An accurate vertex normal computation scheme

Authors:
Huanxi Zhao;Ping Xiao
Affiliations:
School of Information Science and Engineering, Central South University, Changsha, China;School of mathematical science and computing technology, Central South University, Changsha, China
Venue:
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
Year:
2006

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Abstract

There are a number of applications in computer graphics and computer vision that require the accurate estimation of normal vectors at arbitrary vertices on a mesh surface. One common way to obtain a vertex normal over such models is to compute it as a weighted sum of the normals of facets sharing that vertex. But numerical tests and asymptotic analysis indicate that these proposed weighted average algorithms for vertex normal computation are all linear approximations. An open question proposed in [CAGD,17:521-543, 2000] is to find a linear combination scheme of the normals of the triangular faces, based on geometric considerations, that is quadratic convergence in the general mesh case. In this paper, we answer this question in general triangular mesh case. When tested on a few random mesh with valence 4, the scheme proposed by this paper is of second order accuracy, while the existing schemes only provide first order accuracy.