Blending shapes by using subdivision surfaces

Abstract This paper presents a shape-blending algorithm that interpolates between 2D and 3D polyhedrons. Shape blending, which is sometimes called shape metamorphosis or geometric morphing, has applications in such areas as entertainment and medical visualization. Our algorithm directly interpolates vertices of polyhedral source shapes by using variationally optimized subdivision surfaces. To interpolate a pair of 3D polyhedrons, for example, a smooth 4D tetrahedral interpolator subdivision surface is created. Intersecting the 4D subdivision surface with another 4D surface produces a blended 3D mesh. Variational optimization of the interpolator surface ensures a smooth shape transition. At the same time, manipulable nature of the interpolator subdivision surface allows for feature correspondences, shape transition effects, and other controls over the shape blending.

[1]  Shigeo Takahashi,et al.  Multiresolution constraints for designing subdivision surfaces via local smoothing , 1999, Proceedings. Seventh Pacific Conference on Computer Graphics and Applications (Cat. No.PR00293).

[2]  Malcolm A. Sabin,et al.  Behaviour of recursive division surfaces near extraordinary points , 1998 .

[3]  Arie E. Kaufman,et al.  Wavelet-based volume morphing , 1994, Proceedings Visualization '94.

[4]  Gabriel Taubin,et al.  A signal processing approach to fair surface design , 1995, SIGGRAPH.

[5]  J. Udupa,et al.  Shape-based interpolation of multidimensional objects. , 1990, IEEE transactions on medical imaging.

[6]  N. Dyn,et al.  A butterfly subdivision scheme for surface interpolation with tension control , 1990, TOGS.

[7]  Hiromasa Suzuki,et al.  3D geometric metamorphosis based on harmonic map , 1997, Proceedings The Fifth Pacific Conference on Computer Graphics and Applications.

[8]  Dinesh Manocha,et al.  Feature-based surface decomposition for correspondence and morphing between polyhedra , 1998, Proceedings Computer Animation '98 (Cat. No.98EX169).

[9]  Peter Schröder,et al.  Interactive multiresolution mesh editing , 1997, SIGGRAPH.

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

[11]  Charles T. Loop,et al.  Smooth Subdivision Surfaces Based on Triangles , 1987 .

[12]  David P. Dobkin,et al.  MAPS: multiresolution adaptive parameterization of surfaces , 1998, SIGGRAPH.

[13]  Arthur W. Toga,et al.  Distance field manipulation of surface models , 1992, IEEE Computer Graphics and Applications.

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

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

[16]  Anne Verroust-Blondet,et al.  Three-dimensional metamorphosis: a survey , 1998, The Visual Computer.

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

[18]  Daniel Cohen-Or,et al.  Three-dimensional distance field metamorphosis , 1998, TOGS.

[19]  Michael F. Cohen,et al.  Hierarchical and variational geometric modeling with wavelets , 1995, I3D '95.

[20]  James F. O'Brien,et al.  Shape transformation using variational implicit functions , 1999, SIGGRAPH Courses.

[21]  David P. Dobkin,et al.  Multiresolution mesh morphing , 1999, SIGGRAPH.

[22]  Hiromasa Suzuki,et al.  Metamorphosis of Arbitrary Triangular Meshes , 2000, IEEE Computer Graphics and Applications.

[23]  E. Catmull,et al.  Recursively generated B-spline surfaces on arbitrary topological meshes , 1978 .

[24]  Douglas DeCarlo,et al.  Topological Evolution of Surfaces , 1996, Graphics Interface.

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

[26]  Chuck Hansen,et al.  Eurographics '97 , 1998, COMG.

[27]  Andrew P. Witkin,et al.  Variational surface modeling , 1992, SIGGRAPH.

[28]  Tony DeRose,et al.  Multiresolution analysis for surfaces of arbitrary topological type , 1997, TOGS.

[29]  Hiromasa Suzuki,et al.  Three-dimensional geometric metamorphosis based on harmonic maps , 1998, The Visual Computer.

[30]  David Levin.  Multidimensional Reconstruction by Set-valued Approximations , 1986 .