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.

我们考虑定义将三角形网格嵌入到 ${\mathbb{[R}}^3$，取决于其二面角矢量，直到平移，旋转和缩放。从理论上讲，我们证明了从二面角的可实现向量到网格嵌入的局部映射几乎在任何地方都是一对一的。在实现方面，我们对在形状分析中使用二面参数化感兴趣。这需要一种可视化统计结果（例如平均形状）的方法。为此，我们提供了一种启发式方法，将二面体空间中的插值映射到输入网格嵌入之间的插值，并可视化几个有机形状系列的统计分析。