Planar Shape Blending Algorithm with Preserving Interior Similarity

Planar shape blending or morphing, which involves the creation of a smooth transition from a source planar polygon to a target one, has gained widespread use in recent years. In order to obtain good effects in computer animation, a novel and efficient algorithm for planar shape blending is presented, which can preserve the similarity of the interiors of the polygons and avoid local expansion or shrinkage. First, the high quality compatible triangulations between the source and target polygons are constructed. Then, the geometric quantities including the angle and edge ratio at every interior angle of the intermediate triangulation are computed by interpolating the counterparts of the source and target triangulations. Finally, the intermediate triangulation is constructed by solving a linear sparse system, which can be efficiently solved by some solver library. The intermediate polygon is obtained by the boundaries of intermediate triangulation. Planar shape blending is formulated as solving a linear sparse system finally. The feature polygon is introduced to preserve the global visual features of the source and target polygons. This approach is simple and fast and can be used in practical applications in real-time. Many experimental results are presented to show that the approach is applicable and flexible and can obtain satisfactory results for complex polygons.