Applications of Conformal Geometric Algebra in Mesh Deformation

Abstract

We illustrate the suitability of Conformal Geometric Algebra for representing deformable mesh models. State-of-the-art modeling tools allow the user to deform 3D models (or region of interest) by selecting sets of points on the surface, called and move them freely. The deformed surface should look naturally stretched and bent. Mesh representations based on Conformal Geometric Algebra extend, quite naturally, the existing deformable mesh representations by introducing rigid-body-motion a.k.a motor handles, instead of just translation handles. We show how these mesh representations conduct to a fast and easy formulation for the Spline-aligned deformation and a formulation for linear surface deformation based on generalized barycentric coordinates. Also, we reformulate the Free-Form Deformation (FFD), Harmonic Coordinates (HC) and As-Rigid-As-Possible (ARAP) Surface Modeling into the Conformal Geometric Algebra framework and discuss the advantages of these reformulations.