Corner-Sharing Tetrahedra for Modeling Micro-Structure

TL;DR

This paper introduces Corner-Sharing Tetrahedra (CoSTs), a discrete modeling approach for micro-structure that captures local constraints and multi-scale properties, enabling advanced geometric processing and analysis.

Contribution

It presents a novel discrete representation called CoSTs for modeling micro-structures, along with geometry processing operations and continuous approximations.

Findings

CoSTs effectively model various constraint systems.

The framework supports hierarchical refinement and randomization.

Associated continuous representations facilitate analysis.

Abstract

State-of-the-art representations of volumetric multi-scale shape and structure can be classified into three broad categories: continuous, continuous-from-discrete, and discrete representations. We propose modeling micro-structure with a class of discrete Corner-Sharing Tetrahedra (CoSTs). CoSTs can represent bar-joint, tensegrity, line-incidence, and similar constraint systems that capture local physical constraints and global multi-scale properties for design and analysis. The paper develops a palette of simple geometry processing operations on CoSTs including graph manipulation, hierarchical refinement, randomization, and generating associated continuous representations.