Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
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This paper is concerned with algorithmic techniques for the incremental generation of continuous curves that can efficiently cover an abstract surface. We introduce the notion of low-discrepancy curves as an extension of the notion of low-discrepancy sequences—such that sufficiently smooth curves with low-discrepancy properties can be defined and generated. We then devise a procedure for lifting these curves, that efficiently cover the unit cube, to abstract surfaces, such as nonlinear manifolds. We present algorithms that yield suitable fair mappings between the unit cube and the abstract surface. We demonstrate the application of these ideas using some concrete examples of interest in robotics.