Morphing with Laplacian Coordinates and Spatial-Temporal Texture

In this paper, we present a novel method to address the trajectory problem in 2D shape morphing based on the Laplacian coordinates (LCs). Although the LCs capture the geometric details of a shape, they are built in the global coordinate system and thus not rotation invariant [1, 7]. By adding rotation coherence constraints to as-rigid-as-possible transformations applied on the LCs, we make the intermediate morphing shapes highly appealing. Our method successfully alleviates local self-intersections. We also propose to interpolate the textures bounded by simple closed curves using a spatialtemporal structure. In previous texture morphing techniques, textures are usually encoded using triangulations [2]. Therefore, the morphing results depend on the quality of these triangulations. Given two simple closed curves and their interpolated shapes in the time domain, we construct uniformly distributed streamlines, which build a oneto-one mapping between the source and target textures, instead of encoding the textures using triangulation. The resulting mapping makes neighboring pixels morph coherently.