JPH06301752A - Skinning curved surface shape generation device - Google Patents

Abstract

PURPOSE:To interpolate the cross-section of curve segments with an NURBS curved surface even when the number of the curve segments for constituting the cross-section is different. CONSTITUTION:Plural cross-section shapes are generated and the cross-section is arranged at a desired position in a space. Cross-section data are divided by a cross-section dividing means 3 and then transmitted to a vertex node correspondence relation deciding means 4. A gap between the corresponding vertex nodes is made into an NURBS curve by a curve dividing means 5, knot vectors are made identical and then, display is performed at a graphic display device 9 and also storage in a graphic storage part 10 is performed along with correspondence relation and graphics. Then, transmission to a curve connecting means 6 is performed and curves are connected based on the data of the cross- section and vertex node correspondence relation data read from the graphic storage part 10. The connected curves are displayed at the graphic display device 9 and also transmitted to a free curved surface generation means 7 and the generated curved surface is displayed at the graphic display device 9 and also transmitted to the graphic storage part 10.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a skinning curved surface shape generation device, and more specifically, to a skinning curved surface shape generation device capable of generating a skinning curved surface by interpolating a plurality of cross sections arranged in space. The present invention relates to a skinning curved surface shape generation device. For example, it can be applied to a skinning device that interpolates a plurality of different sectional shapes.

[0002]

2. Description of the Related Art As a known document in which the prior art relating to the present invention is described, for example, Wayne Tiller, "Rational B-Spli.
nes for Curve and Surface Representation "(IEEE C
G & A Vol.3, No6, September, 1983, pp61-69). In such a conventional technique, skinning is performed by arranging cross sections and further specifying a vertex correspondence relationship for connecting the cross sections. However, according to such a conventional technique, it is difficult to specify the vertex correspondence for generating the intended smooth skinning solid shape.

In order to solve this point, the applicant of the present invention has proposed a "skinning solid generation method" in Japanese Patent Application No. 1-203870. The present invention is a method for generating a skinning solid from a plurality of cross sections arranged in space, in which a virtual space orbit is generated between the centers of two adjacent cross sections, and adjacent to each other along the generated orbit. Of the two cross-sections that fit together, the front cross-section is tentatively swept so that it is flush with the latter cross-section. The correspondence between the vertices of the cross section before and after
The skinning solid is generated by interpolating the corresponding vertices with a continuous curve and interpolating a curved surface on the surface surrounded by the generated curve. However, there was a limitation that the number of curved segments that make up the cross section must be the same. Further, there is a demerit that the number of skinning curved surfaces generated by this is too large.

[0004]

[Object] The present invention has been made in view of the above-mentioned circumstances, and even if the number of curved segments forming a cross section is different, these cross sections can be interpolated by one NURBS curved surface. The object is to provide a curved surface shape generation device.

[0005]

In order to achieve the above object, the present invention provides (1)
In a three-dimensional curved surface shape generation device that generates a skinning curved surface by interpolating a plurality of cross sections arranged in space, an arrangement means that arranges the plurality of cross sections in space, and a cross section that divides the curves forming each cross section. Dividing means, vertex node relation determining means for finding correspondence between vertex nodes between cross sections, curve dividing means for aligning knot vectors of curves between vertex nodes, and curve joining means for joining a plurality of NURBS curves of the same cross section And a free curved surface generating means for generating a free curved surface, and (2) the cross section dividing means has a cross section composed of one NURBS curve,
Further, (3) the cross section dividing means divides one NURBS curve forming the cross section into a plurality of NURBS curves which are not continuous up to a tangent line, and (4) the above The vertex node relationship determining means is the minimum twist angle method, and (5) the curve dividing means is arranged to align the knot vectors of the corresponding curves, and (6) the curve connecting means. Is multiple NUs
A single NURBS curve is used as the RBS curve, and (7) the free-form surface generating means uses one NURBS curve.
The feature is that an URBS curved surface is generated. Hereinafter, description will be given based on examples of the present invention.

FIG. 1 is a block diagram for explaining an embodiment of a skinning curved surface shape generating device according to the present invention.
1 is a graphic element generating means, 2 is a graphic arranging means, 3 is a sectional dividing means, 4 is a vertex node correspondence determining means, 5 is a curve dividing means, 6 is a curve connecting means, 7 is a free curved surface generating means, 8
Is a graphic display control unit, 9 is a graphic display device, and 10 is a graphic storage unit.

The skinning curved surface in the present invention is a curved surface generated by interpolating a plurality of cross sections arranged in a space as shown in FIG. Each cross-sectional shape is composed of one NURBS curve. The NURBS will be described below. Since the Bezier curve is a polynomial curve and thus the shape of the curve that can be expressed is limited, since the B-spline curve is also a polynomial curve, a conic curve or the like cannot be expressed. A rational B-spline curve is one that can express such a curve by performing rationalization similar to the Bezier curve.

NURBS is Non Uniform Rational
Abbreviation for B-Spline. Non Uniform means that the knot vector in the rational B-spline curve does not have a specific rule such as open uniform or uniform, and may be any knot vector of monotonic increase. Refers to the format. The rational B-spline curve inherits the property of the B-spline curve.
NURBS also inherits the properties of non-uniform B-spline curves. If the knot vector is non-uniform, it is possible to represent a curve as if multiple curves were connected by multiplexing the intermediate knots. Even a curved curve can be represented as a single curve. The above explanation is "Basics and applications of three-dimensional CAD" (written by Koji Sotori, published by Kyoritsu Shuppan Co., Ltd., 19
2/91/25).

First, a plurality of cross-sectional shapes are generated by the graphic element generating means 1 such as a three-dimensional CAD system. Then, the generated cross-sectional shape is input to the graphic display control unit 8, is displayed on the screen of a graphic display device 9 such as a CRT, and is transmitted to the graphic arranging means 2. The figure arranging means 2 arranges the cross section at a desired position in space. The arranged cross section is the graphic display device 9
After being displayed on the screen, the graphic storage unit 10 is stored and
It is transmitted to the section dividing means 3. After the cross-section data is organized, it is transmitted to the vertex node correspondence relation determining means 4. After the vertex node correspondence relation determining means 4 determines the correspondence relation of the vertex nodes between the adjacent cross sections, the correspondence relation of the vertex nodes is stored in the graphic storage unit 10 and transmitted to the curve dividing means 5. After making one NURBS curve between the corresponding vertex nodes by the curve dividing means 5 and making the knot vectors the same, it is displayed on the graphic display device 9 and stored in the graphic storage unit 10 together with the correspondence and the graphic. After that, it is transmitted to the curve combining means 6.

In the curve combining means 6, the graphic storage unit 10
Curve connection is performed based on the cross-section data read from the data and the vertex node correspondence data. The curves combined by the curve combining means 6 are displayed on the graphic display device 9 and transmitted to the free-form surface generating means 7. The curved surface generated by the free curved surface generating means 7 is displayed on the graphic display device 9 and transmitted to the graphic storage unit 10.

Each means will be described below. The figure arranging means 2 arranges a plurality of cross-sectional shapes generated by a three-dimensional CAD system or the like at desired positions in space by moving or rotating, as shown in FIG. Each cross-sectional shape shall consist of one NURBS curve.
The cross-section dividing means 3 divides each cross-sectional shape into the same order, and then divides the segment forming the cross-section into a portion that is not tangential continuous. As a result, as shown in FIG. 3, the cross section is reconstructed by one or a plurality of NURBS curves. The endpoints of each NURBS curve are called vertex nodes.

The vertex node correspondence determining means 4 selects a section having the maximum number of vertex nodes in each section (section 2 in FIG. 3). Then, with reference to the cross section having the maximum number of vertex nodes, the correspondence relationship between the vertex nodes of the adjacent cross sections is sequentially determined from the cross section toward the left cross section group and the right cross section group. The procedure for determining the correspondence between the vertex nodes is as follows.

Step 1 ; An imaginary space trajectory is generated by a free curve between the centers of two adjacent cross sections. Here, the cross section on the start side of two adjacent cross sections is called the front cross section, and the cross section on the end side is called the rear cross section. The positions of the end points of this free-form surface are the center positions of the front section and the back section, respectively, and the tangent vectors at the end points match the normal vectors of the front section and the back section, respectively. The control point position is the position of the intersection of the tangent vectors at both ends of the curve. Also, the weight of both end points of the curve is 1.0. FIG. 4 shows a free curve that represents a virtual space trajectory. step2 ; In order to determine the correspondence between the vertex nodes, as shown in FIG. 5, the front section is temporarily swept along the trajectory obtained in Step 1 and brought to the same plane as the subsequent section.

Step 3 ; The twist angle is calculated in order to determine the correspondence between the vertex nodes of the tentatively swept front section and the rear section obtained in Step 2. In FIG. 6, if the vertex node V7 'of the previous cross section and the vertex node V10 of the subsequent cross section are combined, the angle between the center of the cross section and the vector determined by each vertex node is called the twist angle. . When the number of vertex nodes in two cross sections is different, for each cross section node with a small number of vertex nodes, select the vertex node closest to the twist angle from the vertex nodes in the other cross section (( For example, V7 'and V10, V5' and V9 in FIG. 6). This determines the vertex node correspondence between the true front section and the true rear section (for example, V7 and V10, V5 and V9 in FIG. 5). An unmatched vertex node in a cross section with a large number of vertex nodes (V in FIG. 6)
6'and V8 ') are determined by the curve dividing means 5. In addition, if the number of vertex nodes in the two sections is the same, the vertex node with the previously cross section and the vertex node with the later section that were swept are combined, and the subsequent vertex nodes are ordered. The total sum of the angle between each of them when combined into is called the total twist angle. A combination method that minimizes the total twist angle is selected from a plurality of combinations corresponding to the apex nodes in the swept front section and the rear section. By this combination method, the vertex node correspondence between the true front section and the true rear section is determined. The vertex node correspondence determined in the above is saved.

The curve dividing means 5 is a NU between the corresponding vertex nodes by the vertex node correspondence determining means.
Make the RBS curve and make the knot vectors the same as shown in FIG. It is assumed that the knot vector is normalized. For example, in FIG. 6, it is assumed that V10 corresponds to V7 'and V9 corresponds to V5'. V5, V7 and V9 in FIG.
The knot vectors are made the same after the left and right curves of V and V10 are each made into one NURBS curve. The curve combining means 6 combines a plurality of NURBS curves into one for each cross section. However, the starting point of the NURBS curve is determined by the correspondence between the vertex nodes. Note that the knot vectors of all NURBS curves collected by this are the same. The free-form surface generating means 7, as shown in FIG. 7, generates one NURBS curved surface that interpolates each cross section.

[0016]

As is apparent from the above description, the present invention has the following effects. (1) According to the invention described in claim 1, it is possible to generate a skinning curved surface by interpolating a plurality of cross sections arranged in space. (2) According to the invention described in claim 2, NURBS
It can be adapted to a cross section composed of curves. (3) According to the invention described in claim 4, the correspondence between the cross sections can be automatically determined. (4) According to the invention described in claim 7, it is possible to generate a skinning curved surface which interpolates a plurality of cross sections with one NURBS curved surface. (5) By implementing the present invention in a three-dimensional CAD system or the like, it is possible to easily design a shape such as a wing of an airplane, a propeller, a pipe, or generation of a complicated skinning curved surface in image processing.

[Brief description of drawings]

FIG. 1 is a configuration diagram for explaining an embodiment of a skinning curved surface shape generation device according to the present invention.

FIG. 2 is a diagram in which a plurality of cross-sectional shapes generated according to the present invention are arranged.

FIG. 3 is a NUR having one or more cross sections according to the present invention.
It is the figure reconstructed by the BS curve.

FIG. 4 is a diagram showing generation of a free curve representing a virtual space trajectory according to the present invention.

FIG. 5 is a diagram showing a state in which the surface is temporarily swept from the front section according to the present invention and brought to the same plane as the rear section.

FIG. 6 is a diagram showing a correspondence relationship between vertex nodes according to the present invention.

FIG. 7 is a diagram showing a state in which vertex nodes are connected by free-form curves according to the present invention.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Graphic element generating means, 2 ... Graphic arranging means, 3 ... Section dividing means, 4 ... Vertex node correspondence relationship determining means, 5 ... Curve dividing means, 6 ... Curve connecting means, 7 ... Free curved surface generating means, 8
... Graphic display control unit, 9 ... Graphic display device, 10 ... Graphic storage unit.

Claims (7)

[Claims] 1. A three-dimensional curved surface shape generation device for interpolating a plurality of cross sections arranged in a space to generate a skinning curved surface, and an arrangement means for arranging the plurality of cross sections in the space.
Cross-section dividing means for dividing a curve forming each cross-section, vertex node relationship determining means for finding a correspondence between vertex nodes between cross-sections, curve dividing means for aligning knot vectors of curves between vertex nodes, and a plurality of cross-sections having the same cross-section A skinning curved surface shape generation device comprising: a curve combination means for connecting NURBS curves of a book; and a free curved surface generation means for generating a free curved surface. 2. The skinning curved surface shape generation device according to claim 1, wherein the cross section dividing means has a cross section composed of one NURBS curve. 3. The cross section dividing means divides one NURBS curve forming the cross section into a plurality of NURBS curves which are not continuous up to a tangent line to form a plurality of NURBS curves. Skinning curved surface shape generator. 4. The skinning curved surface shape generation device according to claim 1, wherein the vertex node relation determining means uses a minimum twist angle method. 5. The skinning curved surface shape generation device according to claim 1, wherein the curve dividing means aligns knot vectors of corresponding curves. 6. The curve combining means comprises a plurality of NURBS.
The skinning curved surface shape generation device according to claim 1, wherein the curve is one NURBS curve. 7. The free-form surface generating means is one NUR.
The skinning curved surface shape generation device according to claim 1, wherein a BS curved surface is generated.