An Improved 3D Box-Counting Dimension Computing Technology for Estimating the Complexity of 3D Models

Abstract

The box-counting dimension, which can effectively reflect the complexity and self-similarity of models, is an important method for calculating the fractal dimension of models. To improve the precision of the box-counting dimension algorithm, in this study, we propose an improved 3D box-counting dimension algorithm for models composed of triangular meshes. Through linear coding and optimization of intersection detection between triangles and octree cells, we can accurately calculate the box dimension of models with less memory expense. Through the results of measuring regular geometric bodies and spatial Voronoi bodies, it can be seen that the method has good performance, and the ability of filling space of fractal bodies can be calculated accurately. In the circumstance of 3D box-counting dimension algorithm cannot work well for comparing curvature changes of non-fractal surfaces, the weighted box-counting dimension algorithm can be used to quantitatively analyze the complexity of surface curvature.