Minimos-quadrados e aproximação de superfície de pontos: novas perspectivas e aplicações
Surface reconstruction from unorganized points has been one of the most promising scientific research areas in Computer Graphics. In addition, it has been used successfully for the definition of fluid interface in numerical simulation of fluid flow. There are several reasons to that fact: for instance, considering Computer Graphics, we have the handling of out-of-core data from complicated geometries and subject to noisy information that brings out opportunities for the development of new
... ques. Further, considering Numerical Fluid Mechanics, where the input data does not come from tridimensional scanners, but from fluid interfaces, schemes that define the surface from unorganized points can offer geometrical and computational properties useful to numerical fluid flow simulation. The main goal of this project was the development of novel techniques for reconstructing surfaces from unorganized points with the capability to overcome the main drawbacks of important previous work. To that end, first we focused on the development of techniques based on moving-least-squares and on a robust twofold partition of unity Implicits. Added to the development of surface reconstruction from unorganized points, we proposed a novel scheme for defining fluid flow interfaces. We approach a meshless Lagrangian based on algebraic moving-least-squares surfaces. In addition, we presented several numerical results, convergence tests and comparisons, which state the power of the method to numerical simulation of physical phenomena. Although our main contributions were focused on surface reconstruction from points, we proposed methods to function reconstruction from unorganized volumetric data. Thus, we present two schemes to represent volumetric data from arbitrary meshes, i.e., a unified rendering scheme.