CTSP: CSG Combinations of Tran-Similar Two-Patterns of CSG Cells

Abstract

We propose a paradigm for the design and processing of solid structures that form a bent two-pattern of cells that are similar to each other, but have steadily varying scale and orientation. The proposed CTSP is a procedural representation that extends prior work on periodic lattices from a union of balls and beams, to a CSG combination of unions of cells, each of which is a CSG solid. To ensure consistent connections between neighboring cells, the primitives are defined implicitly in terms of two-patterns of balls. We propose an algorithm, which, in constant time, computes a set of ranges of cells that include all cells that interfere with a given query ball. We also propose an algorithm which enables interactive visualization of these structures, even when they have a large count of cells. We also discuss potential uses of this solution for modeling shelled lattices and multi-resolution periodic structures, where, for example, each cone-beam shell of a coarse shelled lattice is a CTSP.