Polynomial integration on regions defined by a triangle and a conic

  • Authors:

  • David Sevilla;Daniel Wachsmuth

  • Affiliations:

  • Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria;Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria

  • Venue:
  • Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
  • Year:
  • 2010

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Abstract

We present an efficient solution to the following problem, of relevance in a numerical optimization scheme: calculation of integrals of the type EQUATION 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.