SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A cellular texture basis function
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Anisotropic nonlinear diffusion in flow visualization
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Texture and reflection in computer generated images
Communications of the ACM
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Physically-based visual simulation on graphics hardware
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Texturing and Modeling: A Procedural Approach
Texturing and Modeling: A Procedural Approach
Mathematical Statistics with Mathematica with CD-ROM
Mathematical Statistics with Mathematica with CD-ROM
Strategies for Direct Volume Rendering of Diffusion Tensor Fields
IEEE Transactions on Visualization and Computer Graphics
Anisotropic Diffusion in Vector Field Visualization on Euclidean Domains and Surfaces
IEEE Transactions on Visualization and Computer Graphics
A Review of Nonlinear Diffusion Filtering
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Display of Vector Fields Using a Reaction-Diffusion Model
VIS '04 Proceedings of the conference on Visualization '04
Parallel controllable texture synthesis
ACM SIGGRAPH 2005 Papers
Appearance-space texture synthesis
ACM SIGGRAPH 2006 Papers
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We present a method of synthesizing textures based on a modified reaction-diffusion equation. A non-Gaussian model of diffusion is employed to make a new class of textures possible. Whereas the Gaussian diffusion model is characterized by its covariance matrix (a rank-2 tensor), the generalized model of diffusion is characterized by a sequence of tensors of increasing rank which represent higher-order moments of the diffusion displacement probability. A numerical method of solving the new reaction-diffusion equation is described, as well as representative textures generated by this technique. The resulting patterns are inorganic in nature, often featuring sharp corners. The generalized reaction-diffusion textures display spatial inhomogeneity, even when the diffusion process is homogeneous, making it possible to generate complex textures from few parameters when compared with previous techniques employing inhomogeneous reaction-diffusion. The preferred orientations depend on the tensor sequence, and can be inspected prior to texture generation by plotting the non-Gaussian diffusion propagator.