Skeletal Structures for Modeling Generalized Chamfers and Fillets in the Presence of Complex Miters

Abstract

We present a simple algorithm to compute the straight skeleton and mitered offset surfaces of a polyhedral terrain in 3D, i.e., of a z-monotone piecewise-linear surface. Like its 2D pedant, the 3D straight skeleton is the result of a wavefront propagation process, which we simulate in order to construct the skeleton in (worst-case) time O(n 4 log n), where n is the number of vertices of the terrain. Any mitered offset surface can then be obtained from the skeleton in time linear in the combinatorial size of the skeleton.

Ramp Approach Parameter Correction Method for 3-axis Web Machining

“…Similar to other skeletal structures [13], it is also possible to derive three-dimensional terrains from a VRS that can be used as intricate roofs over polygonal footprints of buildings. For a polygonal footprint P , a point p of Computer-Aided Design & Applications, 18(5), 2021, 875-889 © 2021 CAD Solutions, LLC, http://www.cad-journal.net S w (P ), with coordinates (p x , p y ), is lifted to a point in R 3 with coordinates (p x , p y , d w (p, s)).…”

Function Model-based Generation of CAD Model Variants

“…Similar to other skeletal structures [13], it is also possible to derive three-dimensional terrains from a VRS that can be used as intricate roofs over polygonal footprints of buildings. For a polygonal footprint P , a point p of S w (P ), with coordinates (p x , p y ), is lifted to a point in R 3 with coordinates (p x , p y , d w (p, s)).…”