摘要： 针对三角网格模型优化算法对模型几何细节描述不够精确的问题，提出一种基于Laplacian坐标的网格模型全局优化算法。模型几何细节描述方面，采用网格顶点Laplacian坐标。网拓扑结构不变的前提下，可精确描述网格曲面局部几何特性。顶点重新定位方面，采用在最小二乘意义下求解由权重控制的包含顶点位置，以及Laplacian坐标双重约束的线性系统最优解的方法。实验结果表明，该算法在优化提高模型三角面片质量的同时，可较好地保留原始模型的几何细节。
关键词:
STL文件,
三角网格模型,
离散微分几何,
三角面片质量,
全局优化,
顶点重新定位
Abstract: To the problem that the optimization algorithm to triangle quality of mesh mode can not preserve geometry detail very well, this paper introduces an algorithm for global optimization of triangular meshes which is guided by the vertex Laplacians. In term of geometric detail describation, vertex Laplacian is used, on the condiation that topology structure is not changed. Lapacian can describe geomatic features of mesh surface accurately. In terms of vetex relocation, new position of vertexes based on optimum relation of linear system that approximates prescribed Laplacians and positions in a weighted least-squares sense will be computed. The result of experiment shows that the technique successfully improves the quality of the triangle patch while remaining faithful to the original surface geometry.
Key words:
Stereolithography(STL) file,
triangular mesh model,
discrete differential gemmetry,
triangle patch quality,
global optimization,
vertex relocation
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