Differential Coordinates Based Mesh Morphing

With the rapid development of computer graphics and the technology of hardware, as a new industry, computer animation has infiltrated into every corner of people's life, such as commercial advertisement, special effects in movie, cartoons, geometric modeling, industrial design etc. As the main means of computer animation, morphing, belongs to deformation technics, has been investigated in many contexts in recent years, is the gradual transformation of one object (the source) into another (the target). It gives the animator the ability to "fill" an animation between key-framed objects by inbetweening. It allows the designer to blend existing shapes in order to create new shapes. The growing demands stimulate a lot of related work on 3D-object morphing. Here, object can be an digital image, a polygon, a polyhedral, mesh or point cloud, etc. Nowadays the research priority has been given to 3D mesh morphing. In general case, mesh morphing consist of two phrases:1. Mesh correspondence; 2. Shape interpolation.We study on differential coordinates related knowledge and the development of 3D morphing, and do some classification and conclusions. Based on differential coordinates this paper proposes an integrated 3D mesh morphing, due to the problems exist and the properties of differential coordinates. In correspondence phrase, first, we get least square meshes, with some constrains, from the start mesh and target mesh respectively. In itself, we get the new vertices' positions from the adjusted differential coordinates in least square sense, which produces a initial correspondence. Then the double sided distance is minimized. At last, a projective operator is designed to complete the correspondence. In shape interpolation phrase, we directly interpolate differential coordinates between the two meshes with the length adjustment, then we reconstruct the inbetween mesh from them.Compared to traditional approaches, in the correspondence phrase, the algorithm proposed here can be applied to arbitrary manifold meshes no matter what the vertices numbers of input meshes. Our approach directly maps the connectivity of the source mesh onto the target mesh without needing to find the common parameter domain or first segment input meshes and then join them together, thus effectively enhances its utility, simplifies the process and raises the computation speed. In the second phrase, we take advantages of the differential coordinates which are computed through the corresponding process. An improved shape interpolation algorithm based on differential coordinates has been proposed in our work. It effectively avoids volume contraction during the shape interpolation process and produce a visual pleasing effect. In addition, our approach is with less user interactions. Users only have to define the initial correspondence set, then the morphing sequence will be produced by our algorithm...