Adaptive surfaces fairing by geometric diffusion
Geometric modeling
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In this paper we treat discrete data (2-manifold) in IR 3 and function data defined on the surface. A surface and a k-3 dimensional function vector data on the surface can be considered as a discretization of a 2-manifold embedded in IRk. We establish a unified anisotropic diffusion model for such manifolds aiming at smoothing (fairing) out noise both in the 2-manifold in IR3 and the 2-manifold in IRk, while enhancing curve features on both 2-manifolds. We combine the C1 limit function representation of Loop''s subdivision for triangular surface meshes and vector functions on the surface mesh with anisotropic diffusion in a parameterized time setting, to arrive at a sparse linear system of equations. Iteratively, solving the sparse linear system, yields a sequence of faired (smoothed) meshes as well as faired function with specified feature curves, enhanced.