Smooth parametric surfaces retrieval from triangular meshes using RBFs

Quality of physically-based simulation mostly relies upon qualities of the geometrical model of the entities involved. Particularly, Lagrangian formalism (which we focus on since several years) claims for continuous and smooth descriptors. Our current project aims a precise Lagrangian knee kinematics model. The studied knee model has been chosen as built up from actual bones geometries and ligament attachments. In this scheme, contact between femur and tibia must be seen as a constraint between two smooth surfaces. But, most of the time, actual geometric data coming from acquisition devices are modeled as discrete quantities. In this paper, we present a method to retrieve a smooth parametric surface from a triangular mesh. The first step calculates a global parameterization of a disk-like mesh. The second step builds a smooth parametric surface that interpolates the actual data using Radial Basis Functions (RBFs). This scheme allows for smoothly expressing any geometric quantity like tangent vectors or curvature at any point on the smooth surface. Out of the biomechanics area, we mention other possible applications of our framework for mesh refinement and non photorealistic rendering.