GaussLegendreQuadrature.h

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// This file is a part of the OpenSurgSim project.
// Copyright 2012-2013, SimQuest Solutions Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.


#ifndef SURGSIM_MATH_GAUSSLEGENDREQUADRATURE_H
#define SURGSIM_MATH_GAUSSLEGENDREQUADRATURE_H

#include <array>
#include <utility>

namespace SurgSim
{
namespace Math
{

struct gaussQuadraturePoint
{
    gaussQuadraturePoint(double p, double w) : point(p), weight(w){}

    const double point;
    const double weight;
};

struct gaussQuadratureTrianglePoint
{
    gaussQuadratureTrianglePoint(double xi, double eta, double w) : coordinateXi(xi), coordinateEta(eta), weight(w){}

    const double coordinateXi;  
    const double coordinateEta; 
    const double weight;
};

extern const std::array<gaussQuadraturePoint, 1> gaussQuadrature1Point;

extern const std::array<gaussQuadraturePoint, 2> gaussQuadrature2Points;

extern const std::array<gaussQuadraturePoint, 3> gaussQuadrature3Points;

extern const std::array<gaussQuadraturePoint, 4> gaussQuadrature4Points;

extern const std::array<gaussQuadraturePoint, 5> gaussQuadrature5Points;

extern const std::array<gaussQuadraturePoint, 100> gaussQuadrature100Points;

// http://math2.uncc.edu/~shaodeng/TEACHING/math5172/Lectures/Lect_15.PDF
// "Quadrature Formulas in Two Dimensions"
// \int_0^1 \int_0^{1-eta} f(xi, eta) dxi deta = 1/2 sum_i w[i] f(xi[i], eta[i])

extern const std::array<gaussQuadratureTrianglePoint, 3> gaussQuadrature2DTriangle3Points;

extern const std::array<gaussQuadratureTrianglePoint, 6> gaussQuadrature2DTriangle6Points;

extern const std::array<gaussQuadratureTrianglePoint, 12> gaussQuadrature2DTriangle12Points;

};  // namespace Math
};  // namespace SurgSim

#endif  // SURGSIM_MATH_GAUSSLEGENDREQUADRATURE_H