Unit sphere

Unit sphere

Preliminaries

Published in Patrick Knupp, Stanly Steinberg, Fundamentals of Grid Generation, 2020

The surface of the unit sphere is given implicitly by x2 + y2 + z2 = 1. Use spherical coordinates to obtain a parametric description of this surface. Change this parameterization of the sphere to one where the unit square is mapped to the sphere. What change is needed to obtain a hemisphere? §

A multiscale support vector regression method on spheres with data compression

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Journal Information

Published in Applicable Analysis, 2019

Min Zhong, Q. T. Le Gia, Wei Wang

The unit sphere is defined by , where denotes the Euclidean norm of . Spherical harmonics are the restrictions to of the (real) homogeneous polynomials in which satisfy , where is the Laplacian operator in . For , let be the space of all spherical harmonics of degree l in , it has orthonormal basis

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Preliminaries

A multiscale support vector regression method on spheres with data compression