Research On 2D Boolean Operation Method Based On Vertex Merging

Boolean operation technology is one of the most important and complex problems for conformations of complex entities in the computer geometric modeling technology. It has important application in the field of construction engineering, industrial design etc. The Boolean operation can combine a set of simple models to a complex model, or divide a complex model into a set of simple models. In addition, the Boolean operation algorithm is one of the most basic algorithms in computer graphics. Although most of the Boolean operations between entities can get accurate results, but may produce erroneous results in the face of the singular problems and engineering tolerance or other conditions. Therefore, the accuracy, robustness and stability of 2D Boolean operation play a key role in the normal function for entities operations.Boolean operations are also often used for many large-scale engineering. Take architectural engineering application as an example, while developers estimate the project costs budget, the Boolean operations results can help them to get the building materials dosage. In the architectural engineering, models are basically 3D models, but the 3D Boolean operation is more complex than 2D operation. For the construction engineering application or other large-scale engineering, in order to avoid the problem of the computing complexity and slow speed computing with 3D models, this paper adopts the simple and fast 2D operation, reducing the dimensionality of the models from three dimension to two dimension, then perform the 2D Boolean operation. Meanwhile, according to the similarity of components sets in large engineering, this paper employs the similarity evaluation technology to accelerate the engineering computing and improve the engineering calculation efficiency.The main work of this paper are as follows:(1) Aiming at the poor computing of Boolean operation for complex polygons and the common singular problems, coincidence of points or edges, existing in 2D Boolean operation, this paper proposes a 2D Boolean operation method based on vector notion. In this method, four vector arithmetic sides at the intersection are used to compute, and the computing results decide the orientation of Boolean operation result loop. The method can also solve these singular problems. The method based on vector proposed in this paper can solve the common problems in Boolean operation, as well as improve the operation efficiency in a certain extent and save the computing time.(2) To solve poor stability of Boolean operation caused by engineering tolerance, or float operations errors, this paper optimizes our method based on vertex merging. For the problems caused by float computing or engineering error, this paper sets the tolerance threshold and adjusts these data within the tolerance threshold to minimize the errors, so as to improve the result accuracy of complex polygon Boolean operation. The Boolean operation method based on vertex merging is more accurate, and improves the operation accuracy at the same time.(3) In order to speed up the Boolean operation computing process of large-scale engineering with high local similarity, this paper presents a Boolean operation method based on similarity evaluation technology. This paper do the similarity evaluation computing based on models semantic information, geometric properties and topological relationship, and uses the computing results of similar model sets as the operation results. For projects with a high similarity between components, combining with the similarity evaluation technology, Boolean operation computing are more efficient.(4) To verify the method proposed in this paper, this paper designs and constructs Boolean operation simulation system. This paper firstly do the similarity evaluation for large-scale engineering, and then do the Boolean operation for these components sets that do not find similar sets. For these similarity components sets, we can use the operation results that similar with them. Applications show that, the method proposed in this paper combining with similarity evaluation, not only has a fast calculation speed and solves the common singular problems existing in Boolean operation, but also effectively reduces the errors caused by float computing or engineering tolerance.