Iso-phote based adaptive surface fitting to digitized points and its applications in region-based tool path generation, slicing and surface triangulation

An important task in computer graphics, computer-aided design and reverse engineering is the mathematical modeling of three-dimension complex surfaces based on digitized points. However, there are several open problems that are viewed as a bottleneck in the mathematical modeling. The topology is unknown. The reconstruction is based on parameterization and fitting stages. The above problems are influenced mainly by the parameterization, and the issue of parameterization for curve and surface fitting has been a difficult one since the advent of computers in design engineering. To resolve the above problems, in this paper a new strategy based on region-by-region adaptation is presented to surfaces fitting for digitized points. Furthermore, the “regions” used for adaptive surface fitting can be applied extendedly to three industrial applications: (1) tool path generation; (2) slicing; and (3) surface triangulation.