How to morph tilings injectively
The continuous transformation of a geometric configuration into another (analogous to a homotopy) is called \textit{morphing}. Here the authors discuss morphing a (finite) tiling by convex polygons (in the plane) to a \textit{compatible} tiling. Since linear interpolation may produce degenerate tilings, they propose a \textit{convex} morph: Each (interior) vertex is represented as a convex combination of its neighbours which is used for interpolation (by solving the resulting linear system). This leads to a valid morph if the boundary of the tiling is convex and remains unchanged, and to a morph preserving starshape (at least) when distinct boundaries are morphed using polar coordinates. Some examples are given.
scientific article; zbMATH DE number 1331085