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Curvature Computing Based on Shape Operator for Implicit Surfaces
Mao Zhihong * #
Department of Computer Science, Sun Yat-Sen University, Guangzhou, 510275
*Correspondence author
#Submitted by
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Funding: the Doctoral Fund of Ministry of Education of China for new teachers （No.20100171120045）
Opened online:23 December 2013
Accepted by: none
Citation: Mao Zhihong.Curvature Computing Based on Shape Operator for Implicit Surfaces[OL]. [23 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4574762
 
 
The shape operator, whose eigenvalues and eigenvectors are the principal curvature values and directions, have been widely used to compute surface curvature for a parametric surface. In this paper we present mathematical representations to compute the surface curvatures based on the shape operator on implicit surfaces. Compared to the existing curvature formulae for implicit surfaces, our curvature formulae are easy to understand and simple to compute. Moreover, we bridge the gap between the classical differential geometry theories and the curvature computing formulae for implicit surfaces. Finally, we demonstrate our method with several examples.
Keywords:Curvature Computing; Shape Operator; Implicit Surfaces
 
 
 

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