Parametrizações de superfícies triangulares - Telau, Antônio Carlos (2012)
Two types of triangular surface parameterizations are proposed in this work: spherical and planar parameterization. We highlight among the applications of this technique, texture mapping and manipulation/deformation of surfaces. In the planar case, a surface with boundary is parameterized in a planar convex polygon, as from the planar immersion of its graph. The theory presented characterizes the set of parameterizations of a given surface, when convex polygon is fixed, from matrices which satisfy a set of conditions. In the case spherical, advanced results of graph theory are used to determine parameterizations of closed surfaces. In this case, we characterize the set of spherical parameterizations of a given surface as the set of all spherical immersions of your graph where each vertex is a spherical projection of some convex combination of its neighbors. In both cases, algorithms based on the methodology propose have been implemented and we presente some results obtained by the proposed algorithms. The results are analyzed and limitations of the algorithms are discussed