Issue No. 01 - Jan. (2013 vol. 19)

ISSN: 1077-2626

pp: 45-55

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.106

I. Ivrissimtzis , Sch. of Eng. & Comput. Sci., Durham Univ., Durham, UK

Ying Yang , Sch. of Eng. & Comput. Sci., Durham Univ., Durham, UK

N. Peyerimhoff , Dept. of Math. Sci., Durham Univ., Durham, UK

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 θ 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 θ 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 θ and simple functions of the heights of the triangles and thus, θ can be computed efficiently. The addition of uniform spatial noise to a mesh can be seen as a dithered quantization of its vertices. We use the obtained linear correlations between spatial and normal noise to compute the level of dithered quantization of the mesh vertices when a tolerance for the average normal distortion is given.

INDEX TERMS

mesh generation, approximation theory, computational geometry, average normal distortion, linear correlations, spatial noise, normal noise, triangle meshes, uniform noise, dithered vertex quantization, mesh vertices, Noise, Quantization, Degradation, Upper bound, Linear approximation, Rendering (computer graphics), normal noise, mesh generation, approximation theory, computational geometry, average normal distortion, linear correlations, spatial noise, normal noise, triangle meshes, uniform noise, dithered vertex quantization, mesh vertices, Noise, Quantization, Degradation, Upper bound, Linear approximation, Rendering (computer graphics), vertex quantization, Triangle mesh

CITATION

I. Ivrissimtzis, Ying Yang, N. Peyerimhoff, "Linear Correlations between Spatial and Normal Noise in Triangle Meshes",

*IEEE Transactions on Visualization & Computer Graphics*, vol. 19, no. , pp. 45-55, Jan. 2013, doi:10.1109/TVCG.2012.106