# Dihedral Rigidity and Deformation

### Abstract

We consider defining the embedding of a triangle mesh into $\mathbb{R}^3$, up to translation, rotation, and scale, by its vector of dihedral angles. On the theoretical side, we show that locally the map from realizable vectors of dihedrals to mesh embeddings is one-to-one almost everywhere. On the implementation side, we are interested in using the dihedral parameterization in shape analysis. This demands a way to visualize statistical results, for instance an average shape. To this end, we give a heuristic method for mapping interpolations in dihedral space to interpolations between input mesh embeddings, and we visualize statistical analyses of several families of organic shapes.

Publication
Computational Geometry
##### Carlos Rojas
###### Assistant Professor

My research interests include bioinformatics, computing education, visualization, and machine learning.