Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Centroidal Voronoi diagrams for isotropic surface remeshing
Graphical Models - Special issue on SMI 2003
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
IEEE Transactions on Visualization and Computer Graphics
Computing Teichmüller Shape Space
IEEE Transactions on Visualization and Computer Graphics
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2010 papers
Triangle surfaces with discrete equivalence classes
ACM SIGGRAPH 2010 papers
Editing operations for irregular vertices in triangle meshes
ACM SIGGRAPH Asia 2010 papers
Hexagonal global parameterization of arbitrary surfaces
ACM SIGGRAPH ASIA 2010 Sketches
ACM SIGGRAPH 2011 papers
Darboux cyclides and webs from circles
Computer Aided Geometric Design
Beady: interactive beadwork design and construction
SIGGRAPH Asia 2011 Sketches
Beady: interactive beadwork design and construction
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
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Inspired by freeform designs in architecture which involve circles and spheres, we introduce a new kind of triangle mesh whose faces' incircles form a packing. As it turns out, such meshes have a rich geometry and allow us to cover surfaces with circle patterns, sphere packings, approximate circle packings, hexagonal meshes which carry a torsion-free support structure, hybrid tri-hex meshes, and others. We show how triangle meshes can be optimized so as to have the incircle packing property. We explain their relation to conformal geometry and implications on solvability of optimization. The examples we give confirm that this kind of meshes is a rich source of geometric structures relevant to architectural geometry.