On the Riesz energy of measures
Journal of Approximation Theory
Galerkin approximation for elliptic PDEs on spheres
Journal of Approximation Theory
Isocube: Exploiting the Cubemap Hardware
IEEE Transactions on Visualization and Computer Graphics
Data-intensive image based relighting
Proceedings of the 5th international conference on Computer graphics and interactive techniques in Australia and Southeast Asia
The rhombic dodecahedron map: an efficient scheme for encoding panoramic video
IEEE Transactions on Multimedia
Galerkin approximation for elliptic PDEs on spheres
Journal of Approximation Theory
Short note: Efficient and accurate rotation of finite spherical harmonics expansions
Journal of Computational Physics
Density-controlled sampling of parametric surfaces using adaptive space-filling curves
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Spherical Q2-tree for sampling dynamic environment sequences
EGSR'05 Proceedings of the Sixteenth Eurographics conference on Rendering Techniques
Numerical properties of generalized discrepancies on spheres of arbitrary dimension
Journal of Complexity
Bootstrap confidence sets for the Aumann mean of a random closed set
Computational Statistics & Data Analysis
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A concept of generalized discrepancy, which involves pseudodifferential operators to give a criterion of equidistributed pointsets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy. With the help of this formula five kinds of point systems on the sphere, namely lattices in polar coordinates, transformed two-dimensional sequences, rotations on the sphere, triangulations, and "sum of three squares sequence," are investigated. Quantitative tests are done, and the results are compared with one another. Our calculations exhibit different orders of convergence of the generalized discrepancy for different types of point systems.