INTRINSIC MORPHING OF COMPATIBLE TRIANGULATIONS

Intrinsic Morphing of Compatible Triangulations

Two planar triangulations with a correspondence between two vertex sets are compatible (isomorphic) if they are topologically equivalent. This work presents a simple and robust method for morphing two compatible planar triangulations with identical convex boundaries that locally preserves the intrinsic geometric properties of triangles throughout the morph. The method is based on the barycentri...

Morphing Stick Figures Using Optimized Compatible Triangulations

A “stick figure” is a connected straight-line plane graph, sometimes called a “skeleton”. Compatible stick figures are those with the same topological structure. We present a method for naturally morphing between two compatible stick figures in a manner that preserves compatibility throughout the morph. In particular, this guarantees that the intermediate shapes are also stick figures (e.g. the...

Towards Compatible Triangulations

Compatible pointed pseudo-triangulations

For a given point set S (in general position), two pointed pseudo-triangulations are compatible if their union is plane. We show that for any set S there exist two maximally disjoint compatible pointed pseudotriangulations, that is, their union is a triangulation of S. In contrast, we show that there are point sets S and pointed pseudo-triangulations T such that there exists no pointed pseudo-t...

Morphing Schnyder Drawings of Planar Triangulations

We consider the problem of morphing between two planar drawings of the same triangulated graph, maintaining straight-line planarity. A paper in SODA 2013 gave a morph that consists of O(n) steps where each step is a linear morph that moves each of the n vertices in a straight line at uniform speed [1]. However, their method imitates edge contractions so the grid size of the intermediate drawing...