Manifold Processing from scattered points: application to thin shell analysis

DANIEL MILLÁN; ADRIAN ROSOLEN; MARINO ARROYO

Venice

Congreso; 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008); 2008

European Community in Computational Methods in Applied Sciences

We present a method for point-based (embedded) manifold processing avoiding any kind of mesh or tessellation. A fundamental difficulty in this endeavor is the absence of an obvious parametric space for general surfaces. In mesh-based processing, the mesh not only provides a geometric description of the surface, but it also provides a support to local parametric spaces and shape functions. Nonetheless this approach is seriously hindered in high dimensions. We apply weighted principal component analysis together with maximum entropy approximants to provide a robust method for point?based manifold processing.