Least squares and point-based surfaces: new perspectives and Applications

Surface approximation from unorganized points belongs to the state-of-art of computer graphics. In this work, we present approaches for surface reconstruction that are based on efficient numerical schemes for function approximation from scattered data and on sophisticate data structures. In addition, we develop a relevant surface reconstruction method to model moving interfaces, specifically, interfaces of numerically simulated multiphase fluid flow. Finally, from our accumulated experiences on numerical schemes and on the development of surface reconstruction methods, we propose a matrix-free approach for rendering arbitrary volumetric scattered data, which presents interesting properties to be implemented on GPU.