KR100261277B1 - Polyhedral solid translator and method from three orthographic views - Google Patents

Abstract

PURPOSE: A polyhedron conversion system from a three-face drawing and a method for the same are provided to convert all possible polyhedron solids by generating all candidate sides corresponding to each area of a three-face drawing and quickly obtaining all solutions by using a combinatorial search method. CONSTITUTION: A method for converting a polyhedron from a three-face drawing. An area is recognized from a two-dimensional input drawing. A vertex, an edge, a plane, and a side as three-dimensional information are extracted by using consistency with the drawing. A polyhedron is generated to recover a polyhedron solid from a candidate side. The generated polyhedron is verified.

Description

Polyhedral solid transformation system and method from three views

The present invention relates to a system and method for converting polyhedral solids from a three-sided view. In particular, a three-dimensional solid model automatic conversion using a drawing is a system for automatically converting a drawing represented by a three-sided view to a three-dimensional polyhedron. It is a method of automatically restoring the shape of the three-dimensional polyhedron represented by the drawing data created by using.

In general, there are volume-oriented techniques and wireframe-oriented techniques for converting solids from three views. Volume-oriented technology is a relatively efficient way of constructing three-dimensional polyhedrons through Boolean operations on simple blocks consisting of three-dimensional candidate planes, but is generally used to recover simple polyhedrons. In contrast, the Wireframe-oriented technique generates three-dimensional polyhedrons by attaching candidate faces one by one through a combination search for all candidate faces. In general, wireframe-oriented techniques efficiently restore complex polyhedrons. However, since the number of search candidate surfaces is relatively large compared to the number of blocks in the volume-oriented method, a combinatorial check cost is high.

SUMMARY OF THE INVENTION The present invention has been made in view of the above conventional problems, and an object of the present invention is to provide a method of extracting three-dimensional information lost in a projection process and converting the three-dimensional polyhedron with consistency in the drawing.

1 is a schematic overview of a polyhedral solid conversion system from a three-sided view according to the present invention

2 is a three-sided view represented by a line representing a shape of a polyhedron and a line segment indicating a connection relationship between the points

3 is an exemplary view of a recognition region extracted from the three views of FIG. 2.

Figure 4 restore wireframe example

5 is an exemplary view of a reconstructed three-dimensional candidate surface extracted from the wire frame of FIG.

Fig. 6 Combination search algorithm for reconstructed three-dimensional candidate surface

7 is an exemplary view of a polyhedron solid obtained through the search process of FIG. 6 for all candidate surfaces of FIG. 5.

Figure 8 polyhedral solid restoration example converted from three views

Referring to the configuration and operation of the present invention for achieving the above object is as follows.

The automatic conversion system is a system for converting a two-dimensional drawing that has lost three-dimensional information into a polyhedral solid. The present invention provides a new two-dimensional drawing recognition method, three-dimensional information (vertex, edge, plane, plane) extraction method, polyhedron generation method, and Polyhedral verification method and the like were invented. The invented methods utilize knowledge-based rules for determining the authenticity of candidate faces using geometrically generated conditions for matching three-dimensional polyhedrons and matching conditions between three-dimensional and three-sided views.

The present invention recognizes an area from a two-dimensional input drawing and extracts three-dimensional candidate vertices, edges, planes, and faces using the matching with the drawing. In order to generate a polyhedron valid for the three-view through tree search for the extracted candidate faces, the conditions for polyhedron existence, matching conditions of polyhedrons and three-sided views, and polyhedron-generating conditions are regularized and quickly converted into valid polyhedral solids.

The present invention uses a preprocessing step of transforming and extracting two-dimensional three-dimensional input data, extracting three-dimensional vertices, edges, planes, and candidate surfaces, and using a tree search method. It can be divided into a combination, that is, a polyhedron generation step for searching a set of all solutions, and a verification step of the generated polyhedron.

As shown in FIG. 1, the three views are converted to all polyhedra having conformity in the three views using the method proposed by the present invention.

〈Definition of three-sided view and automatic conversion polyhedron〉

In the present invention, the automatic object to be converted is a three-sided view represented by a line representing the shape of the polyhedron and a line segment indicating the connection relationship between the points. The three views consist of three shavings that orthogonally project a polyhedron with respect to the ZX, XY, and YZ planes perpendicular to each other, and are referred to as a front view, a plan view, and a side view, respectively (FIG. 2). 3D polyhedra are orthogonally projected for each plane, and the present system extracts 3D information lost in the projection process and converts it into 3D polyhedrons having consistency in the drawing.

In this system, the polyhedron transformed from three views is one or more polyhedrons placed in three-dimensional space, and each polyhedron is a closed space closed by a set of four or more faces. Each face is a directed plane bounded by traversal of coplanar edges, and the edges that make up the face correspond to two or more faces. Each corner consists of two vertices, each of which is a point in three-dimensional space where three or more corners meet.

<Area recognition method>

The area is a closed area closed by a traversal of line segments in one shave. The terms required to find the domain are as follows.

• Valency of a point p: The number of segments passing through any end point

● Normalized line: Line segment in unit length

• Right-most (left-most) line: To determine the right-most (left-most) line at a given point, consider the point as (0,0) and assume that the previous line segment is the (-) x axis. Update the. There are three cases in which the right-most (left-most) line is determined among the two segments passing through that point. In the new coordinate system, examine

If the second coordinate value of both normalized lines is positive, the line segment with the larger first coordinate value is the right-most (left-most) line.

2. If the second coordinate value of both normalized lines is negative, the line segment with the smaller first coordinate value is the right-most (left-most) line.

3. If the sign of the second coordinate value of the two normalized lines is different from each other, the line segment of which the second coordinate value is negative (positive) is the right-most (left-most) line.

The process of finding the domain is as follows. First, it starts at any starting point for a given shave. This random starting point selects the one with the smallest first and second coordinates. From the start point to the next point follow the left-most line and select the other end point of the line segment. Update the coordinates of this end point to (0,0), update the previous left-most line to the coordinate system on the (-) x axis, and select the next end point from which the right-most line is drawn until the start point is reached. Choose. When you arrive from the starting point back to the starting point, the rough points make up an area. Points selected as points that make up an area decrement the valency by one. Once one region is configured, the starting point for the next region is determined. The next starting point is the point where the valency of the previously configured area search is first greater than three. The process of finding the area after selecting the starting point is the same as above. FIG. 3 shows an example of regions extracted from the three views of FIG. 2.

<Candidate vertex restoration method>

Vertices appear as dots on each shave in three views. A vertex separates an edge and is one end of at least three edges. Vertices and projection points have the same coordinate values in a common coordinate system. That is, when P, Q, and R are sets of points of plan view, front view, and side view, respectively, the x and z coordinates of each point p of P are x (p) and z (p), and the angle of Q If the x and y coordinates of point q are expressed as x (q) and y (q), and the y and z coordinates of each point r of R as y (r) and z (r), the vertices satisfy the equation 1 It consists of points (p, q, r).

<How to restore candidate edges>

Candidate edges are extracted using line segment data for all possible binary pairs of the reconstructed candidate vertices and the corresponding triangular points. For example, when there are any two vertices V1 (p1, q1, r1) and V2 (p2, q2, r2), p1 and p2 are points in the plan view, q1 and q2 are points in the front view, and r1 and r2 are side views Since a point exists at each of the two corresponding points, the edge is created. In other words, there should be a line segment connecting two points p1 and p2 in the plan view, q1 and q2 in the front view, and r1 and r2 in the side view. Also, in the nature of the drawing, when the edge is perpendicular to the projection plane, two different points are projected as one point in the projection plane, so that the line segment is considered to exist. 4 illustrates a wireframe extracted from FIG. 2.

〈Method for Restoring Candidates〉

Three-dimensional candidate surface extraction uses two-dimensional regions, three-dimensional vertices and edges. First, project all edges on the plane onto any projection plane that is not vertical. At this time, a one-to-one correspondence is established between the projected edge and the projected line segment. Therefore, the process of extracting the face is replaced by the process of finding an area of line segments on the two-dimensional projection plane. That is, since the edge and the line segment have a one-to-one relationship, the traversal of the edge forming the plane to be obtained is a set of edges corresponding to the line segment forming the area. For example, given a set of m edges placed on any plane P, E (P) = {e1, e2, ..., em-1, em}, any projection plane that is not perpendicular to plane P The set of line segments projected onto L = {l1, l2, ..., lm-1, lm}. Since the projection line segments of each corner correspond to one-to-one correspondence, if the projection function is called Fprojection, li = Fprojection (ei) (1 ≦ i ≦ m). Therefore, if one region of the projection line L is a = {l1, l2, ..., ln-1, ln} (n≤m), a set of edges on the plane P corresponding to the region a, that is, one Candidate planes of f = {Fprojection-1 (l1), Fprojection-1 (l2), ..., Fprojection-1 (ln-1), Fprojection-1 (ln)}. FIG. 5 shows an example of a surface extracted from the wireframe of FIG. 4.

<How to generate polyhedrons>

The authenticity of the candidate is determined through the combinatorial search of the candidate. In order to speed up the determination of the authenticity of candidate surfaces, knowledge that defines the relationship between candidate surfaces is used. When the determination of all candidate faces is completed, the set of candidate faces determined as true is a polyhedron, and then the set of faces. The search tree that examines 2n all becomes a full two-minute search tree. However, in the simple backtracking method, unnecessary search is required, resulting in poor processing efficiency. So, by geometrically localizing local constraints or features for the existence of three-dimensional objects geometrically, the authenticity of the candidate surface is determined using the following polyhedron generation rules.

<Polyhedron generation rule>

1. In the projection of a three-dimensional object, the corresponding faces of an area are an even number of zero or more if the area does not include the contour as a boundary component, and two or more even numbers if it contains, and there are only two corresponding surfaces. Anything is jean.

2. The surface corresponding to the area having the broken line as the boundary line segment has another surface closer to the viewpoint, which conceals a certain surface at the broken line position.

3. If there is only one corner corresponding to a line segment and two sides connected to the corner, either is true.

6 is a search algorithm applying a rule to a 2-minute tree search. Each node in the search tree uses the polyhedral_solid_check function, which is a function of the polyhedron generation rule, to determine the trueness of its possible face.

In the main program of Fig. 6, the initial value is set in the first set in (1). T is the set of faces of the true, F is the set of faces above, and U is the set of faces that are undetermined. First, a search start node is selected in determination1 (a), and a procedure search is called.

The procedure search determines the authenticity of the face as the center of the search. Use polyhedral_solid_check to determine the trueness of the face. If you find a contradiction here, it is a geometrically wrong branch (3). If U is empty (4), T is one solution. Otherwise, one surface for branching is determined from U in determination2 (b), and the branch is searched (5) after determining the state first in that surface in determination3 (c).

Procedure branch is a procedure that does branching. The branch plane is moved (6) from the set U in accordance with the state of the argument. branch and search call each other and form a recursive procedure (7).

<Polyhedral verification method>

We define some rules for the transformation of three-dimensional polyhedron, which is a kind of combinatorial search problem that finds a combination of all the faces that make up an object, and then search the tree only candidate candidates that satisfy the three-dimensional polyhedron solid.

This is to organize the geometrical properties of three-dimensional polyhedrons into rules of the form that can be implemented programmatically. This rule is based on the fundamental properties of three-dimensional polyhedrons and the constraints and characteristics of candidate faces in three-dimensional space. Therefore, the local constraints or features for geometrically present three-dimensional polyhedrons are regularized to determine the authenticity of candidate surfaces. FIG. 7 shows a polyhedral solution through the search process of FIG. 6 for all candidate surfaces of FIG. 5, and FIG. 8 shows a polyhedral solution converted to a three-sided view.

<Condition of existence of polyhedron>

1. For any corner, the number of faces sharing that corner is two or more even.

2. There may be at most one candidate face among a plurality of candidate planes, that is, intersecting planes, which exist without mediating edges.

<Conditions for Polyhedrons and Three Sides>

1. There is a corresponding edge for all the segments that make up the three view.

2. When the solution is projected on three planes, the projection plane is the same as the original three planes.

As described above, the present invention generates all candidate faces corresponding to the area of the three views, and restores all solutions using a combinatorial search. In addition, the solution is quickly obtained by generating constraints and rules for improving the search efficiency. In addition, the method proposed in the present invention can be used to convert a solid from a three-sided view by adding a rule for generating a surface.

Claims (5)

A system for automatically expressing a drawing represented by a three-sided view as a three-dimensional polyhedron, the first process of recognizing a region from a two-dimensional input drawing, and using the three-dimensional information of vertices, edges, planes, and faces with the drawing And a third process of generating and verifying a polyhedron for restoring the polyhedron solid from the candidate surface and extracting the polyhedron solid from the candidate surface. The method of claim 1, wherein the candidate vertex extraction method in the second process The x and z coordinates of each point p in the plan view P are x (p) and z (p), and the x and y coordinates of each point q in the front view Q are x (q) and y (q). If the y and z coordinates of each point r of the side view (R) are expressed as y (r) and z (r), the vertex is extracted from candidate vertices using three points (p, q, r) satisfying the equation. Polyhedral solid conversion system from three views The method of claim 1, wherein the candidate edge extraction method in the second process A method of converting polyhedral solids from three-sided views to extract candidate edges using line segment data for all possible binary pairs of the restored candidate vertices and corresponding three-sided points. The method of claim 1, wherein the candidate surface extraction method in the second process is A method of converting polyhedral solids from three views, wherein all edges on a plane are projected onto an arbitrary projection plane, not vertical, and a candidate surface is extracted using a one-to-one correspondence between the projected edges and the projected line segments. The method of claim 1, wherein the polyhedron generation and verification method is In order to generate a polyhedron suitable for three-view through tree search on the extracted candidate faces, the polyhedron from polyhedron is converted into a polyhedron by regularizing polyhedron existence conditions, matching conditions of polyhedrons and three-sided views, and generating polyhedron solids. Solid transformation method.

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