JP2000194877A - Curved surface interpolation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To create a curved surface for being smooth inside the curved surface to a boundary curve including a recess designed by a designer and keeping appropriate continuity with an external curved surface as well. SOLUTION: (1) Vertexes V1 and V2 where the connection of curved lines is turned to the recess at the vertex of the supplied boundary curve are detected. (2) The vertexes V6 and V5 to be paired with the detected recessed vertexes V1 and V2 are searched, a plane parallel to the direction of averaging two ridge lines connected to the vertexes passing through the vertexes is defined and the intersection of it and the respective curves is obtained (the vertex that is the closest to the intersection is the vertex to the pair of division). (3) By dividing the surface for connecting the corresponding vertexes V1 and V6; V2 and V5 with each other by the curved lines and recursively repeating the same procedure to the respective surfaces formed by the division, a plurality of recessed vertexes within the supplied boundary curve are all divided. (4) By smoothly interpolating a projected surface, the entire recessed surface is smoothly interpolated.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for interpolating a curved surface, and more particularly to a method for smoothly interpolating a plurality of boundary curves including a concave surface.

[0002]

2. Description of the Related Art When designing a beautiful curved surface, first,
A method of designing a beautiful curved shape is effective. Designers concentrate on curve design only. The system interpolates the surface shape from the curve at the boundary of the surface (the system automatically generates the appropriate surface shape from the surrounding curve shape)
If you implement the method, the curved surface can be automatically generated simply by designing the curved shape.

In the prior art, there is a technique for interpolating a convex N-gon boundary curve. But,
There is no method for interpolating a complicated surface including irregularities. With this, even if the curve is freely designed, if the curve has a concave shape, the system cannot generate a curved shape. The designer must remove the concave surface.

In recent years, point cloud data can be obtained by using a three-dimensional measuring device. However, even when a curved surface is automatically generated from this point cloud data, a case in which a curve becomes concave occurs. Also in this case, by using the present invention, a smooth curved surface can be generated.

[0005]

As described above, there is no method for interpolating a complicated surface including irregularities in the conventional technology, and even if the surface is freely curved,
If the curve had a concave shape, the system could not generate a curved shape and the designer had to remove the concave surface.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned circumstances, and maintains smooth continuity inside a curved surface and appropriate continuity with an external curved surface with respect to a boundary curve including a concave portion designed by a designer. A curved surface can be generated so that the designer can focus only on the original curve design.

[0007]

SUMMARY OF THE INVENTION The present invention detects a vertex having a concave connection between curves at a vertex of a given boundary curve, searches for a vertex that is a pair of the detected concave vertex, Define a plane that is parallel to the average of the two edges connected to the vertices and passes through the vertices, finds the intersection of this and each curve (the vertices closest to this intersection are the vertices that are the pair of divisions), Divide the surface connecting the vertices to be curved with
A curve is generated so that the interpolated surfaces are connected smoothly, and the same procedure is repeated recursively for each surface created by this division, so that multiple concave vertices in a given boundary curve are obtained. Is divided into all, and the convex surfaces are smoothly interpolated (because the interpolated convex surfaces are interpolated smoothly to generate a curve), the whole concave surface is interpolated smoothly. It was done.

[0008]

BEST MODE FOR CARRYING OUT THE INVENTION From a boundary curve including a concave, an appropriate curved surface shape is automatically generated so as to pass through the curve, and a surface such that the curved surface maintains smoothness at a vertex where the connection of the curve is concave. And Gregor on the generated surface
If the y-form surface interpolation method is applied, the inside of the surface is smoothly interpolated. As a result, it is possible to interpolate a surface formed by a boundary curve including a concave, which is impossible with the conventional method. As a result, a curved surface shape can be automatically generated by the system based on the curve input by the designer with his or her own sensitivity, and a design system that does not hinder the intuition of the designer can be implemented.

FIG. 1 shows a boundary curve to which the present invention is applied, FIG. 2 shows a result obtained by dividing the boundary curve shown in FIG. 1,
FIG. 3 is a diagram showing a curved surface interpolated with respect to the divided curved surface shown in FIG.
Therefore, if the interpolation method according to the present invention is used, even if point group data input from outside the system is given, even if a characteristic line of a curved surface can be extracted from it, even if the characteristic line A curved surface can be generated as a boundary curve. As a result, it is possible to automatically generate a curved surface from data from the three-dimensional measuring device.

Here, since the present invention is a problem, it is the method of interpolation of a curved surface itself. The boundary curve of the curved surface may include irregularities, but it is assumed that there is no part that is turned over with respect to the average normal vector defined from the boundary curve. In addition, it is assumed that all boundary curves are straight lines or cubic Beizer curves.

Hereinafter, the curved surface interpolation method according to the present invention will be described.
More specifically, referring to the drawing, a vertex at which the connection between the curves is concave at the vertex of the given boundary curve is detected. In the case of FIG. 4, the vertices V1 and V2 are thus vertices.

A search is made for a vertex that is a pair of the detected concave vertex. A plane parallel to the average direction of the two ridge lines connected to the vertex and passing through the vertex is defined, and the intersection of this and each curve is determined. The vertex closest to this intersection is the vertex that forms the pair for division. If self-interference is caused by this division, the next closest vertex is selected. In the case of FIG. 5, the intersection P between the plane passing through the vertex V1 and each curve is obtained, and this intersection P
Is the point corresponding to V1. Similarly, V5 corresponds to vertex V2.

A surface connecting corresponding vertices with a curve is divided. At this time, a curve is generated so that the interpolated curved surfaces are connected smoothly. Here, the curve uses a cubic Beizer curve. By repeating the same procedure recursively for each surface formed by this division of the procedure, all the concave vertices within the given boundary curve are divided. FIG.
, The corresponding vertices V1, V6 and V2, V5 are connected. This eliminates the concave surface, leaving only the convex surface.

A technique for smoothly interpolating a convex surface is known (see the basics and correspondence of three-dimensional CAD). By using this method, the convex surface can be smoothly interpolated.
Since the interpolated convex surfaces generate a curve so as to be interpolated smoothly, the entire concave surface is interpolated smoothly.

Hereinafter, the method of the present invention will be described in detail. The above-described determination of the depression is performed by the following method. As shown in FIG. 7, the tangent vectors Va,
Find Vb. Further, an average normal vector N defined from the boundary curve is obtained. The unevenness of this vertex can be determined based on whether the direction of N is the same as the vector defined by the outer product of Va and Vb. Specifically, (Va ×
If the value of Vb) · N is positive, it can be determined that V1 is a concave vertex.

The cut surface in the above is determined as follows. A plane including the vector Vb-Va and the average normal vector N and passing through the vertex V1 is defined as a cutting plane.

The curve in the above is determined as follows. As shown in FIG. 8, the control points of the tertiary Beizer to be determined are C0, C1, C2, and C3. Using N defined as follows, vectors V01 and V32 are defined as follows.

N = n × (Pb-Pa) / | n × (Pb-Pa) | V01 = (Voa · N) Via− (Via · N) Voa / | (Voa · N) Via− (Via · N ) Voa | V32 = (Vob ・ N) Vib- (Vib ・ N) Vob / | (Vob ・ N) Vib- (Vib ・ N) Vob |
(However, Pb is concave case) V32 = (Vob ・ N) Vib- (Vib ・ N) Vob / | (Vob ・ N) Vib- (Vib ・ N) Vob |
(However, the case where Pb is convex) At this time, C0, C1, C2, and C3 are defined as follows. C0 = Pa C1 = Pa + 1/3 | Pb-Pa | V01 C2 = Pa + 1/3 | Pb-Pa | V32 C3 = Pb

[0019]

According to the prior art, there is no method for interpolating a complicated surface including irregularities. Even if the curve is freely designed, if the curve has a concave shape, the system will be curved. The shape could not be generated and the designer had to remove the concave surface.However, according to the present invention, the boundary curve including the concave designed by the designer was smooth inside the curved surface, In addition, a curved surface that maintains appropriate continuity with external curved surfaces can be generated, so that the designer can focus on only the original curve design.

[Brief description of the drawings]

FIG. 1 is a diagram showing a boundary curve of a curved surface.

FIG. 2 is a diagram showing a result of division at a concave vertex in FIG. 1;

FIG. 3 is a diagram in which an interpolated curved surface is displayed by shading.

FIG. 4 is a diagram showing a curve sequence including irregularities.

FIG. 5 is a diagram for searching for a point corresponding to a concave vertex.

FIG. 6 is a diagram for dividing a curve sequence including irregularities.

FIG. 7 is a diagram for explaining an example of determining a concave vertex.

FIG. 8 is a diagram for explaining determination of a cutting curve.

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Claims (1)

[Claims] 1. At a vertex of a given boundary curve, a vertex whose connection between curves is concave is detected, a vertex that is a pair of the detected concave vertex is searched for, and two edges connected to the vertex are averaged. Define a plane that is parallel to the direction and passes through the vertices, find the intersection of this and each curve, divide the surface that connects the corresponding vertices with a curve, and apply the same procedure to each surface created by this division. By recursively repeating, all the concave vertices in the given boundary curve are divided, and by interpolating the convex surface smoothly, the entire concave surface is smoothly interpolated. Curved surface interpolation method.