On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
An algorithm for discrete constant mean curvature surfaces
Visualization and mathematics
Constrained Centroidal Voronoi Tessellations for Surfaces
SIAM Journal on Scientific Computing
Three applications of optimization in computer graphics
Three applications of optimization in computer graphics
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
A Discrete Laplace–Beltrami Operator for Simplicial Surfaces
Discrete & Computational Geometry
A general framework for surface modeling using geometric partial differential equations
Computer Aided Geometric Design
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram
SGP '09 Proceedings of the Symposium on Geometry Processing
Efficient computation of 3d clipped voronoi diagram
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Asymptotically optimal block quantization
IEEE Transactions on Information Theory
Robust fairing via conformal curvature flow
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
A trust region method for constructing triangle-mesh approximations of parametric minimal surfaces
Applied Numerical Mathematics
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We present a new method for modeling discrete constant mean curvature (CMC) surfaces, which arise frequently in nature and are highly demanded in architecture and other engineering applications. Our method is based on a novel use of the CVT (centroidal Voronoi tessellation) optimization framework. We devise a CVT-CMC energy function defined as a combination of an extended CVT energy and a volume functional. We show that minimizing the CVT-CMC energy is asymptotically equivalent to minimizing mesh surface area with a fixed volume, thus defining a discrete CMC surface. The CVT term in the energy function ensures high mesh quality throughout the evolution of a CMC surface in an interactive design process for form finding. Our method is capable of modeling CMC surfaces with fixed or free boundaries and is robust with respect to input mesh quality and topology changes. Experiments show that the new method generates discrete CMC surfaces of improved mesh quality over existing methods.