Multiresolution shape deformations for meshes with dynamic vertex connectivity

Multiresolution shape representation is a very effective way to decompose s urface geometry into several levels of detail. Geometric modeling with such representations enables flexible modifications of the global shape while p reserving the detail information. Many schemes for modeling with multiresol ution decompositions based on splines, polygonal meshes and subdivision sur faces have been proposed recently. In this paper we modify the classical co ncept of multiresolution representation by no longer requiring a global hie rarchical structure that links the different levels of detail. Instead we r epresent the detail information implicitly by the geometric difference betw een independent meshes. The detail function is evaluated by shooting rays i n normal direction from one surface to the other without assuming a consist ent tesselation. In the context of multiresolution shape deformation, we pr opose a dynamic mesh representation which adapts the connectivity during th e modification in order to maintain a prescribed mesh quality. Combing the two techniques leads to an efficient mechanism which enables extreme deform ations of the global shape while preventing the mesh from degenerating. Dur ing the deformation, the detail is reconstructed in a natural and robust wa y. The key to the intuitive detail preservation is a transformation map whi ch associates points on the original and the modified geometry with minimum distortion. We show several examples which demonstrate the effectiveness a nd robustness of our approach including the editing multiresolution models and models with texture.