As a direct consequence of software quirks, designer errors, and representation flaws, often three-dimensional shapes are stored in formats that introduce inconsistencies such as small gaps and… (More)

Let K be a simplicial complex and g the rank of itsp-th homology groupHp(K) defined withZ2 coefficients. We show that we can compute a basis H of Hp(K) and annotate each p-simplex ofK with a binary… (More)

Bubbles and foams are important features of liquid surface phenomena, but they are difficult to animate due to their thin films and complex interactions in the real world. In particular, small… (More)

The persistent homology provides a mathematical tool to describe “features” in a principled manner. The persistence algorithm proposed by Edelsbrunner et al. [9] can compute not only the persistent… (More)

The fractures of thin plates often exhibit complex physical behaviors in the real world. In particular, fractures caused by tearing are different from fractures caused by in-plane motions. In this… (More)

In this work, we propose an alternative algorithm for annotating simplices of a simplicial complex K with sub-bases of a basis B of its p-dimensional homology group H1(K). Such annotations, summed… (More)