Constructing fully symmetric cubature formulae for the sphere |
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Authors: | Sangwoo Heo Yuan Xu |
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Institution: | Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222 ; Division of Science and Mathematics, University of Minnesota-Morris, Morris, Minnesota 56267 |
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Abstract: | We construct symmetric cubature formulae of degrees in the 13-39 range for the surface measure on the unit sphere. We exploit a recently published correspondence between cubature formulae on the sphere and on the triangle. Specifically, a fully symmetric cubature formula for the surface measure on the unit sphere corresponds to a symmetric cubature formula for the triangle with weight function , where , , and are homogeneous coordinates. |
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Keywords: | Cubature formulae on the unit sphere on the triangle symmetric formula on a triangle octahedral symmetry |
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