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non_iterative_mesh_smoothing.md

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Non-Iterative, Feature-Preserving Mesh Smoothing

Author: Jones

Year: 2003

Notes:

  • Mesh Smoothing algorithm applicable to every "triangle soup" with robust statistics
  • pb: remove noise while preserving the shape
  • previous work: isotropic algorithm (smooth salient features), diffusion equations (significant computationnal time), diffusion on normal field (same as before)
  • capture the smoothness of a surface with local first order predictors

Method

  • predict the surface of a triangle $q$ with a tangent plane $\Pi_q$
  • estimate the position of a vertex $p$ based on the predictions $\Pi_q(p)$
  • the estimate of a point is then the weighted average of all the predictors of $q \in S$ $\Pi_q(p)$ on a given surface $S$ $$ p^{\prime}=\frac{1}{k(p)} \sum_{q \in S} \Pi_q(p) a_q f\left(\left|c_q-p\right|\right) g\left(\left|\Pi_q(p)-p\right|\right) $$ with $k(p)$ the normalizing factor: $$ k(p)=\sum_{q \in S} a_q f\left(\left|c_q-p\right|\right) g\left(\left|\Pi_q(p)-p\right|\right) $$
  • Then mollification (i.e. smoothing of the normals (with the same method as before ?))