JPS6319075A - Convex closing system for concave area - Google Patents

Abstract

PURPOSE:To determine efficiently a closing surface by detecting a closing ridgeline with a peak point having an attribute, a convexo-concave peak point as a center, deciding whether or not a closing curved line composed of the closing ridgeline is on the plane shape and further, deciding whether or not the convex closing is executed for the concave area. CONSTITUTION:A peak point attribute determining part 1 first determines the attribute of the peak point to constitute a concave area. Next, a closing ridgeline detecting part 2, with the peak point having the attribute, a convexo- concave peak point as a center, detects the closing ridgeline by an attribute relation. It is decided whether or not the closed curved line composed of the detected closing ridgeline on the plane, and when the line is judged not to be on the plane, a closing surface convex dividing part 3 convex-divides the closing surface. Finally, a completing conditions deciding part 4 decides whether or not the convex closing is completely executed for the concave area and when the area is decided not to be complete, the closing ridgeline detecting part 2 is returned.

Description

[Detailed Description of the Invention] [Summary] In shape processing by a computer, in order to solve the problem of how to perform convex closure of a concave region, attributes (concave vertices, convex vertices, concave and convex vertices) are assigned to the vertices forming the concave region. ), etc., and the closure surfaces forming the convex hull are determined based on the relationships between them.

[Industrial application field]

The present invention relates to polyhedral shape processing, particularly to a convex hull method for concave regions.

Unlike convex strips, shape processing of concave strips is difficult because of the presence of concave areas, which is easy to do with convex strips. Therefore, a method can be considered in which the concave striped surface is approximated by a convex striped surface and then only the concave areas are processed. Here, the convex ray surface approximation is performed by convexly closing the concave region.

[Conventional technology]

Conventionally, shape processing for a concave striped surface body has been performed without being aware of the concave areas. That is, the shape processing of the polyhedron is performed using an algorithm that can be applied to both convex and concave strips. For this reason, when there are only a few concave areas, it is sufficient to process only these areas later, but since the same algorithm is used to process the shape of the entire area, the disadvantage is that it takes a long time to process.

The present invention was created in view of these points, and aims to provide a concave region extraction method that can efficiently determine a closure surface that convexly closes a concave region of a polyhedron. .

[Means for solving problems]

FIG. 1 is a block diagram of the principle of the present invention. In FIG. 1, 1 is a vertex attribute determination unit, 2 is a closure edge detection unit, 3 is a closure plane image division unit, 4 is a termination condition determination unit, 5 is a memory for storing vertex attributes and closure vertices, and 6 is a closure edge This is a memory that stores the and closure surface.

Note that FIG. 1 is a block diagram showing the functions performed by a computer under the control of a program.

[Effect]

The vertex attribute determining unit 1 first determines the attributes of vertices (concave vertices, convex vertices, uneven vertices) constituting the concave area. Next, the closed edge detection unit 2 detects closed edges based on attribute relationships, centering on vertices having an attribute called uneven vertices. It is determined whether or not the closed curve formed by the detected closure edges is on a plane, and if it is determined that it is not on a plane, the closure surface is divided into convex sections by convex division section 3.
Do it with Finally, the end condition determining unit 4 determines whether the concave area is completely convexly closed, and if it is determined that the convex closure is not complete, the process returns to the closure edge detecting unit 2.

〔Example〕

FIG. 2 is a diagram showing an example of a concave area. In Figure 2, P
+, Pl, Ps, and Pb indicate convex vertices, and P3 and P4 indicate uneven vertices. The straight line connecting Pl and P becomes a closure edge, and the straight line connecting Pl and P6 also becomes a closure edge. A convex vertex is one in which all the ridge lines coming out from that vertex are convex edges. Although not shown in Fig. 2, the concave apex is
All of the ridgelines coming out from the apex are concave ridgelines.

The uneven apex refers to anything else. A convex ridgeline is one in which the angle formed by two planes forming the ridgeline is greater than 180 degrees when measured outward. A concave ridgeline is one in which the angle formed by two planes forming the ridgeline is smaller than 180 degrees when measured outward.

FIG. 3 is a flowchart illustrating the processing performed by the apparatus shown in FIG. In the same figure, 1xx (X is 0, 9
) indicates the processing performed by the attribute determination unit 1, 2xx indicates the processing performed by the closure edge detection unit 2, 3xx indicates the processing performed by the closure plane division unit 3, and 4xx indicates the processing performed by the termination condition determination unit 4. Indicates the processing to be performed. Note that the process of picking out vertices related to a concave area is described in the filed application for "Concave Area Extraction Method." Briefly, a concave edge is used as a clue to search until all boundary edges become convex edges. Therefore, the vertices forming the concave region are a set of end points of the boundary edge.

(101) First, the attributes of the vertices (concave apex, convex apex, uneven apex) constituting the concave area are determined.

(201) The next process is determined by the existence of a convex vertex attribute. If Yes, process (202) is performed, and if No, process (204) is performed.

(202) Trace along the boundary of the concave area from both sides of one concave/convex vertex to find the first convex vertex on each side. These two convex vertices are defined as the end points of the closure edge, and the closed curve surrounded by the traced boundary line and the closure edge is defined as a temporary closure surface.

(203) The closed envelope edge is stored in the memory 6, and all the initial uneven vertices and the uneven vertices that appeared during tracking (that is, uneven vertices in the closed surface) are deleted from the uneven vertex memory 5.

(204) If there are no convex vertices, the -temporal closure surface is a closed curve formed by all the concave and convex vertices.

(205) All uneven vertices are deleted from the memory 5.

(301) Next, it is checked whether the temporarily determined closure surface is a plane. If Yes, process (302) is performed, and if No, process (303) is performed.

(302) If it is a plane, the closure plane is registered as is.

(303) If it is not a plane, the closed surface is divided into convex parts so that all dividing edges become convex edges.

(304) Then, the divided closure surfaces and dividing edges are registered.

(401) Check whether there is an uneven vertex or not. If Yes, return to the process of (201), and if No, perform the process of (402).

(402) When the uneven vertices are eliminated, completion of the convex hull is determined based on whether there are any convex vertices (unprocessed convex end points) other than the closure vertices that are the end points of the closure ridge.

If there are no convex vertices other than closure vertices, the process ends.

(403) If they exist, the closure vertices connected to them are set as new uneven vertices.

(404) Furthermore, the uneven vertices are deleted from the convex vertices, and the process returns to (201) again.

FIG. 4 is a diagram showing an example of convex division of a closed surface.

If the four points are not on the plane as shown in Figure 4,
It is convexly divided by either diagonal.

FIG. 5 is a diagram showing another example of the concave area. Processes (403) and (404) will be explained with reference to FIG. In the case of the solid shown in Fig. 5, P6. Using the concavo-convex apex of P7 as a clue, the closing edges of P, P2 and PaPs can be drawn. Therefore,
P,,P,,P,,P,are closure vertices. Processing (40
3), p2. p4 becomes the next uneven vertex, and the process (
404), Pz.

P4 will be removed from the set of convex vertices.

〔Effect of the invention〕

As is clear from the explanation above, according to the present invention, the concave region can be closed in a convex manner, so that the shape processing for the convex strip surface body, which can be performed relatively easily, can be applied directly to the concave strip surface body. By post-processing only the concave areas, it is possible to completely process the shape of the concave strip.

[Brief explanation of drawings]

Fig. 1 is a diagram of the principle of the present invention, Fig. 2 is a diagram showing an example of a concave region, Fig. 3 is a flowchart explaining the processing performed by the apparatus of Fig. 1, and Fig. 4 is a diagram of convex division of a closed surface. FIG. 5 is a diagram showing another example of the concave area. 1... Vertex attribute determination unit, 2... Closing edge detection unit, 3
. . . Closure white division section, 4. Termination condition determination section, 5.
. . . Memory for storing vertex attributes and closure vertices; 6. Memory for storing closure edges and closure surfaces.

Claims (1)

[Scope of Claims] A method for convexly enclosing a concave region of a polyhedron includes a vertex attribute determination unit (1) that adds attributes such as concave vertices, convex vertices, and concave and convex vertices to vertices constituting the concave region; A closing edge detection unit (2) that determines a closing edge as the center, and a closing edge detection unit (2) that determines whether a closed curve formed by the closing edge is on a plane, and if it is not on a plane, performs convex division to detect the closure. A concave area convex closure method characterized by comprising: a convex closure surface dividing section (3) for determining a surface;