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Fast Rendering of Diffusion Curves with Triangles
July-Aug. 2012 (vol. 32 no. 4)
pp. 68-78
Wai-Man Pang, Caritas Institute of Higher Education
Jing Qin, Chinese Univeristy of Hong Kong
Michael Cohen, University of Aizu
Pheng-Ann Heng, Chinese University of Hong Kong
Kup-Sze Choi, Hong Kong Polytechnic University
Diffusion curves are a new kind of primitive in vector graphics, capable of representing smooth color transitions among boundaries. Their rendering requires solving Poisson's equation; much previous research relied on traditional solvers, which commonly require GPU acceleration to achieve real-time rasterization. This obviously restricts deployment on the Internet—for example, as rich Internet applications, in which various computing environments are involved. Diffusion effects are similar to locally defined interpolation with a particular orientation and magnitude. Inspired by that observation, a mesh-based framework combined with mean value coordinates (MVC) interpolants efficiently renders diffusion curve images on a CPU. This method employs a visibility algorithm to efficiently find and sort neighboring curve nodes for each vertex. It then assigns the vertex colors according to MVC interpolation with the neighboring curve nodes. Experiments produced rendering results comparable to traditional solvers, but this method is computationally more efficient and runs much faster on a CPU.

1. A. Orzan et al., “Diffusion Curves: A Vector Representation for Smooth-Shaded Images,” ACM Trans. Graphics, vol. 27, no. 3, 2008, article 92.
2. S. Jeschke, D. Cline, and P. Wonka, “A GPU Laplacian Solver for Diffusion Curves and Poisson Image Editing,” ACM Trans. Graphics, vol. 28, no. 5, 2009, article 116.
3. J.R. Shewchuk, “Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator,” Applied Computational Geometry: Towards Geometric Engineering, LNCS 1148, Springer, 1996, pp. 203–222.
4. G.S. Watkins, “A Real Time Visible Surface Algorithm,” PhD thesis, Computer Science Division, Univ. of Utah, 1970.
5. M. Kazhdan and H. Hoppe, “Streaming Multigrid for Gradient-Domain Operations on Large Images,” ACM Trans. Graphics, vol. 27, no. 3, 2008, article 21.
6. A. Agarwala, “Efficient Gradient-Domain Compositing Using Quadtrees,” ACM Trans. Graphics, vol. 26, no. 3, 2007, article 94.
1. G. Lecot and B. Levy, “Ardeco: Automatic Region Detection and Conversion,” Proc. 17th Eurographics Symp. Rendering (EGSR 06), Eurographics Assoc., 2006, pp. 349–360.
2. J. McCann and N.S. Pollard, “Real-Time Gradient-Domain Painting,” ACM Trans. Graphics, vol. 27, no. 3, 2008, article 93.
3. A. Orzan et al., “Diffusion Curves: A Vector Representation for Smooth-Shaded Images,” ACM Trans. Graphics, vol. 27, no. 3, 2008, article 92.
4. J. Sun et al., “Image Vectorization Using Optimized Gradient Meshes,” ACM Trans. Graphics, vol. 26, no. 3, 2007, article 11.
5. T. Xia, B. Liao, and Y. Yu, “Patch-Based Image Vectorization with Automatic Curvilinear Feature Alignment,” ACM Trans. Graphics, vol. 28, no. 5, 2009, article 115.
6. S. Jeschke, D. Cline, and P. Wonka, “A GPU Laplacian Solver for Diffusion Curves and Poisson Image Editing,” ACM Trans. Graphics, vol. 28, no. 5, 2009, article 116.
7. S. Jeschke, D. Cline, and P. Wonka, “Rendering Surface Details with Diffusion Curves,” ACM Trans. Graphics, vol. 28, no. 5, 2009, article 117.
8. J.C. Bowers, J. Leahey, and R. Wang, “A Ray Tracing Approach to Diffusion Curves,” Computer Graphics Forum, vol. 30, no. 4, 2011, pp. 1345–1352.
9. H. Bezerra et al., “Diffusion Constraints for Vector Graphics,” Proc. 8th Int'l Symp. Non-photorealistic Animation and Rendering (NPAR 10), ACM, 2010, pp. 35–42.
10. K. Takayama et al., “Volumetric Modeling with Diffusion Surfaces,” ACM Trans. Graphics, vol. 29, no. 6, 2010, article 180.
11. M.S. Floater, “Mean Value Coordinates,” Computer Aided Geometric Design, vol. 20, no. 1, 2003, pp. 19–27.
12. Y. Lipman et al., “GPU-Assisted Positive Mean Value Coordinates for Mesh Deformations,” Proc. 5th Eurographics Symp. Geometry Processing, Eurographics Assoc., 2007, pp. 117–123.
13. Z. Farbman et al., “Coordinates for Instant Image Cloning,” ACM Trans. Graphics, vol. 28, no. 3, 2009, article 67.

Index Terms:
Image color analysis,Rendering (computer graphics),Interpolation,DIffusion processes,Graphics processing unit,Curves,Harmonic analysis,harmonic maps,Image color analysis,Rendering (computer graphics),Interpolation,DIffusion processes,Graphics processing unit,Curves,Harmonic analysis,nonphotorealistic rendering,Image color analysis,Rendering (computer graphics),Interpolation,Color,Graphics processing unit,Nickel,computer graphics,diffusion curves,vector graphics rendering,mean value coordinates
Citation:
Wai-Man Pang, Jing Qin, Michael Cohen, Pheng-Ann Heng, Kup-Sze Choi, "Fast Rendering of Diffusion Curves with Triangles," IEEE Computer Graphics and Applications, vol. 32, no. 4, pp. 68-78, July-Aug. 2012, doi:10.1109/MCG.2011.86
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