2D Shape Deformations Using Moving Least-Squares with Topology-Aware Distance Metric

Detail-preserving deformations of two-dimensional shapes have recently received wide attention in the field of computer graphics. Among them, the deformation method using Moving Least-Squares (MLS) proved to produce smooth deformations with low computational costs. However, it suffers from artifacts due to the ignorance of the topological structure of the shape. This paper presents a novel algorithm that accounts for the topology of the shape in order to eliminate the artifacts. The present algorithm replaces the Euclidian distances used in the weight functions of MLS with the distances measured along the shape, which yields more realistic results. Furthermore, by adjusting the distance field partially, the present algorithm can configure the stiffness of the shape around the regions specified by the user, and can extend the controllability of deformations.