Topological Evolution of Surfaces

This paper presents a framework for generating smoothlooking transformations between pairs of surfaces that may differ in topology. The user controls the transformation by specifying a sparse control mesh on each surface and by associating each face in one control mesh with a corresponding face in the other. The algorithm builds a transformation from this information in two steps. The first step constructs a series of shapes and meshes (according the theory of topological surgery) that describes how topological changes should occur at critical points during the transformation. This makes possible the second step, which establishes smooth transformations by combining intermediate shapes in this series. Control meshes allow the user precise but intuitive control of the morph, while the 3D surfaces that result can be used for rendering or keyframing.

[1]  W SederbergThomas,et al.  A physically based approach to 2D shape blending , 1992 .

[2]  Thomas W. Sederberg,et al.  A physically based approach to 2–D shape blending , 1992, SIGGRAPH.

[3]  H. Delingette,et al.  Simplex Based Animation , 1993 .

[4]  John F. Hughes,et al.  Scheduled Fourier volume morphing , 1992, SIGGRAPH.

[5]  Richard E. Parent.  Shape transformation by boundary representation interpolation: A recursive approach to establishing face correspondences , 1992, Comput. Animat. Virtual Worlds.

[6]  Marc Levoy,et al.  Feature-based volume metamorphosis , 1995, SIGGRAPH.

[7]  E. W. Bethel,et al.  Shape Distortion in Computer-Assisted Keyframe Animation , 1989 .

[8]  Thaddeus Beier,et al.  Feature-based image metamorphosis , 1998 .

[9]  Wayne E. Carlson,et al.  Shape transformation for polyhedral objects , 1992, SIGGRAPH.

[10]  Andrew P. Witkin,et al.  Free-form shape design using triangulated surfaces , 1994, SIGGRAPH.

[11]  Craig Gotsman,et al.  Polygon morphing using a multiresolution representation , 1995 .

[12]  Jarek Rossignac,et al.  Solid-interpolating deformations: Construction and animation of PIPs , 1991, Comput. Graph..

[13]  Jan J. Koenderink,et al.  Solid shape , 1990 .

[14]  J. Milnor.  Topology from the differentiable viewpoint , 1965 .

[15]  Francis Lazarus,et al.  Feature-based shape transformation for polyhedral objects , 1994 .

[16]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.