Algorithms, Vol. 14, Pages 304: Analytic Form Fitting in Poor Triangular Meshes (Algorithms)

Fitting of analytic forms to point or triangle sets is central to computer-aided design, manufacturing, reverse engineering, dimensional control, etc. The existing approaches for this fitting assume an input of statistically strong point or triangle sets. In contrast, this manuscript reports the design (and industrial application) of fitting algorithms whose inputs are specifically poor triangular meshes. The analytic forms currently addressed are planes, cones, cylinders and spheres. Our algorithm also extracts the support submesh responsible for the analytic primitive. We implement spatial hashing and boundary representation for a preprocessing sequence. When the submesh supporting the analytic form holds strict C0-continuity at its border, submesh extraction is independent of fitting, and our algorithm is a real-time one. Otherwise, segmentation and fitting are codependent and our algorithm, albeit correct in the analytic form identification, cannot perform in real-time.