Mesh Simplification For CAD Models Based On Global Features Preserving

In many fields, such as mechanical manufacture, architecture, medical treatment, military affairs, electronic business and geography information, the applications of the visualization and the transmission on Internet of three-dimensional model have already become widespread. Triangle mesh is a basic geometry unit supported by almost all graphics hardware, and three-dimensional mesh model based on triangle mesh is a universal presentation format for application system of model rendering. With the development of relative technology of these application fields, the presenting precision and complexity of three-dimensional model increase continuously and thus the number of triangle meshes used for three-dimensional model increase sharply, so it always exceeds the hardware capabilities for rendering such complex meshes at an interactive rate, and it also usually goes beyond the network abilities for real-time transmitting. Mesh simplification is one of the most important methods for solving the above problems.Mechanical models in the application fields of digital manufacturing and digital products developing are usually CAD models. Generally speaking, surface of mechanical products is composed of some surfaces of regular forms, and thus mechanical CAD model has characteristics of regular forms, distinct feature shape. While applying the existing mesh simplification algorithms to these CAD model, the simplification results are always poor in global shape features preserving. Using the relevant research achievements for reference, the problems of the simplification of mechanical CAD model and the preservation of global shape features after simplification is deeply researched in this dissertation, and a simplification method based on the preserving of global shape features, which is suitable for mechanical CAD model is presented.Firstly, aiming at the facts that meshes on the surface of mechanical CAD models are usually sparse and non-uniform, we propose a hybrid algorithm of twice features detections and surface segmentation: for the first of which we adopt edge-based method, namely in terms of variance of vector included angle, which takes from adjacent triangle meshes after mergence of planes, the corresponding process will be executed in order to eliminate affection for estimation of discrete curvature because of the meshes on the surface being sparse and non-uniform, and thus implement region segmentation and features detection for plane and sparse mesh surface; for the second of which we adopt the method of analysis of discrete curvature based on the vertex, calculating approximate curvature of every mesh first, and then through region growing to implement segmentation and feature detection for other surface regions. The algorithm can not only solve the problem of incorrect features segmentation from edge-based method because of incomplete features detection, but also cover the shortages from vertex-based method, such as mis-segmentation, loss of shape features and big error of curvature estimation. Toward the problem of over-segmentation, we also propose a region-combination method based on curvature error. The above proposed algorithm significantly improve the results of shape features detection and surface segmentation for mechanical CAD model, and it provides essential information for features preserving in the process of the subsequent mesh simplification.Secondly, as the shape of the boundary curves of mechanical CAD models is always equilateral and symmetry, we present a polygonal approximation of digitized curves algorithm based on particle swarm optimization (PSO), and further implement the simplification of global features preserving for the detected mesh model. In the algorithm, each particle represented as a binary vector corresponds to a candidate solution to the polygonal approximation, the centroid offset error of polygon between the original one and simplified one and variance of Euclidean distance are imported to the fitness evaluation, constant accelerating factor has been replaced by the sigmoid function which represents iterative number to control global and local search features in the process for targeting the optimal solution of PSO algorithm. The algorithm has better results for preserving shape features of regular curves of polygon after simplification. In order to reduce degree of adjustment for vertices of polygon created by the subsequent QEM simplification algorithm, the position of vertices of corresponding polygon is taken as restriction condition, and further we give polygon approximation algorithm which has restrictions of reference solution, through adjusting affecting factors we realize flexible control of the capacity of adjustment and degree of preserving of global and local features. Finally, we further propose the mesh simplification method for mechanical CAD mesh model based on global shape features preserving. The algorithm deals with the problem of the existing universal simplification algorithms, which can not preserve the global shape features efficiently for mechanical CAD mesh model. For one thing, we adopt a hybrid algorithm, namely twice features detections and surface segmentation proposed in our paper, to implement the shape features detection for mechanical CAD mesh model, so that the following steps can implement the simplification for the preserving of global shape features; for another, we adopt improved QEM simplification algorithm to pre-simplify the mesh model and then get simplified model and the position of vertices; furthermore, simplification algorithm of polygonal approximation based on PSO is used, which proposed in this paper. Through importing the restrictions to the fitness evaluation, such as centroid position errors between the original one and simplified one, vertices errors and corresponding vertices offset errors of features shape, we get the approximated polygon which not only preserves global shape features but also has the results of QEM simplification ; at last, in terms of approximated polygon, the features shape of QEM simplified model is registered and the vertices position is adjusted for optimization, and then it preferably preserves the global shape features of original CAD mesh model.