function [xi,w]=fifthOrderHexagonCubPoints()
%%FIFTHORDERHEXAGONCUBPOINTS Generate fifth-order cubature points for
%               integration over a two-dimensional hexagon with vertices
%               (+/-1,0) and (+/-(1/2),+/-(1/2)*sqrt(3)).
%
%INPUTS: None
%
%OUTPUTS: xi A numDim X numCubaturePoints matrix containing the cubature
%            points (Each "point" is a vector).
%          w A numCubaturePoints X 1 vector of the weights associated with
%            the cubature points.
%
%This function implements Formula H_2 5-1 in [1], pg. 336, 7 points.
%
%REFERENCES:
%[1] A.H. Stroud, Approximate Calculation of Multiple Integrals. Cliffs,
%    NJ: Prentice-Hall, Inc., 1971.
%
%March 2017 David F. Crouse, Naval Research Laboratory, Washington D.C.
%(UNCLASSIFIED) DISTRIBUTION STATEMENT A. Approved for public release.

r=sqrt(14/25);
s=sqrt(14/100);
t=sqrt(42/100);

xi=[[0;0],PMCombos([r;0]),PMCombos([s;t])];

V=3*sqrt(3)/2;
A=(258/1008)*V;
B=(125/1008)*V;
w=[A;B*ones(6,1)];
end

%LICENSE:
%
%The source code is in the public domain and not licensed or under
%copyright. The information and software may be used freely by the public.
%As required by 17 U.S.C. 403, third parties producing copyrighted works
%consisting predominantly of the material produced by U.S. government
%agencies must provide notice with such work(s) identifying the U.S.
%Government material incorporated and stating that such material is not
%subject to copyright protection.
%
%Derived works shall not identify themselves in a manner that implies an
%endorsement by or an affiliation with the Naval Research Laboratory.
%
%RECIPIENT BEARS ALL RISK RELATING TO QUALITY AND PERFORMANCE OF THE
%SOFTWARE AND ANY RELATED MATERIALS, AND AGREES TO INDEMNIFY THE NAVAL
%RESEARCH LABORATORY FOR ALL THIRD-PARTY CLAIMS RESULTING FROM THE ACTIONS
%OF RECIPIENT IN THE USE OF THE SOFTWARE.

USNavalResearchLaboratory
github-repos/MATLAB/USNavalResearchLaboratory-TrackerComponentLibrary/TrackerComponentLibrary-9f6e329de5be06a371757c4b853200beb6def2d0/Mathematical_Functions/Numerical_Integration/Cubature_Points/Hexagon/fifthOrderHexagonCubPoints.m
TrackerComponentLibrary
github-repos/MATLAB/USNavalResearchLaboratory-TrackerComponentLibrary
9f6e329de5be06a371757c4b853200beb6def2d0