Curvature in Triangle Meshes
In many cases notions from differential geometry can be usefully extended to piecewise planar surfaces, and this chapter covers curvature measures on triangle meshes. A frequently used principle is to obtain a smooth surface approximation and to estimate the curvature from this approximation. Alternatively, the integral of some curvature measures can be computed from a small region of the mesh and then normalized by dividing by the area of that region.
Following these principles, we first discuss how to extend the definition of a surface normal to the edges and vertices of a triangle mesh. Next, we cover the estimation of Gaußian and mean curvature on a triangle mesh. Finally, techniques for computing the shape operator are discussed—followed by a discussion on how to obtain the principal curvatures from the shape operator.
KeywordsSmooth Surface Principal Curvature Principal Direction Curvature Measure Shape Operator
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