An Accurate Vertex Normal Computation Scheme

  • Huanxi Zhao
  • Ping Xiao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4035)


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.


Normal Vector Order Accuracy Quadratic Convergence Vertex Angle Darboux Frame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Huanxi Zhao
    • 1
  • Ping Xiao
    • 2
  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaChina
  2. 2.School of mathematical science and computing technologyCentral South UniversityChangshaChina

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