Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Discontinuity Meshing for Accurate Radiosity
IEEE Computer Graphics and Applications
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Efficient Graph-Based Image Segmentation
International Journal of Computer Vision
Variational shape approximation
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2005 Papers
GI '07 Proceedings of Graphics Interface 2007
Image vectorization using optimized gradient meshes
ACM SIGGRAPH 2007 papers
A meshless hierarchical representation for light transport
ACM SIGGRAPH 2008 papers
Diffusion curves: a vector representation for smooth-shaded images
ACM SIGGRAPH 2008 papers
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram
SGP '09 Proceedings of the Symposium on Geometry Processing
Lp Centroidal Voronoi Tessellation and its applications
ACM SIGGRAPH 2010 papers
Blue noise through optimal transport
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Combining higher-order wavelets and discontinuity meshing: a compact representation for radiosity
EGSR'04 Proceedings of the Fifteenth Eurographics conference on Rendering Techniques
Ardeco: automatic region detection and conversion
EGSR'06 Proceedings of the 17th Eurographics conference on Rendering Techniques
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We propose a method that computes a piecewise constant approximation of a function defined on a mesh. The approximation is associated with the cells of a restricted Voronoï diagram. Our method optimizes an objective function measuring the quality of the approximation. This objective function depends on the placement of the samples that define the restricted Voronoï diagram and their associated function values. We study the continuity of the objective function, derive the closed-form expression of its derivatives and use them to design a numerical solution mechanism. The method can be applied to a function that has discontinuities, and the result aligns the boundaries of the Voronoï cells with the discontinuities. Some examples are shown, suggesting potential applications in image vectorization and compact representation of lighting.