Polynomial integration on regions defined by a triangle and a conic

David Sevilla, Daniel Wachsmuth
2010 Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation - ISSAC '10  
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