量化三维网格模型复杂度的Fractal Dimension^(+)方法

Fractal Dimension^(+)Method for Quantifying the Complexity of 3D Mesh Models

对三维网格模型复杂度的评估及应用进行研究,提出基于Fractal Dimension^(+)方法量化三维网格模型复杂度。该方法利用分形几何学的分形维度来确定三维网格模型的不规则性;为了全面量化复杂度并且提高量化的准确性和可信度,在分形维度算法中添加孔隙比和亏格数的概念,全面考虑介质内部空间分布和几何结构的连接性以及孔洞分布的信息。对大量三维网格模型进行实验,结果表明Fractal Dimension^(+)方法可以有效计算出准确的复杂度。

This study investigates the evaluation and application of 3D mesh model complexity,and proposes a Fractal Dimension+method to quantify the complexity of 3D mesh models.The method uses the fractal dimension of fractal geometry to determine the irregularity of 3D mesh models.To fully quantify complexity and improve the accuracy and reliability of quantification,the concept of porosity ratio and genus number are added to the fractal dimension algorithm.The addition provides a comprehensive consideration of the connectivity of the internal spatial distribution,geometric structure of the medium,and hole distribution information.Experiments conducted on a large number of 3D mesh models demonstrate that the Fractal Dimension^(+)can effectively calculate accurate complexity.