Structure Preserving Manipulation and Interpolation for Multi‐element 2D Shapes

This paper presents a method that generates natural and intuitive deformations via direct manipulation and smooth interpolation for multi‐element 2D shapes. Observing that the structural relationships between different parts of a multi‐element 2D shape are important for capturing its feature semantics, we introduce a simple structure called a feature frame to represent such relationships. A constrained optimization is solved for shape manipulation to find optimal deformed shapes under user‐specified handle constraints. Based on the feature frame, local feature preservation and structural relationship maintenance are directly encoded into the objective function. Beyond deforming a given multi‐element 2D shape into a new one at each key frame, our method can automatically generate a sequence of natural intermediate deformations by interpolating the shapes between the key frames. The method is computationally efficient, allowing real‐time manipulation and interpolation, as well as generating natural and visually plausible results.

[1]  Hans-Peter Seidel,et al.  MovieReshape: tracking and reshaping of humans in videos , 2010, SIGGRAPH 2010.

[2]  Katsu Yamane,et al.  Natural Motion Animation through Constraining and Deconstraining at Will , 2003, IEEE Trans. Vis. Comput. Graph..

[3]  Scott Schaefer,et al.  Image deformation using moving least squares , 2006, ACM Trans. Graph..

[4]  Leif Kobbelt,et al.  Character animation from 2D pictures and 3D motion data , 2007, TOGS.

[5]  Marc Alexa,et al.  As-rigid-as-possible shape interpolation , 2000, SIGGRAPH.

[6]  Ralph R. Martin,et al.  Vectorizing Cartoon Animations , 2009, IEEE Transactions on Visualization and Computer Graphics.

[7]  M. Pauly,et al.  Embedded deformation for shape manipulation , 2007, SIGGRAPH 2007.

[8]  Takeo Igarashi,et al.  As-rigid-as-possible shape manipulation , 2005, SIGGRAPH '05.

[9]  M. V. D. Panne,et al.  Joint-aware manipulation of deformable models , 2009, SIGGRAPH 2009.

[10]  Christian Rössl,et al.  Laplacian surface editing , 2004, SGP '04.

[11]  Peisheng Gao,et al.  2-D shape blending: an intrinsic solution to the vertex path problem , 1993, SIGGRAPH.

[12]  Daniel Cohen-Or,et al.  iWIRES: an analyze-and-edit approach to shape manipulation , 2009, ACM Trans. Graph..

[13]  Dmitry Chetverikov,et al.  A Simple and Efficient Algorithm for Detection of High Curvature Points in Planar Curves , 2003, CAIP.

[14]  Siu Chi Hsu,et al.  Drawing and animation using skeletal strokes , 1994, SIGGRAPH.

[15]  Daniel Cohen-Or,et al.  Component‐wise Controllers for Structure‐Preserving Shape Manipulation , 2011, Comput. Graph. Forum.

[16]  Baptiste Caramiaux,et al.  Multiresolution morphing for planar curves , 2006, Computing.

[17]  David A. Forsyth,et al.  Generalizing motion edits with Gaussian processes , 2009, ACM Trans. Graph..

[18]  John Dingliana,et al.  Adding Depth to Cartoons Using Sparse Depth (In)equalities , 2010, Comput. Graph. Forum.

[19]  Kun Zhou,et al.  Mesh editing with poisson-based gradient field manipulation , 2004, SIGGRAPH 2004.

[20]  Dominique Bechmann,et al.  A survey of spatial deformation from a user-centered perspective , 2008, TOGS.

[21]  Olga Sorkine-Hornung,et al.  On Linear Variational Surface Deformation Methods , 2008, IEEE Transactions on Visualization and Computer Graphics.

[22]  Markus H. Gross,et al.  BetweenIT: An Interactive Tool for Tight Inbetweening , 2010, Comput. Graph. Forum.

[23]  Bobby Bodenheimer,et al.  Synthesis and evaluation of linear motion transitions , 2008, TOGS.

[24]  Kun Zhou,et al.  Mesh editing with poisson-based gradient field manipulation , 2004, ACM Trans. Graph..

[25]  Timothy A. Davis,et al.  Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method , 2004, TOMS.

[26]  Kun Zhou,et al.  Deformation Transfer to Multi‐Component Objects , 2010, Comput. Graph. Forum.

[27]  Takeo Igarashi,et al.  As-rigid-as-possible shape manipulation , 2005, ACM Trans. Graph..

[28]  John P. Lewis,et al.  Pose Space Deformation: A Unified Approach to Shape Interpolation and Skeleton-Driven Deformation , 2000, SIGGRAPH.

[29]  Kun Zhou,et al.  2D shape deformation using nonlinear least squares optimization , 2006, The Visual Computer.

[30]  Taku Komura,et al.  Spatial relationship preserving character motion adaptation , 2010, SIGGRAPH 2010.

[31]  Jieqing Feng,et al.  2D shape manipulation via topology‐aware rigid grid , 2009, Comput. Animat. Virtual Worlds.

[32]  John Dingliana,et al.  As-rigid-as-possible image registration for hand-drawn cartoon animations , 2009, NPAR '09.

[33]  Jieqing Feng,et al.  2D shape morphing via automatic feature matching and hierarchical interpolation , 2009, Comput. Graph..

[34]  William V. Baxter,et al.  Compatible Embedding for 2D Shape Animation , 2009, IEEE Transactions on Visualization and Computer Graphics.

[35]  Marc Alexa,et al.  As-rigid-as-possible surface modeling , 2007, Symposium on Geometry Processing.

[36]  Edmond S. L. Ho,et al.  Spatial relationship preserving character motion adaptation , 2010, ACM Trans. Graph..