Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis
Computer Aided Geometric Design
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Energy functionals, numerical integration and asymptotic equidistribution on the sphere
Journal of Complexity
The random walk on the boundary method for calculating capacitance
Journal of Computational Physics
Computational cost of the Fekete problem I: The Forces Method on the 2-sphere
Journal of Computational Physics
Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra
SIAM Journal on Numerical Analysis
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We aim here at presenting a new procedure to numerically estimate the Fekete points of a wide variety of compact sets in R^3. We understand the Fekete point problem in terms of the identification of near equilibrium configurations for a potential energy that depends on the relative position of N particles. The compact sets for which our procedure works are basically the finite union of piecewise regular surfaces and curves. In order to determine a good initial configuration to start the search of the Fekete points of these objects, we construct a sequence of approximating regular surfaces. Our algorithm is based on the concept of disequilibrium degree, which is defined from a physical interpretation of the behavior of a system of particles when they search for a minimum energy configuration. Moreover, the algorithm is efficient and robust independently of the considered compact set as well as of the kernel used to define the energy. The numerical experimentation carried out suggests that a local minimum can be localized with a computational cost of order less than N^3.