WO2018132989A1

WO2018132989A1 - Segmental arc polygon two-dimensional boolean operating method

Info

Publication number: WO2018132989A1
Application number: PCT/CN2017/071640
Authority: WO
Inventors: 蔡熙炫; 曾波; 刘忠军; 刘静
Original assignee: 深圳市百能信息技术有限公司
Priority date: 2017-01-19
Filing date: 2017-01-19
Publication date: 2018-07-26

Abstract

A segmental arc polygon two-dimensional Boolean operating method, comprising: reading the data of a main body A and a main body B sequentially, and removing the excess collinear points of the main body A and the main body B (S101); calculating the islands and holes of the main body A and the main body B as well as the data of the corresponding intersection points and sub-edges of each island and hole, and calculating the lowest sub-edge of the islands (S102); creating a hash mapping relationship between the islands and holes and their corresponding intersection points, and establishing a mapping relationship between each of the intersection points and the sub-edges (S103); calculating the winding number values of the sub-edges of each island and hole by means of an iterative algorithm (S104); and carrying out union, subtraction and intersection Boolean operations on the main body A and the main body B by means of the winding number values (S105). By means of the segmental arc polygon two-dimensional Boolean operating method, the curve-type two-dimensional graph Boolean operation can be effectively solved, the cost is low, and the operation is fast.

Description

A two-dimensional Boolean operation method for arc segment polygon

Technical field

The invention relates to the technical field of graphic processing, in particular to a two-dimensional Boolean operation method for an arc segment polygon.

Background technique

Two-dimensional Boolean operation is one of the important contents of computational geometry and computer graphics. Its main function and result is that simple graphics can obtain complex graphics after Boolean operations, in many fields such as mechanical part design, architectural graphic design, shipbuilding and so on. There are a wide range of applications. As one of the most commonly used and basic algorithm tools, two-dimensional Boolean operations are also widely used in the PCB circuit board manufacturing industry.

The existing two-dimensional Boolean algorithm generally describes the boundary of the graph in the form of "ring". For example, the currently widely used two-dimensional Boolean open source library Clipper is a very sophisticated library of two-dimensional Boolean operations, but it is similar to other similar The two-dimensional Boolean operation library has a common shortcoming, that is, the curve cannot be processed, and the curve needs to be cut into approximate multiple straight line segments before it can be processed. This increases the amount of data and changes the data type, and the processing is complicated. The prior art also uses a three-dimensional Boolean operation library to realize the requirements of two-dimensional Boolean operations, but the three-dimensional library has large capacity, high cost, and high price.

Summary of the invention

In view of the above problems, the object of the present invention is to design a two-dimensional polygon of a curved section. The Boolean operation method can effectively solve the two-dimensional graphics Boolean operation of the curve type, and the cost is low and the operation is fast.

The specific technical solution of the present invention is as follows:

A two-dimensional Boolean operation method for an arc segment polygon, comprising:

Step S101, sequentially reading the data of the main body A and the main body B, and eliminating the redundant collinear points of the main body A and the main body B;

Step S102, calculating data of the islands, holes, and intersections and sub-edges of the main body A and the main body B, and calculating the lowest sub-edge of the island;

Step S103, creating a hash mapping relationship between the island and the intersection point of the hole corresponding to itself, and establishing a mapping relationship with the child edge for each intersection point;

Step S104, calculating a winding value of each island and a sub-edge of the hole by using an iterative algorithm;

Step S105, performing a union, a difference set, and an intersection Boolean operation of the subject A and the subject B by the wrap value.

Specifically, the island of the present invention is a closed counterclockwise direction polygon; the hole is a smoothing direction polygon in the island; the intersection point is an interface or intersection point of the two sides of the polygon; The sub-edge is the edge between the two intersections.

Specifically, the hash mapping relationship of the intersection point of the island and the hole corresponding to the self is established according to the present invention, and the mapping relationship between the island and the hole is established for each intersection, and specifically includes:

An iterative method is used to establish a mapping relationship between each intersection and a child edge.

Specifically, the method for calculating the winding value of each sub-edge of each island and hole by using an iterative algorithm includes:

Define the rounding value as the number of times the child edge is surrounded by the polygon;

The initial value of the sub-edge is 0. If the sub-edge is surrounded by a polygon, if the polygon is counterclockwise, then the value of the sub-edge is incremented by one; if the polygon is clockwise, the value of the sub-edge is decremented by one. .

Compared with the prior art, the two-dimensional Boolean operation method of the arc segment polygon provided by the invention can solve the Boolean operation of the curve type two-dimensional graphics, and has the advantages of low precision, high efficiency and high efficiency.

DRAWINGS

The embodiments of the present invention are further described below with reference to the accompanying drawings, wherein:

Figure 1 is a topological definition map of the present invention;

Figure 2 is a Boolean operation diagram of the present invention;

Figure 3 is a flow chart of the present invention;

Figure 4 is a flow chart showing the data calculation process of the present invention;

Figure 5 is a flow chart of establishing a mapping relationship of the present invention;

Figure 6 is a flow chart of numerical calculation of the sub-edge winding of the present invention;

Figure 7 is a flow chart showing the calculation results of the present invention.

detailed description

The invention will be further described in detail below with reference to the drawings and specific embodiments.

The invention proposes a two-dimensional Boolean operation method for an arc segment polygon, which can solve a two-dimensional graph Boolean operation of a curve class.

Referring to Figure 1, the relevant topology is defined as follows:

Island: Close to the polygon in a counterclockwise direction;

Hole: the smoothing polygon in the island;

Interaction: The intersection of two sides of a polygon and the intersection of two or two sides are collectively called intersections;

Edge Edge: The edge between two intersections.

Each 2D entity must have only one island, and the island can contain multiple holes.

Referring to FIG. 2, the present invention can implement three Boolean operations, a union operation (A∪B), a difference set operation (A-B), and an intersection operation (A∩B).

Please refer to FIG. 3, which specifically includes the following steps:

In step S101, the data of the main body A and the main body B are sequentially read, and the collinear points of the main body A and the main body B are eliminated.

Step S102, calculating data of the islands, holes, and intersections and sub-edges of the main body A and the main body B, and calculating the lowest sub-edge of the island.

Specifically, referring to FIG. 4, each data of the main body A and the main body B is counted according to the above-mentioned island, hole, and the definition method of the intersection point and the sub-edge corresponding to each island and hole. At the same time, it is necessary to eliminate the extra collinear points of the main body A and the main body B.

In step S103, a hash mapping relationship between the island and the intersection point corresponding to the hole is created, and a mapping relationship between the island and the sub-edge is established for each intersection.

Specifically, an iterative method is used to establish a mapping relationship between each intersection and a sub-edge. For details, see Figure 5.

In step S104, the winding value of each island and the sub-edge of the hole is calculated by an iterative algorithm.

Specifically, the wrap value is the number of times the sub-edges are surrounded by how many polygons. The initial value of the sub-edge is 0, the winding is a vector, if the edge Edge is surrounded by a polygon Poly, if Poly is counterclockwise, then the number of Edge is +1; if Poly is clockwise, then the number of Edge is -1. Because the sub-edges of each island are surrounded by themselves, the number of turns of the child edges of the independent island is equal to 1. If the independent island contains a hole, then the sub-edge of the hole is surrounded by the island and surrounded by the hole, so the number of word edges of the hole is zero. See Figure 6 for the specific winding calculation process.

Specifically, the present invention implements three Boolean operations, a union operation (A∪B), a difference set operation (A-B), and an intersection operation (A∩B).

Referring to FIG. 7, the union, difference, and intersection Boolean operations of the subject A and the subject B by the wrap value are easily summarized by the values of the sub-edges, and the boolean geometric rules are converted into wraps. The manifestation of several algebras.

Pathfinding for picking results: Iterate each island, hole, and start the path from the lowest edge of the island, only the sub-edge that satisfies the Boolean operation picking condition, walk through and set the mark to prevent repeated traversal, when the next one is found The road is gone, which means that the result of the pickup generates a closed loop, and then the search for the sub-edge that has not passed the condition is completed, and all the sub-edges of the loop iteration are iterated before ending.

All new holes (clockwise polygons) need to be re-find for their belonging island. Standardize the new island hole.

The specific embodiments of the invention described above are not intended to limit the scope of the invention. Any other various changes and modifications made in accordance with the technical idea of the present invention are intended to be included within the scope of the appended claims.

Claims

An arc segment polygon two-dimensional Boolean operation method, comprising:

Step S101, sequentially reading the data of the main body A and the main body B, and eliminating the redundant collinear points of the main body A and the main body B;

Step S102, calculating data of the islands, holes, and intersections and sub-edges of the main body A and the main body B, and calculating the lowest sub-edge of the island;

Step S103, creating a hash mapping relationship between the island and the intersection point of the hole corresponding to itself, and establishing a mapping relationship with the child edge for each intersection point;

Step S104, calculating a winding value of each island and a sub-edge of the hole by using an iterative algorithm;

Step S105, performing a union, a difference set, and an intersection Boolean operation of the subject A and the subject B by the wrap value.
The arc segment polygon two-dimensional Boolean operation method according to claim 1, wherein the island is a closed counterclockwise direction polygon; the hole is a smooth clockwise polygon in the island; The intersection point is the junction or intersection point of the two sides of the polygon; the sub-edge is the edge between the two intersections.
The arc segment polygon two-dimensional Boolean operation method according to claim 2, wherein the hash mapping relationship between the island and the intersection point corresponding to the hole is created, and the mapping between the sub-edge and the sub-edge is established for each intersection. Relationships, including:

An iterative method is used to establish a mapping relationship between each intersection and a child edge.
The two-dimensional Boolean operation method of the arc segment polygon according to claim 1, wherein the calculation of the winding value of the sub-edge of each island and the hole by the iterative algorithm comprises:

Define the rounding value as the number of times the child edge is surrounded by the polygon;

The initial value of the sub-edge is 0. If the sub-edge is surrounded by a polygon, if the polygon is counterclockwise, then the value of the sub-edge is incremented by one; if the polygon is clockwise, the value of the sub-edge is decremented by one. .