Linear Correlations between Spatial and Normal Noise in Triangle Meshes

Yang, Ying; Norbert, Peyerimhoff; Ivrissimtzis, Ioannis

Abstract

We study the relationship between the noise in the vertex coordinates of a triangle mesh and normal noise. First, we compute in closed form the expectation for the angle  between the new and the old normal when uniform noise is added to a single vertex of a triangle. Next, we propose and experimentally validate an approximation and lower and upper bounds for  when uniform noise is added to all three vertices of the triangle. In all cases, for small amounts of spatial noise that do not severely distort the mesh, there is a linear correlation between  and simple functions of the heights of the triangles and thus,  can be computed efficiently. The addition of uniform spatial noise to a mesh can be seen as a dithered quantisation of its vertices. We use the obtained linear correlations between spatial and normal noise to compute the level of dithered quantisation of the mesh vertices when a tolerance for the average normal distortion is given.

Citation

Yang, Y., Norbert, P., & Ivrissimtzis, I. (2013). Linear Correlations between Spatial and Normal Noise in Triangle Meshes. IEEE Transactions on Visualization and Computer Graphics, 19(1), 45-55. https://doi.org/10.1109/tvcg.2012.106

• Journal Article Type: Article
• Publication Date: 2013-01
• Deposit Date: Nov 29, 2012
• Journal: IEEE Transactions on Visualization and Computer Graphics
• Print ISSN: 1077-2626
• Electronic ISSN: 1941-0506
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 19
• Issue: 1
• Pages: 45-55
• DOI: https://doi.org/10.1109/tvcg.2012.106
• Public URL: https://durham-repository.worktribe.com/output/1492053