Fast Computation of Vertex Normals for Linearly Deforming Meshes

Abstract

In this paper, we deal with shading of linearly deforming triangular meshes that deform in time so that each vertex travels independently along its linear trajectory. We will show how the vertex normal can be computed efficiently for an arbitrary triangular polygon mesh under linear deformation using the weighting scheme referred to by Jin et al. as "mean weighted by areas of adjacent triangles." Our computation approach is also faster than simple normal recomputation. Moreover, it is more accurate than the usual linear interpolation. The proposed approach is general enough to be used to compute the vertex normal for any number of adjacent faces.