ON 2D SOLID α-COMPLEXES OF POISSON DISC SAMPLINGS
ESDRAS MEDEIROS, Luiz Carlos Pacheco Rodrigues Velho, Hélio Lopes, Thomas Lewiner · International Journal of Shape Modeling · 2009
This paper studies triangulations obtained from Poisson disc sampling. The Poisson disc sampling strategy with radius parameter α can be used to obtain a set of points in the interior or on the boundary of a given solid object in the plane. Using this sampling, we study a certain triangulation from its α-complex which results in two contributions. First, if we choose the same parameter α for the Poisson disc sampling and for the solid α-complex, we prove that all the triangles in the complex have aspect ratio less or equal than , which is only three times the aspect ratio of an equilateral triangle. Moreover, we prove that this bound is tight. Second, we establish a condition on the parameter α that allows to recover, with topological guarantees, the original solid object from the α-complex representation.