Fast multipole representation of diffusion curves and points

We propose a new algorithm for random-access evaluation of diffusion curve images (DCIs) using the fast multipole method. Unlike all previous methods, our algorithm achieves real-time performance for rasterization and texture-mapping DCIs of up to millions of curves. After precomputation, computing the color at a single pixel takes nearly constant time. We also incorporate Gaussian radial basis functions into our fast multipole representation using the fast Gauss transform. The fast multipole representation is not only a data structure for fast color evaluation, but also a framework for vector graphics analogues of bitmap editing operations. We exhibit this capability by devising new tools for fast diffusion curve Poisson cloning and composition with masks.

[1]  Ramani Duraiswami,et al.  Fast multipole method for the biharmonic equation in three dimensions , 2006, J. Comput. Phys..

[2]  Kup-Sze Choi,et al.  Fast Rendering of Diffusion Curves with Triangles , 2012, IEEE Computer Graphics and Applications.

[3]  Pascal Barla,et al.  Diffusion curves: a vector representation for smooth-shaded images , 2008, ACM Trans. Graph..

[4]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[5]  Pascal Barla,et al.  A vectorial solver for free-form vector gradients , 2012, ACM Trans. Graph..

[6]  Pascal Barla,et al.  Diffusion curves: a vector representation for smooth-shaded images , 2008, SIGGRAPH 2008.

[7]  Stephen Lin,et al.  Diffusion curve textures for resolution independent texture mapping , 2012, ACM Trans. Graph..

[8]  Doug L. James,et al.  Rigid-body fracture sound with precomputed soundbanks , 2010, ACM Trans. Graph..

[9]  Edward H. Adelson,et al.  Compressing and companding high dynamic range images with subband architectures , 2005, ACM Trans. Graph..

[10]  Stefan Jeschke,et al.  A GPU Laplacian solver for diffusion curves and Poisson image editing , 2009, ACM Trans. Graph..

[11]  Robert Bridson,et al.  Linear-time smoke animation with vortex sheet meshes , 2012, SCA '12.

[12]  Takeo Igarashi,et al.  Volumetric modeling with diffusion surfaces , 2010, ACM Trans. Graph..

[13]  Edward H. Adelson,et al.  Compressing and companding high dynamic range images with subband architectures , 2005, SIGGRAPH 2005.

[14]  John Snyder,et al.  Freeform vector graphics with controlled thin-plate splines , 2011, ACM Trans. Graph..

[15]  Pat Hanrahan,et al.  A rapid hierarchical radiosity algorithm , 1991, SIGGRAPH.

[16]  Cyril Concolato,et al.  Biharmonic diffusion curve images from boundary elements , 2013, ACM Trans. Graph..

[17]  Tom Duff,et al.  Compositing digital images , 1984, SIGGRAPH.

[18]  Dani Lischinski,et al.  Coordinates for instant image cloning , 2009, SIGGRAPH 2009.

[19]  Andrew Nealen,et al.  Volumetric modeling with diffusion surfaces , 2010, SIGGRAPH 2010.

[20]  Peter Wonka,et al.  A GPU Laplacian solver for diffusion curves and Poisson image editing , 2009, ACM Transactions on Graphics.

[21]  Nigel Williams,et al.  STRANGE ATTRACTORS , 2019, Chaos and Dynamical Systems.

[22]  Hugues Hoppe,et al.  Parallel controllable texture synthesis , 2005, SIGGRAPH 2005.

[23]  N. Nishimura,et al.  The fast multipole boundary element method for potential problems: A tutorial , 2006 .

[24]  David Salesin,et al.  Interactive digital photomontage , 2004, SIGGRAPH 2004.

[25]  Leslie Greengard,et al.  The Fast Gauss Transform , 1991, SIAM J. Sci. Comput..

[26]  Doug L. James,et al.  Toward high-quality modal contact sound , 2011, SIGGRAPH 2011.

[27]  Rui Wang,et al.  A Ray Tracing Approach to Diffusion Curves , 2011, EGSR '11.

[28]  Joëlle Thollot,et al.  Diffusion constraints for vector graphics , 2010, NPAR.

[29]  Martin Kemp.  Attractive attractors , 1998, Nature.

[30]  Zeev Farbman,et al.  Coordinates for instant image cloning , 2009, ACM Trans. Graph..

[31]  David Salesin,et al.  Interactive digital photomontage , 2004, ACM Trans. Graph..

[32]  Sylvain Lefebvre,et al.  Parallel controllable texture synthesis , 2005, ACM Trans. Graph..

[33]  Patrick Pérez,et al.  Poisson image editing , 2003, ACM Trans. Graph..

[34]  Doug L. James,et al.  Rigid-body fracture sound with precomputed soundbanks , 2010, SIGGRAPH 2010.

[35]  Tomas Akenine-Möller,et al.  High dynamic range texture compression for graphics hardware , 2006, ACM Trans. Graph..

[36]  Doug L. James,et al.  Toward high-quality modal contact sound , 2011, ACM Trans. Graph..

[37]  Tomas Akenine-Möller,et al.  High dynamic range texture compression for graphics hardware , 2006, SIGGRAPH 2006.