Jinesh Machchhar (CS, Technion)
Solid sweep is the envelope of the swept volume of a given solid moving along a one parameter family of rigid motions in 3 dimensional space. Solid sweep is a powerful and versatile surface design tool which has found uses in many areas like CNC-machining verification, collision detection and packaging. This work aims to develop a robust computational framework for sweeps in the realm of boundary representation (brep) format, wherein, the input solid as well as the outputted swept volume are represented in brep. This involves the following considerations: (i) Giving an accurate parametrization of the faces and edges in the brep of the swept volume, (ii) Resolving self-intersections and singularities, and (iii) Computing topological information, viz., adjacency relations amongst the faces, edges and vertices of the swept volume as well as the orientation of these.
In almost all non-trivial sweeps, there exists no closed form parametrization of the envelope surface. We address this problem via the procedural paradigm in which the parametric definitions of curves and surfaces are stored as numerical procedures.
We give a novel classification of sweeps into simple, decomposable and non-decomposable based on the complexity of trim regions. A novel geometric invariant aids in efficient classification as well as in locating the trim curves.
We show that while the global brep structure of the input solid and that of the envelope are quite different, locally they are similar. This aids in lifting the brep structure of the solid to that of the envelope.
(Based on joint work with Milind Sohoni and Bharat Adsul).