JP3321451B2 - 3D shape processing method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a three-dimensional shape processing method, and more particularly, to row <br/> cormorant three-dimensional shape processing method of intersection calculation unloading between 3 curved. For example, the present invention is applied to a set operation device for solids and a free-form surface processing device.

[0002]

2. Description of the Related Art The following are known documents describing the prior art according to the present invention. (1) Barnhill, RE, Farin, G., Jordan, M. and Piper, B.
R., "Surface / Surface Inte-rsection" (Computer aide
d geometric design, 1987, vol.4, No.1-3,, pp.3-16.) (2) Barnhill, REand Kersey, SN, "A marching me
thod for parametric surfa-ce / surface intersectio
n ”(Computer aided geometric design, 1990, vol. 7, N
o.1, pp.257-280.) (3) Chen, JJand Ozsoy, TM, “Predictor-Correcto
r Type of IntersectoinAl-gorithm for C ² Parametric
Surfaces ”(Computer Aided Design, 1988, vol.20, No.
6, pp.347-352.)

In the above (1) and (2), there is a description of a tracking vector, a tracking end condition, and an intersection between intersection lines in the calculation of interference between free-form surfaces, but there is no description of others. In the above (3), the tracking vector and the tracking end condition in the interference calculation between free-form surfaces are described.
There is no other description .

[0004] Other known documents include the following. (4) Fujisawa, Takamura, "Method of calculating interference between free curve and plane of arbitrary order"
Oct., pp. 936-937.) (5) AGO'Neill, Takamura, "Method of calculating interference between free curve and plane of arbitrary order," (Transactions of the 39th IPSJ Conference, Oct., pp.) .938-939.) In (4), there is a description of a method of calculating the interference between a free curve and a plane, and in (5), there is a description of a method of calculating the interference between a free curve and a quadric surface. According to such a conventional technique, it is difficult to realize an apparatus or a method for performing an interference calculation between an arbitrary free curve and an arbitrary free curved surface. Also,
Regarding the method of obtaining the intersection of three curved surfaces, a method of obtaining the intersection of a low-order algebraic surface such as three planes has been known, but the method of obtaining the intersection of the curved surfaces has not been known.

Further, (6) Chandru, V. and Kochar, BS (1987).
echniques for geometric in-tersection problems ''
(Geometric Modeling, Farin, G. (Ed), SIAM, Philadelphi
a, pp. 305-318.), it is difficult to perform the processing unless the points are accurately placed on the curved surface because the method is analytically determined. In addition, the processing depends on the type of the curved surface, and when the degree of the curved surface increases, the processing becomes difficult.

[0006]

[0008] The present invention has been made in view of such circumstances described above, to provide a three-dimensional shape processing scheme to allow the this obtaining an intersection of three curved surfaces It was made for the purpose.

[0007]

SUMMARY OF THE INVENTION In order to achieve the above object, the present invention provides: (1) a parameter value for obtaining a coordinate value and a parameter value of a point obtained by projecting an approximate point of an intersection of three curved surfaces onto each curved surface; Generating means, a tangent plane generating means for obtaining a tangent plane at a point projected on each of the curved surfaces using a normal vector of the curved surface, and an intersection generating means for obtaining an intersection of tangent planes obtained by the tangent plane generating means. the intersection of the tangent plane
<br/> Rukoto points projected on each surface and a determined Mel projection point generating means, or obtained in (2) the intersection generating means
Between the intersection and the point projected on each curved surface by the projection point generation means.
Based on the distance, the intersection determined by the intersection generation means is
It is characterized in that it is determined that it is the intersection of the three curved surfaces . Hereinafter, a description will be given based on examples of the present invention.

[0008]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a block diagram for explaining an example of a three-dimensional three-dimensional shape processing method. In the drawing, reference numeral 1 denotes free-form surface data, 2 denotes free-form surface data, and 3 denotes inter-convex hull interference inspection. Device, 4 is a convex hull calculation device for a free-form surface and a control point, 5 is an interference line tracing start point generation device, 6 is a device for calculating the intersection of a free-form surface and a free curve, and 7 is an interference point calculation device inside two free-form surfaces ,
8 is an interference line tracking direction generation device, 9 is a device for calculating coordinate values on a free-form surface, 10 is a device for calculating a normal vector of the free-form surface,
11 is a tracking start point selecting device, 12 is an interference ray tracking device, 1
Reference numeral 3 denotes a curve line generating device, 14 denotes an interference line dividing device, and 15 denotes an interference line data section.

In the apparatus for calculating an intersection between free-form surfaces, a point which can be an end point of an interference line is registered in advance in an end point table, and it is checked whether or not it can be traced from the obtained point. The convergence calculation is performed so that the point at the end of is on both surfaces. The process of determining the tracking direction and calculating the convergence is repeated until the tracking end condition is satisfied. An intersection between the intersection lines obtained by the processing is obtained, and divided there. Conventional techniques used in carrying out the present invention include a convex hull calculation device for a control point of a free-form surface, a device for calculating an intersection between a free-form surface and a free curve, a device for calculating an interference point inside two free-form surfaces, and coordinates on the free-form surface. A device for calculating a value, a device for calculating a normal vector of a free-form surface, and a device for calculating a partial derivative vector of a free-form surface are used.

The operation of the present apparatus is as follows. The convex hull of the two curved surfaces is obtained by the convex hull calculator 4 of the control points of the free-form surface, and interference between the convex hulls is checked. If the convex hulls do not interfere with each other, the process ends because there is no possibility that the two curved surfaces intersect. A partial device that performs this process is referred to as a convex hull interference inspection device 3. The points obtained by the calculation of the interference between the surface and the line using the intersection calculating device 6 of the free-form surface and the free curve or the calculation of the internal interference points using the interference calculating device 7 inside the two free-form surfaces are registered in the end point table. I do. If no point is registered in the end point table, 2
The process ends because the two faces do not intersect. A partial device that performs this processing is referred to as an interference line tracking start point generation device 5.

In the following description, u [1, i], v
[1, i], r [2, i] and s [2, i] correspond as shown in Table 1.

[0012]

[Table 1]

A tracking direction from each end point of the end point table is determined. For this purpose, the end point table is scanned to determine the direction of the tracking vector v from each end point. Two curved surfaces are S ₁ and S ₂
S _{1 of the} end point Pi registered in the end point table
U [1, i] parameter values in, v [1, i], the parameter value of S ₂ r [2, i], and s [2, i]. Also, S ₁ (u [1, i], calculated using a device for calculating a coordinate value on a free-form surface and a device for calculating a normal vector of the free-form surface
v [1, i]) and S ₂ (r [2, i], s [2,
When the line of intersection of the tangent plane in i]) and L, P _i definitive 2
The direction vector of the curved interference line has the same direction as the straight line L. A partial device that performs this processing is referred to as an interference line tracking direction generation device 8.

From the end point table, a point and a vector having a vector not to be tracked are extracted. This point is represented by P _i (i is an index of the end point table), the parameter values of this point on the surface S ₁ are u [1, i], v [1, i], and the parameter values on the surface S ₂ are r [2, i ], S [2, i]. A partial device that performs this processing is referred to as a tracking start point selecting device 11.
A point on the interference line and a direction vector in each tracking process are obtained. Tracking is performed until the termination condition is satisfied. Using these, a tracking vector is generated by an appropriate length in the direction from P _i to v, and a point on the two surfaces from the end points of the tracking vector is determined by the geometric Newton-Raphson method. Follow up further as a starting point. By repeating this process until the tracking end condition is satisfied, a sequence of points on the interference line between the two curved surfaces is obtained. At this time, the tracking vector at each point is also known at the same time. The shorter the point where the tracking vector has the same direction in this point sequence and each point, and the shorter the point where the direction of the tracking vector changes greatly, the shorter it should be.

The conditions for terminating the tracking are as follows. (1) than the coordinate value P _t point on the trimming edge line in the endpoint P _e and the edge point table tracking vector, shorter than the distance between the two points tracing vector length and vector is set to P _t If so, the tracking vector and that vector point in the same direction. (2) The tip of the tracking vector protrudes from the parameter space of the two curved surfaces. This is when either (1) or (2) is satisfied. A partial device that performs this processing is referred to as an interference line tracking device 12.

A curve sequence is generated from the points on the interference line and the direction vector obtained by the interference line tracking device 12. A partial device that performs this processing is referred to as a curve sequence generating device 13. When a plurality of curve lines are obtained by the curve line generation device 13, an interference point between the curve lines is obtained, and if obtained, an interference line is divided at that point. A partial device that performs this processing is referred to as an interference line dividing device 14. From the convex space interference inspection device 3 to the interference line splitting device 1
The interference lines between the two free-form surfaces can be obtained by sequentially combining the four. FIG. 3 shows the obtained interference line C.
Is shown.

FIG. 2 is a flowchart for explaining the convergence calculation inside the interference line tracking apparatus. step 1: The partial derivative 曲 S ₁ (u _i , v _i ) / of the surface S ₁ at u _i , v _i by the device for calculating the partial derivative vector of the device free curve
_{∂u, ∂S 1 (u i,} v i) / ∂v, and r _i curved S _2, partial derivatives .differential.S ₂ in _{s i (r i, s i} ) / ∂u, ∂S 2 (r _i , s _i ) / ∂v. step2: To find the parameter value on the curved surface at the point at the tip of the tracking vector v,

[0018]

(Equation 1)

By solving the above equation, δu _i , δv _i , δr _i , δs _i are obtained. Thus, the parameter value u ′,
v ', r', s' is u 'Motomeraru by _{= u i + δu i v'} = v i + δv i r '= r i + δr i s' = s i + δs i. Step 3: Coordinate values at u ′, v ′ of the curved surface S ₁ using a device 9 for calculating a coordinate value on the free-form surface, a device 10 for calculating a normal vector of the free-form surface, and a device for calculating a vector of a partial derivative of the free-form surface S ₁ (u ′, v ′), partial derivative ∂S ₁ (u ′, v ′) / ∂u, ∂
S ₁ (u ′, v ′) / ∂v and the tangent plane P ₁ are obtained. Similarly, the coordinate value S ₂ (r ′, s ′) of the curved surface S ₂ at r ′, s ′, the partial derivative ∂S ₂ (r ′, s ′) / ∂r, ∂S ₂ (r ′, s ') / ∂ _s and the tangent plane P ₂ . step 4: If the two tangent planes P ₁ and P ₂ are parallel,
P ′ = (S ₁ (u ′, v ′) + S ₂ (r ′, s ′)) / 2, if not, find the line of intersection of the two planes and S
The midpoint of the point where ₁ (u ′, v ′) and S ₂ (r ′, s ′) are projected is defined as P ′. step5: Assuming that v ₁ = P′−S ₁ (u ′, v ′),

[0020]

(Equation 2)

Is solved to obtain δu ′, δv ′. Similarly, v ₂ =
P′−S ₂ (r ′, s ′)

[0022]

(Equation 3)

Is solved to obtain δr ′ and δs ′. Step 6: If δu ′, δv ′, δr ′, δs ′ are sufficiently small, u ′, v ′, r ′, s ′ indicate parameter values on the interference line, and thus the processing is terminated. Step 7: Update u ', v', r ', s' as follows, and return to step 3. u ′ = u ′ + δu ′ v ′ = v ′ + δv ′ r ′ = r ′ + δr ′ s ′ = s ′ + δs ′

Next, another example of the three-dimensional three-dimensional shape processing method will be described with reference to FIG. In the figure, 21 is free-form surface data, 22 is free curve data, 23 is an interference inspection device, 24
Is a convex hull calculator for control points of a free curve, 25 is a convex hull calculator for control points of a free-form surface, 26 is a rough intersection generator, 27
Is a polyhedron for a free-form surface, 28 is a polyline for a free curve, 29 is a device for calculating an intersection between a plane and a straight line, 30 is an intersection adjuster, 31 is a device for calculating a coordinate value and a derivative on a free-form surface, 32 Is a device for calculating a coordinate value and a derivative on a free curve, and 33 is intersection data.

In an apparatus for calculating an intersection between a free-form surface and a free curve, an approximate intersection is obtained, the obtained approximate intersection is corrected to a more accurate intersection using derivatives of the curved surface and the curve, and this process is repeated. By checking whether the accuracy of the obtained intersection is within the range of an allowable error, an accurate intersection is obtained. Conventional techniques used in implementing this embodiment include a convex hull calculation device for control points of a free curve, a convex hull calculation device for control points of a free-form surface, a polyhedron conversion device for a free-form surface, and a polyline (many lines). A device for calculating the intersection of a plane and a straight line, a device for calculating a coordinate on a free-form surface, a device for calculating a derivative on a free-form surface, a device for calculating a coordinate value on a free-form curve, and a device for calculating a derivative on a free-form curve.

Using these, a device for calculating the intersection of a free-form surface and a free curve has been proposed. This device C ² as an input the free-form surface data continuity (S (u, v)) and C ² continuous free curve data (C (t)), and outputs a seat miscellaneous value of the intersections P ( (FIG. 7). At this time, the processing apparatus of the present invention comprises the following sub-devices.

1. Convex hull calculator 24 for control points of free curve
Is used to obtain the convex hull of the control points of the free curve and the convex hull of the control points of the free curved surface using the convex hull calculator 25, and checks for interference between the two convex hulls and approximates them. An interference inspection device 23 for performing an effective interference check. 2. The free-form surface is converted into a polyhedron using a polyhedron
A free-form surface is converted into a polyline using a polyline forming device 28, and an intersection between a plane and a straight line is calculated using a plane-straight intersection calculating device 29. At the same time, a parameter value on the curved surface of the intersection and a parameter value on the curved surface are calculated. Intersection generator 26. 3. Rough intersection obtained by the rough intersection generator 26,
And an intersection adjustment device 30 that adjusts an accurate intersection using parameter values on the curved surface and the curve.

FIG. 6 is a flowchart for obtaining an accurate value from an approximate point of the intersection in the interior of the intersection adjustment device. Hereinafter, the steps will be sequentially described. The parameter value of the approximate point on the curve P (t) is t ₀ , and the surface S
Let the parameter values at (u, v) be u ₀ and v ₀ (FIG. 5). Step 1: Using the coordinate value calculating device and the derivative calculating device on the free curve, passing through the coordinate value P (t ₀ ) on the free curve, and ΔP (t
₀ ) / Δt is calculated. From this, it passes through P (t ₀ ) and ∂P (t
₀ ) / Ｌt is obtained as a straight line L having a direction vector. Step 2: Coordinate values S (u ₀ , v ₀ ) on the free-form surface and derivatives ∂S using the device for calculating the coordinate values on the free-form surface and the device for calculating the derivative.
(u ₀ , v ₀ ) / ∂u and ∂S (u ₀ , v ₀ ) / ∂v are calculated. This than through the _{S (u 0, v 0)} , ∂S (u 0, v 0) / ∂u × ∂S (u 0, v 0)
A plane P having / ∂v as a normal vector is created. step3: find the intersection to Q ₁ and the plane P and the straight line L with the intersection calculation unit for a planar and straight, Q ₁ from P vector v ₁ from (t ₀₎ to _{Q 1, S (u 0,} v 0) determine the vector v ₂ to. step 4:

[0029]

(Equation 4)

Is solved to obtain δt. step5:

[0031]

(Equation 5)

To solve for δu and δv. step6: When δt, δu, δv are 0, the process is terminated. step7: t ₀ = t ₀ + δt, u ₀ = u ₀ + δu, v ₀ = v ₀ +
Return to step 1 as δv.

An accurate solution is obtained from the approximate values t ₀ , u ₀ , v _{0 of} the intersection by the intersection adjusting device. This method does not depend on the form of a curve or a surface as long as a coordinate value and a differential vector when parameters are given are obtained. FIG. 4 is the same as FIG.
Is determined as one of the methods for obtaining the starting point of.

Next, an embodiment of the three-dimensional three-dimensional shape processing system according to the present invention will be described. This embodiment is positioned as a part of a device for calculating the intersection of a free-form surface and a free curve in FIG. 1 or as one subcontractor. In an intersection calculation device between three curved surfaces, an intersection obtained approximately is obtained as an intersection having more accurate coordinate values irrespective of the type of the curved surface. Conventional techniques used to realize this embodiment include a device for calculating a coordinate value on a free-form surface, a device for calculating a point by projecting a point on an algebraic surface, a device for calculating a normal vector of a surface, and the derivation of a free-form surface. A device for calculating a function vector, a device for calculating an intersection of three planes, and a device for calculating a parameter value of a point on a free-form surface which is the shortest from a designated point are used.

FIG. 8 is a flowchart for explaining the operation of the present apparatus. The input is an approximate value of the intersection of the three curved surfaces and the three curved surfaces obtained by a processing device different from the present device. Let the three curved surfaces be S ₁ , S ₂ , and S ₃ respectively. Also, let P be the intersection of the three approximated curved surfaces. The processing at this time is as follows.

Steps 1 and 2: The coordinate values and parameter values of the point where P is projected onto each curved surface are obtained. At this time, if the surface is an algebraic surface, the coordinates of the point at which P is projected onto the surface are obtained by using a device for calculating a point obtained by projecting the point on the algebraic surface. A parameter value of a point at which P is projected on a curved surface is obtained by using a parameter value calculating device for a point on a certain free-form surface. step 3: A tangent plane at the point projected on the curved surface obtained in the above step is obtained by using a device for calculating a normal vector of the curved surface. step 4: Find the intersection P 'of the three tangent planes. step5,6: The point Pi (i = 1,1) where P 'was projected on the curved surface
2, 3) are obtained for each curved surface. At this time,
If the surface is an algebraic surface, the point P 'is projected onto the surface using a device that calculates the point projected on the algebraic surface. If the surface is a free-form surface, the vector P'-Pi and the partial derivative vector of the free-form surface Using the partial derivative vector of the curved surface obtained using the calculation device,

[0037]

(Equation 6)

Is solved to obtain δui and δvi. This is it
And the parameter value of the point where P 'is projected on the free-form surface is u
i + δui, vi + δvi. step7,8: The distance between the newly obtained points is close enough
If so, end the process. Otherwise, contact at each point
Obtain a plane and return to step 3. FIG. 9 shows three curved surfaces.
In the figure showing the exact intersection, the curved surface S₁And curved surface S_TwoIs L
₁₂, Curved surface S₁And curved surface S_ThreeIs L₁₃, Curved surface S_TwoAnd curved surface
S_ThreeIs L_{twenty three}It is.

Next, still another embodiment of the three-dimensional three-dimensional shape processing system according to the present invention will be described. In this example,
It is positioned as a subsequent process of the interference point calculation device inside the two free-form surfaces at the time of registration of the end point of the interference line tracking start point generation device in FIG. In obtaining the parameter value of a point on a free-form surface, it is not necessary for the point to be exactly on the surface, regardless of the type of the surface. As a conventional technique used to realize this embodiment, a device for converting a free-form surface into a polyhedron, a device for projecting points on a plane, a device for obtaining a partial derivative of a curved surface, and a device for calculating a normal vector of a curved surface are used.

FIG. 10 is a block diagram of this embodiment.
41 is free-form surface data, point data, 42 is a rough parameter value generating device, 43 is a rough parameter value adjusting device, 44
Is a parameter value generation unit on a free-form surface of a point. The free-form surface data S and the point P are input, and the parameter value of the point P in the free-form surface data S is output. When the point P is not exactly on the curved surface, the parameter value of the point obtained by projecting the point P on the curved surface is output. FIGS. 13A and 13B show this state. A free-form surface S in a three-dimensional space and a coordinate value P of a point are input. The parameter value of the point P on the curved surface S is output. When the point P is not on the curved surface S, the parameter value of the point P ′ obtained by projecting the point P on the curved surface S is output.

First, in the rough parameter value generator 42, an approximate parameter value on a curved surface of a point is obtained. Next, the rough parameter value adjusting device 43 converts the approximate parameter value obtained by the rough parameter value generating device 42 into an accurate parameter value.

FIG. 11 is a flowchart for explaining the operation of the rough parameter value generating device. Hereinafter, the steps will be sequentially described. step 1: Input free-form surface data and point data. Step 2: The polyhedron of the curved surface is performed using a device for polyhedralizing the free-form surface. step 3: Obtain a polyhedral surface (polygon) near the point. step 4: When making a polyhedron, parameters are held at the end points of each surface. That is, the approximate parameter value of the point is obtained from the parameter value of the polygon end point. step 5: Approximately obtain a parameter value on the curved surface of the point using an apparatus for projecting the point on a plane.

FIG. 12 is a flowchart for explaining the operation of the rough parameter value adjusting device. Hereinafter, the steps will be sequentially described. Step 1 and 2: From the parameter values u ₀ and v ₀ on the approximate surface obtained by the rough parameter value generation device, calculate the tangent plane of the surface S at the parameter value using the device for calculating the normal vector of the surface. I do. step 3: A point P is projected onto the tangent plane using a device for projecting the point onto the plane to obtain P ′. step 4: The derivative is obtained from the device for calculating the normal vector of the curved surface, and the following equations are solved to obtain δu and δv.

[0044]

(Equation 7)

Steps 5-7: If δu and δv are sufficiently small, the processing is terminated. Otherwise, u ₀ = u ₀ + δu v ₀ = v ₀ + δv and return to step 2.

FIG. 14 shows a curved surface S₁(u, v) and surface S_Two(r, s)
Intersection P₁It is a figure for explaining how to ask for. Interference line C_t
The parameter value t at₀And the curved surface S₁(u, v)
Parameter value u ₀, v₀At intersection P₁Is specified. This intersection P
₁From curved surface S_TwoParameter value r in (r, s)₀, S₀Seeking
Round. That is, the intersection P₁Is the curved surface S₁(u, v)
Parameter value u₀, v₀And the curved surface S_Twopara in (r, s)
Meter value r₀, S₀Will have. Therefore
P₁Can be obtained.

As is apparent from the above description, according to the present invention, the type of freedom curved, it is possible to find the intersection of three free-form surface regardless of the order. Thus, in the set operation between the solids, the coordinates of the end point can be set to an accurate value when obtaining the interference line between the curved surfaces.

[Brief description of the drawings]

FIG. 1 is a configuration diagram for explaining an example of a three-dimensional three-dimensional shape processing method.

FIG. 2 is a flowchart for explaining a convergence calculation inside the interference line straight-line device.

FIG. 3 is a diagram showing an interference line obtained in the configuration diagram of FIG. 1;

FIG. 4 is a diagram showing another example of a three-dimensional three-dimensional shape processing method.

FIG. 5 is an explanatory diagram for obtaining an accurate intersection from an approximate point of the intersection.

FIG. 6 is a flowchart for obtaining an accurate intersection from an approximate point of the intersection inside the intersection adjustment device.

FIG. 7 is a diagram illustrating an intersection of a free-form surface and a free curve.

FIG. 8 is a flowchart illustrating an example of a three-dimensional three-dimensional shape processing method according to the present invention.

FIG. 9 is a diagram showing accurate intersections of three curved surfaces.

FIG. 10 is a diagram showing another example of the three-dimensional three-dimensional shape processing method according to the present invention.

FIG. 11 is a flowchart for explaining the operation of the rough parameter value generation device.

FIG. 12 is a flowchart for explaining the operation of the rough parameter value adjusting device.

FIG. 13 is a diagram showing an output of parameter values of a point obtained by projecting a point P on a curved surface.

14 is a diagram for curved S ₁ to (u, v) and the curved surface S ₂ (r, s) how to determine the intersection point P ₁ will be described.

[Explanation of symbols]

1 free-form surface data, 2 free-form surface data, 3 inter-convex hull interference inspection device, 4 free-form surface and control point convex hull calculation device,
5 ... Interference line tracking start point generation device, 6 ... Intersection calculation device between free curved surface and free curve, 7 ... Interference point calculation device inside two free curved surfaces, 8 ... Interference line tracking direction generation device, 9 ... On free curved surface Calculating device for coordinate values of 10; normal vector calculating device for free-form surface; 11 tracking start point selecting device; 12 interference line tracking device; 13 curve line generating device; 14 interference line dividing device; Line data section.

──────────────────────────────────────────────────続 き Continued on front page (58) Field surveyed (Int.Cl. ⁷ , DB name) G06F 17/50 626

Claims (2)

(57) [Claims] 1. A parameter value generating means for calculating coordinate values and parameter values of points at which an approximate point of an intersection of three curved surfaces is projected on each curved surface, and a tangent plane at each of the projected points on each curved surface being a method of the curved surface. a tangent plane producing means for determining using a linear vector, and the intersection generating means for obtaining an intersection of the resultant tangential plane by該接plane generating means, determined Mel a point obtained through projection of the intersection of the tangent plane on the respective curved three-dimensional shape processing method according to claim Rukoto and a projection point generating means. 2. The method according to claim 1, further comprising the step of :
Based on the distance from the point projected on each curved surface by the projection point generation means.
The intersections obtained by the intersection generation means are
Wherein the intersection is determined to be the intersection of the curved surfaces.
3. The three-dimensional solid shape processing method according to 1.