Quadrature formulas on spherical triangles

What is it about?

We describe an explicit construction of quadrature rules exact for integrating multivariate trigonometric polynomials of a given coordinatewise degree on a spherical triangle. The theory is presented in the more general setting of quadrature formulas on a compact subset of the unit hypersphere, S^q , embedded in the Euclidean space R^(q+1). The number of points at which the polynomials are sampled is commensurate with the dimension of the polynomial space.

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