said second free curve, the free curve, based on a plurality of the arc and the point group on the arc, the least squares approximation
Sculptured surface generating device according to claim 5 or claim 7, characterized in that approximates generate Fuiretsuto curved.