Shape Representation Using a Generalized Potential Field Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Skeletonization of Three-Dimensional Object Using Generalized Potential Field
IEEE Transactions on Pattern Analysis and Machine Intelligence
Asymptotic approximations of integrals
Asymptotic approximations of integrals
Computer Aided Geometric Design
Heterogeneous material modeling with distance fields
Computer Aided Geometric Design
Approximate distance fields with non-vanishing gradients
Graphical Models
Interactive modeling of topologically complex geometric detail
ACM SIGGRAPH 2004 Papers
Thick surfaces: interactive modeling of topologically complex geometric details
Thick surfaces: interactive modeling of topologically complex geometric details
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
Transfinite mean value interpolation
Computer Aided Geometric Design
Coordinates for instant image cloning
ACM SIGGRAPH 2009 papers
Transfinite mean value interpolation in general dimension
Journal of Computational and Applied Mathematics
Finite element analysis in situ
Finite Elements in Analysis and Design
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We introduce and study a family of generalized double-layer potentials which are used to build smooth and accurate approximants for the signed distance function. Given a surface, the value of an approximant at a given point is a power mean of distances from the point to the surface points parameterized by the angle they are viewed from the given point. We analyze mathematical properties of the potentials and corresponding approximants. In particular, approximation accuracy estimates are derived. Our theoretical results are supported by numerical experiments which reveal the high practical potential of our approach.