Blending polygonal shapes with different topologies

In this paper, we propose a new method for morphing between two polygonal, possibly non-simply connected, shapes in the plane. The method is based on reconstructing an xy-monotone surface whose extreme cross-sections coincide with the given shapes. The surface generated by our algorithm does not contain any self-intersections, does not change the topologies of the input slices, does not contain any horizontal triangles, and guarantees that all the topology changes occur at a mid-height which is a degenerate form of both input topologies. All these properties are highly desirable for blending shapes of di!erent topologies. ( 2001 Elsevier Science Ltd. All rights reserved.