Exact Representations and Geometric Queries for Lattice Structures with Quador Beams. (October 2019) - Gupta, Ashish; Allen, George; Rossignac, Jarek
Abstract: Objects with architected internal structure often consist of a lattice of beams that are interconnected at nodes. Compared to the conventional cylindrical and conical beams, quador-beams are bounded by quadrics-of-revolution. We decompose the lattice into an assembly of hubs, wherein a hub is the union of a node (ball) with the half-beams incident upon it. In this paper, we propose (1) a hybrid representation of a quador-hub (hub with quador half-beams) consisting of exact CSG + CST + Boundary models, (2) a compact data structure and associated operators to work with the hybrid representation, and (3) algorithms to perform fundamental geometric queries on the hub. We provide the operators to query the half-beams of the hub, to inquire the trimming planes of a surface, or to traverse the faces, edges and vertices of the hub. We suggest efficient algorithms, that take advantage of the hybrid representation, for geometric queries such as point membership classification, planar slicing, surface meshing, and area/volume computation. We outline a possible approach for computing exact answers to all tests that are required for computing the exact topology of the proposed representation of the hub. Finally, we show that the simplified geometry of quador hubs leads to smaller data sizes and improved performance in a commercial modeler. Graphical abstract: Highlights: A hub defined as the union of a ball and incident quadric-of-revolution half-beams. Lattice decomposition into an assembly of hubs. Exact hybrid (CSG + CST + Boundary) representation of a hub. Compact data structure and related operators to work with the hybrid representation. Efficient algorithms to perform fundamental geometric queries on a hub.