Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Discrete exterior calculus
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Stable, circulation-preserving, simplicial fluids
ACM Transactions on Graphics (TOG)
Discrete calculus methods for diffusion
Journal of Computational Physics
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Lp Centroidal Voronoi Tessellation and its applications
ACM SIGGRAPH 2010 papers
Discrete Calculus: Applied Analysis on Graphs for Computational Science
Discrete Calculus: Applied Analysis on Graphs for Computational Science
SIAM Journal on Scientific Computing
New Bounds on the Size of Optimal Meshes
Computer Graphics Forum
Blue noise through optimal transport
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Technical note: Delaunay Hodge star
Computer-Aided Design
Computing self-supporting surfaces by regular triangulation
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
On the equilibrium of simplicial masonry structures
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Digital geometry processing with discrete exterior calculus
ACM SIGGRAPH 2013 Courses
The chain collocation method: A spectrally accurate calculus of forms
Journal of Computational Physics
Hi-index | 0.00 |
We introduce Hodge-optimized triangulations (HOT), a family of well-shaped primal-dual pairs of complexes designed for fast and accurate computations in computer graphics. Previous work most commonly employs barycentric or circumcentric duals; while barycentric duals guarantee that the dual of each simplex lies within the simplex, circumcentric duals are often preferred due to the induced orthogonality between primal and dual complexes. We instead promote the use of weighted duals ("power diagrams"). They allow greater flexibility in the location of dual vertices while keeping primal-dual orthogonality, thus providing a valuable extension to the usual choices of dual by only adding one additional scalar per primal vertex. Furthermore, we introduce a family of functionals on pairs of complexes that we derive from bounds on the errors induced by diagonal Hodge stars, commonly used in discrete computations. The minimizers of these functionals, called HOT meshes, are shown to be generalizations of Centroidal Voronoi Tesselations and Optimal Delaunay Triangulations, and to provide increased accuracy and flexibility for a variety of computational purposes.