Linear interpolation of shape operators for umbilical points via local parameterization

分类： 计算机科学 >> 计算机应用技术 提交时间： 2017-03-10

Che, Wujun

摘要： Principal curvatures and principal directions are exploited ubiquitously in shape analysis. On one hand, umbilical points severely hinder the analysis as the singularities in the vector field of principal directions; on the other hand, providing shape-intrinsic qualitative information about a surface, they are desirable quantities in some applications. Umbilical points are fundamental for geometric analysis, but their accurate computation on a discrete surface is still challenging. In this paper, we develop a simple and effective method to detect umbilical points on a triangle mesh, in which any parametrization works. In particular, we propose two practical processes for local parametrization by orthogonally projecting or conformally transforming the matrix onto a specified parametric plane. Furthermore, we make a systematic analysis on our method and demonstrate its convergence behavior. The algorithm of our approach is flexible and easy to implement for a triangular mesh of arbitrary topology.

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