Abstract
Triangular meshes play critical roles in many applications, such as numerical simulation and additive manufacturing. However, the triangular meshes transformed from computer-aided design models using common algorithms may have many undesirable narrow triangles, which tends to affect the downstream applications. In this paper, we proposed two algorithms for Delaunay mesh construction and simplification to improve the quality of the triangular meshes. Two improved mesh operations of inserting vertices and collapsing vertices based on the principle of minimum volume destruction were designed. The improved vertex inserting operation is able to modify the local mesh so that it will conform to the local Delaunay property. The improved vertex collapsing operation can realize the simplification of the original mesh while maintaining the local Delaunay property. The results of visualized rendering and thermal diffusion simulations verified the improvement of the proposed algorithms in the aspects of the quantity and quality of the meshes.
Highlights
Preserving Based on Minimal VolumeComputer-aided design (CAD) models have played crucial roles in technical fields, such as numerical simulation, additive manufacturing and visualization
Garland and Heckbert [3] proposed a kind of quadratic error metrics (QEM) simplification method, which is regarded as the general model simplification algorithm
As the number of vertices reduce, the geometric features of the original mesh can still be effectively displayed. These results demonstrate the effectiveness of the simplification algorithm in preserving geometric information
Summary
Computer-aided design (CAD) models have played crucial roles in technical fields, such as numerical simulation, additive manufacturing and visualization. Triangular meshes, which are always transformed directly from a CAD model, usually have the defects of excessively small or large angles, and redundant or irregular vertices These defects tend to reduce the accuracy of the numerical simulation based on triangular meshes. Khan et al [7] tried to plan a more reasonable distribution of the number of vertex-to-vertex connections and optimize the meshes by constraining the range of angles Most of these algorithms were based on the method of area-equalizing triangulation, which were used to achieve optimization and simplification of meshes in forms of regular triangles. The regular triangles can improve the computational accuracy of simulation results, the overemphasis on the evenly constructed triangular elements may limit the reduction of data storage and cause destruction to the geometric feature information of the original model. The experiments show that the proposed algorithms were effective for optimizing the non-Delaunay meshes, and especially for the improvement of the quality and quantity of the Delaunay meshes
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