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Polynomial integration on regions defined by a triangle and a conic

2010
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Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation - ISSAC '10
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We present an efficient solution to the following problem, of relevance in a numerical optimization scheme: calculation of integrals of the type for quadratic polynomials f, φ1, φ2 on a plane triangle T . The naive approach would involve consideration of the many possible shapes of T ∩ {f ≥ 0} (possibly after a convenient transformation) and parameterizing its border, in order to integrate the variables separately. Our solution involves partitioning the triangle into smaller triangles on which integration is much simpler.

doi:10.1145/1837934.1837968
dblp:conf/issac/SevillaW10
fatcat:tahxcresrzdkziatotcsb36qr4