JPH06348792A - Boundary condition generator for curved surface - Google Patents

Abstract

PURPOSE:To provide a boundary condition generator for a curved surface capable of both calculating a boundary traverse vector from a general parametric curve/curved surface and calculating the boundary traverse vector on which the shape of an area to be interpolated is reflected. CONSTITUTION:This generator is equipped with a boundary condition setting part 12 which sets a designated curve/curved surface as the boundary condition of a curved surface to be interpolated, a boundary curve approximate calculation part 13 which calculates by approximating a boundary curve from the boundary condition set by the boundary condition setting part, a reference curve calculation part 14 which calculates a reference curve based on the boundary curve obtained by the boundary curve approximate calculation part, and a boundary traverse vector approximate calculation part 15 which calculates by approximating the boundary traverse vector by referring to the reference curve obtained by the reference curve calculation part.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to boundary conditions used in generating curved surfaces smoothly connected to adjacent curved surfaces 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 a boundary crossing vector is calculated, a boundary portion of a region where a curved surface is to be interpolated (hereinafter referred to as an interpolation region) is defined by the curved surface (see FIG. 1).
For 0 (a), the boundary crossing vector of the curved surface is taken out as it is and is used as the boundary crossing vector of the interpolation area. When the curved surface is a curved surface defined by control vertices, such as a Bezier surface, the boundary crossing vector is given by the control vertex string representing the boundary curve part and the control vertex string connected in the cross direction to the boundary curve part. be able to.

Also, the boundary part of the interpolation area is given by a curve.
If it is (see Figure 10 (b)), Kyoritsu Publishing Stock Association
Published by Hiroshi Toriya, Hiroaki Chiyokura, "The basics of 3D CAD"
On the boundary curve as described in
Expression expressing tangential plane continuity condition i (v) ∂S_b(0, v) / ∂u = k (v) ∂S
_a(0, v) / ∂u + h (v) ∂S_a(0, v) / ∂v (However, i (v), k (v), h (v) are parameters of v
, Which represents the scalar function
It was common to ask for Tor. At that time, the scalar function
As the number, the following linear function is used.

I (v) = 1 k (v) = k ₀ (1-v) + k ₁ v h (v) = h ₀ (1-v) + h ₁ v where 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 , h ₁ are control vertices connected to both end points of the boundary curve (a0, b0, in FIG. 10B). c0 and a3, b3, c2).

[0006]

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

When the boundary condition is a curved surface, the boundary crossing vector of the curved surface is directly set as the boundary crossing vector of the interpolation area. Therefore, when the boundary crossing vector does not well represent the shape of the interpolation area. (See FIG. 11 (a))
Has a problem that a distorted shape is generated.

Further, when the boundary condition is given as a curved net, the change amount of the crossing vector is given by the scalar function, so that the boundary crossing vector more suited to the shape of the interpolation area can be obtained than when the curved surface is used. The scalar function used is a linear function, and since the scalar constant that expresses the way the crossing vector changes is determined only by the control vertices connected to the endpoints of the boundary curve, it cannot be represented by the control vertices connected to the endpoints. As for the non-existent shape (see FIG. 11B), there is a problem that a distorted shape is generated as in the case of the curved surface.

An object of the present invention is to provide a boundary condition generating device for a curved surface, which can calculate the boundary crossing vector from a general parametric curve / curved surface and can calculate the boundary crossing vector reflecting the shape of the area to be interpolated. .

[0010]

SUMMARY OF THE INVENTION An object of the present invention is to set boundary condition setting means for setting a specified curve / curved surface as a boundary condition of a curved surface to be interpolated, and boundary conditions 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 based on the boundary curve obtained by the boundary curve approximation calculation means, and reference curve obtained by the reference curve calculation means And a boundary boundary vector approximating means for approximating and calculating a boundary boundary vector.

[0011]

In the boundary crossing vector approximation generator of the present invention,
The boundary condition setting means inputs a curved line or a ridgeline of a curved surface or a part thereof on the space representing the boundary portion of the interpolation area, sets the boundary condition according to the type of the input element, and the boundary curve approximation calculating means A boundary curve is calculated from the set boundary conditions by using an approximate method, and the reference curve calculation means calculates a reference curve that gives the direction of the boundary crossing vector together with the boundary curve using the calculated boundary curve, The crossing vector approximation calculating means calculates the boundary crossing vector by projecting the difference vector between the reference curve and the boundary curve onto a plane defined by the normal vector of the curved surface of the boundary condition on the boundary curve.

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the boundary crossing vector approximation generation device of the present invention will be described below with reference to the drawings.

FIG. 1 shows the configuration of an embodiment of the boundary crossing vector approximation generation device of the present invention.

The boundary crossing vector approximation generation device of FIG.
An input unit 10 for inputting a curved line and a curved surface surrounding an interpolation area selected by using a CAD system or the like, and a control unit 1 connected to the input unit 10 and controlling each unit 12 to 15 described later.
1. A boundary condition setting unit 12, which is connected to the control unit 11 and which sets the boundary condition of a curve and a curved surface that represents the boundary portion of the interpolation region, and a boundary condition which is connected to the control unit 11 and approximates the boundary curve. Boundary curve approximation calculation unit 1 calculated by
3. Reference curve calculation unit 14 connected to the control unit 11 for calculating a reference curve used when calculating the boundary crossing vector, boundary crossing connected to the control unit 11 for calculating the boundary crossing vector by approximation Vector approximation calculator 1
5. The output unit 16 is connected to the control unit 11 and outputs the boundary crossing vector to a processing unit (not shown) such as a CAD system.

Next, referring to the flowchart of FIG.
The processing operation of the boundary crossing vector approximation generation device in FIG. 1 will be described.

First, the 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 by using the CAD system or the like.

The curves and curved surfaces input to the input unit 10 are
It is sent to the boundary condition setting unit 12 via the control unit 11.

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

The boundary curve approximation calculating 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 calculating unit 13 is sent to the reference curve calculating unit 14 via the control unit 11 together with the boundary condition.

The reference curve calculation unit 14 uses the input boundary curve to calculate a reference curve that gives the direction of the boundary crossing vector (step S3). The reference curve calculated by the reference curve calculation unit 14 is sent to the boundary crossing vector approximation calculation unit 15 together with the boundary condition and the boundary curve.

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

Next, each of the above steps S2 (calculation of the boundary curve), step S3 (calculation of the reference curve) and step S
Each processing of 4 (calculation of boundary crossing vector) will be described in detail.

First, the boundary curve calculation processing 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 edge or a curve of a curved surface. Next, the curve given by the boundary condition is divided into a point sequence group with an arbitrary division number (step S2).
02). A part of this point sequence group becomes a passing point of the boundary curve.
A boundary curve is generated by approximating the point sequence group obtained in step S202 by a parametric curve (step S203). Here, a cubic B-Spline curve is used as the curve expression representing the boundary curve.

As a method for approximating the point sequence group by a cubic B-Spline curve, the method disclosed in Japanese Patent Laid-Open No. 143919/1992 is used.

The cubic B-Spline curve is shown in "Shape engineering [II] by computer display [II]" by Fujio Yamaguchi, published by Nikkan Kogyo Shimbun, from the tangent vector and passing point obtained in step S201. Generate using the method.

When the boundary conditions facing the present processing unit are simultaneously input, the curves given by these two boundary conditions are calculated at the same time by using the method disclosed in Japanese Patent Laid-Open No. 143919/1992. In this way, it is possible to generate a B-Spline curve with a small number of passing points by the simultaneous determination, and the process of aligning the knots required when generating a curved surface from a plurality of B-Spline curves becomes unnecessary.

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

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

The boundary conditions are two closed boundary curves as shown in FIG. 5 (a), three closed boundary curves as shown in FIG. 5 (b), and as shown in FIG. 5 (c). In the case of four boundary curves closed at 1, the reference curve is calculated as follows.

When there are two boundary curves, the degenerate cubic B-Spl is formed at the vertex 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 B-Spline curve of third order degenerated at any one of the vertices is similarly generated.

By newly generating and adding the degenerate ridge lines as described above, when the number of boundary curves is two and three, the same processing as in the case of four boundary curves can be handled thereafter.

When there are four boundary curves, first, a cubic B-Spline curved surface is generated using the boundary curves. The generation method is as described in G. Farin, supervised by Fumihiko Kimura, translated by Yasushi Yamaguchi, published by Kyoritsu Shuppan Co., Ltd., "Practical Usage of Curve / Surface Theory for CAGD". By applying it, the control vertex of the B-Spline curved surface can be obtained.

A control vertex row of control vertices of the B-Spline curved surface shown in FIG. 6 which are adjacent to each other in parallel with the respective boundary curved surfaces indicated by thick lines in the drawing is taken out. A cubic B-Spline curve having this control vertex array is used as a reference curve.

Next, the boundary crossing vector approximation calculation processing will be described in detail with reference to the flowchart of FIG.

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

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

First, the vector of each point sequence point of the boundary crossing vector function defined by the boundary curve and the reference curve is obtained (step S421). All the curves / curved surfaces generated in this embodiment have BS with multiplicity equal to the number of orders at both ends.
Since it is defined by the pline curve / curved surface, the function expressing the boundary crossing vector has a B-Spline having a difference vector between the control vertices of the boundary curve and the reference curve as a control vertex.
It can be defined as a curve. Next, the normal vector of the curved surface, which is the boundary condition of each point sequence point, is obtained to define the plane (step S422), and the projection direction vector of each point sequence point is obtained (step S423). This is the above step S421.
The outer product vector between the vector of each point and the tangent vector of the boundary curve at that point is given as this projection direction vector. The vector obtained in step S421 is projected on the plane obtained in step S422 as the projection vector obtained in step S422 (step S424). This projected vector becomes the boundary crossing vector of the curve to be interpolated at each point sequence point.

Now, referring again to FIG. 7, step S
The processing shifts to 403. However, if the boundary condition is a curve or a degenerate ridgeline, 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 represented by B-Sp representing the boundary crossing vector.
It is registered in the point sequence list as an initial point of passage (that is, knot) of the line curve. Based on the point sequence list generated in step S403, the boundary crossing vector is approximately obtained by the 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 above, step S421
The boundary crossing vector created in 404 is two B-
It is a Spline curve.

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

First, a cubic B-Spline curve that interpolates the passing points stored in the point sequence list as the tangent vectors obtained at step 401 using the vectors of both end points is generated (step S441). Here, as the interpolation method, the method described in "Shape Processing Engineering by Computer Display [II]" by Fujio Yamaguchi, published by Nikkan Kogyo Shimbun, is used. Finally, this curve becomes the boundary curve. Hereinafter, this curve will be referred to as wire.

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

Next, the values of wire and bdwire at the center point between the point sequences stored in the point sequence list and the curved surface which is 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 (hereinafter tvec), a boundary crossing vector (hereinafter bdvec) at that point is obtained from 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 this vector and nrm are in the same direction within a certain threshold value (step S444). If they are not in the same direction, pos is inserted in the point sequence list (step S445), and the process proceeds to step S446 described later. If the same direction is determined in step S444, the process proceeds to step S446 described later.

It is checked whether or not the accuracy of the normal vector of all the points existing in the point sequence list is satisfied (step S446). If satisfied, the process is terminated, and if not satisfied, the process returns to step S441.

Since the curved boundary condition generating device of the present invention is configured as described above, the curve / curved surface used as the boundary condition is not limited to a particular special curved surface / curved surface, and therefore evaluation is performed by parameters. It can be applied to any curve / curved surface as long as it is a general parametric curve / curved surface that can be used, and therefore can be used in any CAD system. Further, the boundary crossing vector generated by the curved surface boundary condition generation device of the present invention is
Since it is a B-Spline curve, this curve equation is an industry standard expression in this field, and thus,
Good compatibility with CAD system. Since the rationality of the generated curve is also unrational and the order is cubic, there is no problem of complexity of processing by rational expression and instability of processing by higher order.

[0049]

EFFECT OF THE INVENTION The boundary condition generating device for a curved surface according to the present invention comprises a boundary condition setting means for setting a designated curve / curved surface as a boundary condition for an interpolated curved surface, 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 based on the boundary curve obtained by the boundary curve approximating means,
Since the boundary crossing vector approximation calculating means for approximating the boundary crossing vector with reference to the reference curve obtained by the reference curve calculating means is provided, the reference curve is used when determining the direction of the boundary crossing vector. A boundary crossing vector that better reflects the shape of the interpolation area can be generated. As a result, a smoother curved surface can be generated.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of an embodiment of a curved surface boundary condition generation device of the present invention.

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

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

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 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.

FIG. 7 is a flowchart for explaining the operation of the boundary crossing vector approximation calculation unit in FIG.

FIG. 8 is a flowchart illustrating a boundary crossing vector calculation process.

FIG. 9 is a flowchart illustrating a boundary crossing vector calculation process.

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

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

[Explanation of symbols]

 10 Input Section 11 Control Section 12 Boundary Condition Setting Section 13 Boundary Curve Approximation Calculation Section 14 Reference Curve Calculation Section 15 Boundary Crossing Vector Approximation Calculation Section 16 Output Section

Claims (1)

[Claims] 1. A region surrounded by a plurality of curves and curved surfaces,
A boundary condition generation device for a curved surface used in a curved surface generation device for interpolating a curved surface satisfying continuity at a boundary portion, and setting a specified curve / curved surface as a boundary condition for the curved 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 reference curve based on the boundary curve obtained by the boundary curve approximation calculation means. Boundary condition generation of curved surface, comprising reference curve calculation means and boundary crossing vector approximation calculation means for approximating a boundary crossing vector with reference to the reference curve obtained by the reference curve calculation means. apparatus.