SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Extrapolated surface charge method for capacity calculation of polygons and polyhedra
Journal of Computational Physics
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design
ACM SIGGRAPH 2003 Papers
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
SMI '04 Proceedings of the Shape Modeling International 2004
A Fast and Simple Stretch-Minimizing Mesh Parameterization
SMI '04 Proceedings of the Shape Modeling International 2004
Interactive modeling of topologically complex geometric detail
ACM SIGGRAPH 2004 Papers
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
Handle-aware isolines for scalable shape editing
ACM SIGGRAPH 2007 papers
Unconstrained isosurface extraction on arbitrary octrees
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
ACM SIGGRAPH 2008 papers
High-performance implementation of the level-3 BLAS
ACM Transactions on Mathematical Software (TOMS)
ACM SIGGRAPH 2009 papers
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Spatial relationship preserving character motion adaptation
ACM SIGGRAPH 2010 papers
Apparent layer operations for the manipulation of deformable objects
ACM SIGGRAPH 2010 papers
OverCoat: an implicit canvas for 3D painting
ACM SIGGRAPH 2011 papers
Manipulation of Flexible Objects by Geodesic Control
Computer Graphics Forum
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In this article, we introduce a method to apply ideas from electrostatics to parameterize the open space around an object. By simulating the object as a virtually charged conductor, we can define an object-centric coordinate system which we call Electric Coordinates. It parameterizes the outer space of a reference object in a way analogous to polar coordinates. We also introduce a measure that quantifies the extent to which an object is wrapped by a surface. This measure can be computed as the electric flux through the wrapping surface due to the electric field around the charged conductor. The electrostatic parameters, which comprise the Electric Coordinates and flux, have several applications in computer graphics, including: texturing, morphing, meshing, path planning relative to a target object, mesh parameterization, designing deformable objects, and computing coverage. Our method works for objects of arbitrary geometry and topology, and thus is applicable in a wide variety of scenarios.