JP3019283B2 - Curved boundary condition generator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a boundary condition used for generating a curved surface that is smoothly connected to an adjacent curved surface in the field of shape processing such as computer-aided design (CAD) and computer-aided production (CAM). Regarding generation.

[0002]

2. Description of the Related Art Generally, when calculating a boundary crossing vector, a boundary portion of a region where a curved surface is to be interpolated (hereinafter referred to as an interpolated region) is defined by a curved surface (FIG. 1).
0 (a)), the boundary crossing vector of the curved surface is extracted as it is, and is taken as the boundary crossing vector of the interpolation area. When the surface is a surface defined by control vertices such as a Bezier surface, a boundary traversal vector is given by a control vertex sequence representing a boundary curve portion and a control vertex sequence connected to the boundary curve portion in a transverse direction. be able to.

Also, the boundary of the interpolation area is given by a curve.
(See Figure 10 (b))
Published by Hiroshi Toritani and Hiroaki Chiyokura, "Basics of 3D CAD"
And applications, as described in
Expression i (v) ∂S representing tangent plane continuity condition_b(0, v) / ∂u = k (v) ∂S
_a(0, v) / ∂u + h (v) ∂S_a(0, v) / ∂v (where i (v), k (v) and h (v) are parameters of v
Scalar function)
It was common to seek torr. At that time,
As the numbers, the following linear functions are used.

[0004] i (v) = 1 k ( v) = k 0 (1-v) + k 1 v h (v) = h 0 (1-v) + h 1 v _{Here, k 0, k 1, h} 0 , H ₁ represents an arbitrary scalar constant.

In this method, a Bezier curve is used as a boundary curve, and scalar constants k ₀ , k ₁ , h ₀ , and h ₁ are used as control vertices (a 0, b 0, and b 0 in FIG. 10B) connected to both end points of the boundary curve. c0 and a3, b3, c2).

[0006]

However, in the above-mentioned conventional method, the curve net and the curved surface for obtaining the boundary crossing vector are limited to a specific curved surface formula, for example, a curved surface formula such as a Bezier curve / curved surface. However, it cannot be applied to general parametric curves / surfaces.

Further, when the boundary condition is a curved surface, the boundary traversing vector of the curved surface is set as it is as the boundary traversing vector of the interpolation region, so that the boundary traversing vector does not well represent the shape of the interpolation region. (See FIG. 11A)
However, there is a problem that a distorted shape is generated.

Further, when the boundary condition is given as a curved net, the amount of change of the traversing vector is given by a scalar function, so that a boundary traversing vector that matches the shape of the interpolation area can be obtained more than in the case of a curved surface. The scalar function used is a linear function, and the scalar constant representing the way of changing the crossing vector is determined only by the control vertices connected to both ends of the boundary curve, and can be completely expressed by the control vertices connected to both ends. With respect to a non-existent shape (see FIG. 11B), there is a problem that a distorted shape is generated as in the case of a curved surface.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a curved surface boundary condition generating apparatus capable of calculating a boundary crossing vector from a general parametric curve / surface and calculating a boundary crossing vector reflecting the shape of an area to be interpolated. .

[0010]

SUMMARY OF THE INVENTION An object of the present invention is to provide a boundary condition setting means for setting a designated curve / curved surface as a boundary condition of a surface to be interpolated, and a boundary condition set by the boundary condition setting means. Boundary curve approximation calculation means for approximating a curve, reference curve calculation means for calculating a reference curve giving the direction of a boundary crossing vector based on the boundary curve obtained by the boundary curve approximation calculation means , and boundary curve approximation calculation means so
This is achieved by a curved surface boundary condition generation device including: a boundary crossing vector approximation calculating unit that approximately calculates a boundary crossing vector using the obtained boundary curve and the reference curve obtained by the reference curve calculating unit. .

[0011]

In the curved boundary condition generating apparatus according to the present invention, the boundary condition setting means receives a curve or a ridge line of the curved surface representing a boundary portion of the interpolation area or a part thereof, and determines the type of the input element. The boundary curve approximation calculating means calculates a boundary curve from the set boundary conditions using an approximate method, and the reference curve calculating means uses the calculated boundary curve together with the boundary curve. A reference curve giving the direction of the boundary crossing vector is calculated, and the boundary crossing vector approximation calculating means sets a difference vector between the reference curve and the boundary curve on a plane defined by a normal vector of a curved surface having boundary conditions on the boundary curve. Projection is performed to calculate the boundary crossing vector.

[0012]

EXAMPLES The following curved surface boundary conditions of the present invention with reference to the accompanying drawings
An embodiment of the case generation device will be described.

FIG. 1 shows a configuration of an embodiment of a curved surface boundary condition generating apparatus according to the present invention.

The apparatus for generating boundary conditions of a curved surface shown in FIG.
An input unit 10 for inputting a curve and a curved surface surrounding an interpolation area selected by using a system or the like, connected to the input unit 10 and connected to a control unit 11 for controlling each of units 12 to 15 described below, and a control unit 11 A boundary condition setting unit 12 that sets a curve representing a boundary portion of the interpolation region and a boundary surface of a region into which a curved surface is to be interpolated, and a boundary curve approximation calculation unit that is connected to the control unit 11 and calculates the boundary curve by approximation. 13. a reference curve calculation unit 14, which is connected to the control unit 11 and calculates a reference curve used when calculating the boundary crossing vector;
A boundary crossing vector approximation calculating unit 15 connected to the control unit 11 for calculating the boundary crossing vector by approximation; an output connected to the control unit 11 for outputting the boundary crossing vector to a processing unit (not shown) such as a CAD system; It is constituted by a unit 16.

Next, referring to the flowchart of FIG.
The processing operation of the curved surface boundary condition generating device of FIG. 1 will be described.

First, an input unit 10 connected to a processing unit such as a CAD system inputs a curve and a curved surface surrounding an interpolation area selected using a CAD system or the like.

The curves and surfaces input to the input unit 10 are as follows:
The data is sent to the boundary condition setting unit 12 via the control unit 11.

The boundary condition setting section 12 sets a boundary condition (step S1). There are three types of boundary conditions set by the boundary condition setting unit 12, namely, (a) a boundary ridge line of a curved surface, (b) a curve, and (c) a degenerate ridge line (a zero-length ridge line). The set boundary conditions are sent to the boundary curve approximation calculation unit 13 via the control unit 11.

The boundary curve approximation calculation unit 13 generates a boundary curve of the interpolation area according to the boundary condition by using an approximation method described later (step S2). The boundary curve calculated by the boundary curve approximation calculation unit 13 is sent to the reference curve calculation unit 14 via the control unit 11 together with the boundary conditions.

The reference curve calculation unit 14 calculates a reference curve giving the direction of the boundary crossing vector using the input boundary curve (step S3). The reference curve calculated by the reference curve calculation unit 14 is sent to the cross-boundary vector approximation calculation unit 15 together with the boundary condition and the boundary curve.

The cross-boundary vector approximation calculation unit 15 calculates a cross-boundary vector by an approximation method described later using the input boundary condition, boundary curve, and reference curve (step S4). The boundary traversing vector calculated by the boundary traversing vector approximation calculating unit 15 is output to the output unit 1 via the control unit 11.
6 and output by the output unit 16 to a processing unit such as a CAD system.

Next, steps S2 (calculation of a boundary curve), step S3 (calculation of a reference curve) and step S2 are performed.
4 (calculation of a cross-boundary vector) will be described in detail.

First, the calculation process of the boundary curve will be described with reference to the flowchart of FIG.

The tangent vectors at both ends of the curve given by the boundary conditions set by the boundary condition setting unit 12 are obtained (step S201). The curve given by the boundary condition is a boundary ridgeline or a curve of a curved surface. Next, the curve given by the boundary condition is divided into a point sequence group by an arbitrary number of divisions (step S2).
02). A part of the point sequence group becomes a passing point of the boundary curve.
A boundary curve is generated by approximating the group of points obtained in step S202 with a parametric curve (step S203). Here, a cubic B-Spline curve is used as a curve expression representing the boundary curve.

As a method of approximating a point sequence group by a cubic B-Spline curve, a method disclosed in Japanese Patent Application Laid-Open No. 4-143919 is used.

Further, the cubic B-Spline curve is shown in "Shape Processing Engineering by Computer Display [II]" by Fujio Yamaguchi, published by Nikkan Kogyo Shimbun, based on the tangent vector and the passing point obtained in step S201. Generate using the method.

When the boundary conditions facing the present processing unit are input simultaneously, the curves given by these two boundary conditions are simultaneously calculated using the method described in Japanese Patent Laid-Open No. 4-143919. The simultaneous determination can generate a B-Spline curve with a small number of passing points and eliminates the process of aligning knots required when generating a curved surface from a plurality of B-Spline curves.

FIGS. 4, 5 (a), 5 (b) and 5
An arrangement example of the boundary condition shown in (c) and BS shown in FIG.
The calculation process of the reference curve will be described in detail using the control vertices of the plane surface.

If the boundary curves obtained by the boundary curve approximation calculation unit 13 are two curves facing each other as shown in FIG. 4, the boundary curves of the other are set as their own reference curves.

The boundary conditions include two closed boundary curves as shown in FIG. 5A, three closed boundary curves as shown in FIG. 5B, and FIG. 5C. In the case of four closed boundary curves, the reference curve is calculated as follows.

When there are two boundary curves, the degenerate cubic B-Spl is added to the vertices where the boundary curves are connected to each other.
An ine curve (a curve in which all control vertices are at the same vertex position) is generated.

When there are three boundary curves, a cubic B-Spline curve degenerated at any one of the vertices is similarly generated.

By newly generating and adding a degenerate edge line as described above, the case where the number of boundary curves is two or three can be handled by the same processing as the case where the number of boundary curves is four.

If there are four boundary curves, a cubic B-Spline surface is first generated using the boundary curves. The generation method is described in G. The bilinear or bicubic Koons blend described in "Practical Usage of Curve and Surface Theory for CAGD" by Farin, edited by Fumihiko Kimura and Yasushi Yamaguchi, Kyoritsu Shuppan Co., Ltd. By performing this, the control vertex of the B-Spline curved surface can be obtained.

A control vertex row adjacent to the control vertices of the B-Spline surface shown in FIG. 6 in parallel with each boundary surface shown by a thick line in the drawing is extracted. A cubic B-Spline curve having this control vertex sequence is set as a reference curve.

Next, referring to the flowchart of FIG. 7, the process of calculating the approximation of the crossing boundary vector will be described in detail.

First, tangent vectors at both ends of the boundary curve are obtained (step S401). Next, the above step S20
A vector representing the boundary traversing vector of the point sequence group point obtained in step 2 is calculated using the boundary curve and the reference curve (step S).
402).

Here, the process of calculating the boundary crossing vector will be described with reference to the flowchart of FIG.

First, a vector at each point in the sequence of points of the boundary crossing vector function defined by the boundary curve and the reference curve is obtained (step S421). The curves / surfaces generated in the present embodiment all have BS at the both ends having the multiplicity of the rank.
Since the function is represented by a plane curve / surface, a function representing a boundary traversing vector is a B-Spline having a difference vector between a control vertex of the boundary curve and a reference curve as a control vertex.
Can be defined as a curve. Next, a plane is defined by obtaining a normal vector of a curved surface as a boundary condition of each point sequence point (step S422), and a projection direction vector of each point sequence point is determined (step S423). This corresponds to step S421 described above.
The cross product vector between the vector of each point obtained in the above and the tangent vector of the boundary curve at the point is given as the projection direction vector. Then, the vector obtained in step S421 is projected onto the plane obtained in step S422 with the projection direction as the projection vector obtained in step S422 (step S424). This projected vector is a cross-boundary vector of the interpolated curve at each point sequence point.

Here, referring again to FIG.
The processing shifts to 403. However, if the boundary condition is a curve or a degenerate ridge line, the process proceeds to step S403 without performing the process shown in FIG.

Next, in step S403, the passing point of the input boundary curve is set to a B-Sp
It is registered in the point sequence list as the initial point of passage (that is, knot) of the line curve. Based on the point sequence list generated in step S403, a cross-boundary vector is approximately obtained by a convergence method (step S404). Since the boundary crossing vector to be obtained is given by two B-Spline curves (one of which represents a boundary curve), as described in the description of the step S421, the step S421 is performed.
The cross-boundary vector created in 404 is two B-
It is a Spline curve.

Next, referring to the flowchart of FIG.
The above-described boundary crossing vector calculation processing in step S404 will be described in detail. However, if the boundary condition is a curve or a degenerate ridge line, the following processing is not performed. In this case, the curve finally output is only the boundary curve.

First, a cubic B-Spline curve is generated which interpolates the passing points stored in the point sequence list as the tangent vectors obtained at step 401 at both end points (step S441). Here, as the interpolation method, a method described in "Shape processing engineering by computer display [II]" by Fujio Yamaguchi, published by Nikkan Kogyo Shimbun, Ltd. is used. Finally, this curve becomes the boundary curve. Hereinafter, this curve is represented as “wire”.

A cubic B for interpolating the vector of the point point stored in the point sequence list, which is obtained in step S402 above.
-Generate a Spline curve (step S442).
As the interpolation method, a method similarly described in “Shape processing engineering by computer display [II]” is used. Hereinafter, this curve is represented as bdwire.

Next, the values of wire and bdwire at the middle point between the point sequences stored in the point sequence list and the curved surface as the boundary condition of the point are evaluated (step S4).
43). From the wire, the coordinate value of the point (hereinafter, p
os) and a tangent vector (hereafter referred to as tvec), bdvec gives a cross-boundary vector at that point (hereafter referred to as bdvec), and
A normal vector (hereinafter referred to as nrm) is obtained from the curved surface.

An outer product vector of tvec and bdvec is obtained, and it is checked whether or not this vector and nrm face the same direction within a certain threshold (step S444). If they are not in the same direction, pos is inserted into the point sequence list (step S445), and the process proceeds to step S446 described later. If it is determined in step S444 that the orientation is the same, the process proceeds to step S446 described later.

It is checked whether or not the accuracy of all the normal vectors of all the points existing in the point sequence list is satisfied (step S446). If they are satisfied, the process ends. If they are not all satisfied, the process returns to step S441.

With the configuration described above, the curved surface boundary condition generating apparatus of the present invention is not limited to a particular curve / curved surface as a curve / curved surface used as a boundary condition. The present invention can be applied to any curve / surface as long as it can perform general parametric curves / surfaces, and therefore can be used in any CAD system. Further, the boundary crossing vector generated by the curved boundary condition generating device of the present invention is:
Since this is a B-Spline curve, this curve equation is an industry standard expression in this field.
Good compatibility with CAD systems. Since the rationality of the generated curve is also irrational and the order is tertiary, there is no problem of the complexity of the process by the rational expression or the instability of the process by the higher order.

[0049]

The boundary condition generating apparatus for a curved surface according to the present invention comprises a boundary condition setting means for setting a designated curve / surface as a boundary condition of a surface to be interpolated, and a boundary condition set by the boundary condition setting means. Boundary curve approximation calculating means for approximating a boundary curve, reference curve calculating means for calculating a reference curve giving the direction of a boundary crossing vector based on the boundary curve obtained by the boundary curve approximation calculating means, and boundary curve approximation calculation hand
A boundary curve obtained in stage, using a reference curve obtained with the reference curve calculation unit, since a cross-boundary vector approximation calculating means for approximating calculating the cross-boundary vector, the orientation of the cross-boundary vectors decide when, because of the use of reference curve can be generated cross-boundary vector reflecting the better of the inner挿領zone shape. As a result, a smoother curved surface can be generated.

[Brief description of the drawings]

FIG. 1 is a block diagram showing the configuration of an embodiment of a curved surface boundary condition generating apparatus according to the present invention.

FIG. 2 is a flowchart for explaining the operation of the curved surface boundary condition generation device of FIG. 1;

FIG. 3 is a flowchart for explaining the operation of a boundary curve approximation calculation unit in FIG. 1;

FIG. 4 is an explanatory diagram of an arrangement of two boundary curves in a three-dimensional space.

FIG. 5 is an explanatory diagram of an arrangement of a closed boundary curve in a three-dimensional space.

FIG. 6 is an explanatory diagram of a reference curve calculation unit in FIG. 1;

FIG. 7 is a flowchart for explaining the operation of a cross-boundary vector approximation calculation unit in FIG. 1;

FIG. 8 is a flowchart for explaining a boundary crossing vector calculation process.

FIG. 9 is a flowchart illustrating a process of calculating a boundary crossing vector.

FIG. 10 is an explanatory diagram of conventional generation of a boundary crossing vector.

FIG. 11 is an explanatory diagram of a problem of the conventional method.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 Input part 11 Control part 12 Boundary condition setting part 13 Boundary curve approximation calculation part 14 Reference curve calculation part 15 Boundary crossing vector approximation calculation part 16 Output part

────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP-A-4-344984 (JP, A) JP-A-4-57172 (JP, A) JP-A-5-35826 (JP, A) Lecture by Japan Society for Design Engineering Transactions No. 93-Spring 53-56 Naoshi Morisue et al. "A B-spline surface approximation conversion method for parametric surfaces" (58) Fields investigated (Int. Cl. ⁷ , DB name) G06T 17/00 JICST file (JOIS)

Claims (1)

(57) [Claims] 1. An area surrounded by a plurality of curves and curved surfaces,
A boundary condition generation device for a surface used in a surface generation device for interpolating a surface satisfying continuity at a boundary portion, wherein a boundary condition setting in which a specified curve / surface is set as a boundary condition of a surface to be interpolated. Means, a boundary curve approximation calculation means for approximating a boundary curve from the boundary conditions set by the boundary condition setting means, and a boundary crossing vector based on the boundary curve obtained by the boundary curve approximation calculation means . Reference curve calculation means for calculating a reference curve giving a direction, and the boundary curve obtained by the boundary curve approximation calculation means,
Using said reference curve obtained with the reference curve calculation means
And a boundary crossing vector approximation calculating means for approximately calculating a crossing boundary vector.