Geração de nuvem de pontos para métodos sem malhas

Abstract

A technique to generate point clouds for meshless methods which are constrained by an specified density function and by the input geometry is presented. Initially, points are distributed along the geometry edges identifying their limits and the boundaries between different materials. To generate points inside the geometry, two different approaches are used: (i) random distribution and (ii) a subdivision-based quadtree, where the smallest square that surrounds the geometry is recursively subdivided into four, with the creation of a new point in the center of each square. In both cases, the iterative process stops when the points density approximates the specified density function. The initial points are redistributed using an iterative Lloyd refinement algorithm, until the expected distribution is met. Uniform distributions of points as well non-uniform ones, where the density function is not constant, can be met. The final quality of the resulting cloud just depends on the Lloyd refinement algorithm. However, the algorithm that generates initial points based on quadtrees, although more complex than the random generation, needs less iterations of the Lloyd algorithm to achieve the expected quality. This is due to the fact that its initial points distribution already takes into account the specified density function.