QUADOR: QUADric-Of-Revolution beams for lattices. (September 2018) - Gupta, Ashish; Allen, George; Rossignac, Jarek
Abstract: Objects with designed internal structure often consist a lattice of beams, in which the surface of each beam smoothly connects two spheres, possibly of different radii. We propose a geometric model for these beams that provides a compromise between shape flexibility and ease of computation: each beam is either a single quadric of revolution ("quador"), or two smoothly connected ones ("biquador"). Quador and biquador beams can be specified using easily adjustable parameters. They simplify and accelerate several common geometric queries, including point classification, ray casting, planar slicing, and boundary evaluation. We compare quadors and biquadors with other possible beam shapes, and show that these alternatives have either reduced flexibility or increased computational cost. We advocate decomposing the lattice into an assembly of hubs, each hub defined as the union of a sphere with the half-beams (stumps) that connect to it. We describe approaches for computing an exact polyhedral Constructive Solid Trimming expression of each face and the exact edges and vertices of the hub. Graphical abstract: Highlights: Lattice beam bound by quadric-of-revolution smoothly connecting two sphere-nodes. Provides both shape flexibility and ease of computation. Lattice decomposition into an assembly of quasi-disjoint half-beams and nodes. Exact polyhedral CSG expressions for the Active Zone of each half-beam and node. Intersection of two quadors connected to a node is a conic section or is empty.