The Gauss-Legendre product rule on the unit sphere with N rings, exact through degree 2N - 1. More...

#include <GaussLegendreSphere.hpp>

Public Types
using	value_type = Scalar

Static Public Member Functions
static constexpr Kokkos::Array< Scalar, 3 *num_points >	points ()
	The points as (x, y, z) triples: ring by ring from the north pole, by increasing longitude within a ring.
static constexpr Kokkos::Array< Scalar, num_points >	weights ()
	The num_points weights, in the order of points().
template<class Function>
static constexpr auto	integrate (const Function &f)
	sum_i w_i f(x_i, y_i, z_i), approximating the integral of f over the unit sphere.

Static Public Attributes
static constexpr unsigned	num_rings = N
static constexpr unsigned	num_points = 2 * N * N

Detailed Description

template<class Scalar, unsigned N>
class mundy::GaussLegendreSphere< Scalar, N >

The points and weights are correctly rounded to Scalar and computed by the compiler, so every member is a constant expression. Like GaussLegendre's rule, it integrates on the unit sphere; scale for other radii.