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function plotGrid(gridType,p)
%plotGrid - Plot spherical quadrature grids
%
% plotGrid(gridtype) plots a quadrature grid. The parameter gridType specifies
% the point set to plot and can take the following values:
% 0: Gauss-Legendre quadrature grid,
% 1: Clenshaw-Curtis qudrature grid,
% 2: HEALPix point set,
% 3: Equidistribution point set.
%
% Copyright (c) 2002, 2017 Jens Keiner, Stefan Kunis, Daniel Potts
% Copyright (c) 2002, 2017 Jens Keiner, Stefan Kunis, Daniel Potts
%
% This program is free software; you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free Software
% Foundation; either version 2 of the License, or (at your option) any later
% version.
%
% This program is distributed in the hope that it will be useful, but WITHOUT
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
% FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
% details.
%
% You should have received a copy of the GNU General Public License along with
% this program; if not, write to the Free Software Foundation, Inc., 51
% Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
%
if (gridType == 0)
[theta,w] = lgwt(p(1)+1,-1,1);
theta = acos(theta);
phi = 2*pi*(0:(2*p(1)+1))./(2*p(1)+2);
[Y,X] = meshgrid(theta,phi);
gridName = 'Gauss-Legendre';
temp = repmat(w,[1,length(phi)])';
[Y(:),X(:),temp(:)]
size(Y(:))
elseif (gridType == 1)
theta = pi*(0:2*p(1))./(2*p(1));
phi = 2*pi*(0:(2*p(1)+1))./(2*p(1)+2);
[X,Y] = meshgrid(phi,theta);
gridName = 'Clenshaw-Curtis';
elseif (gridType == 2)
if log2(p(1)) ~= fix(log2(p(1)))
error('NS has to be an INTEGER power of 2')
end
% initialization of the parameters
Y=zeros(12*p(1)^2,1);
X=zeros(12*p(1)^2,1);
ncoo=0;
% North pole
for ii=1:p(1)-1
for hh=0:4*ii-1
ncoo=ncoo+1;
Y(ncoo)=1-ii^2/(3*p(1)^2);
X(ncoo)=2*pi/(4*ii)*(hh+0.5);
end
end
ncoo1=ncoo;
% Equator
for ii=p(1):3*p(1)
for hh=0:4*p(1)-1
ncoo=ncoo+1;
Y(ncoo)=2/(3*p(1))*(2*p(1)-ii);
X(ncoo)=2*pi/(4*p(1))*(hh+codd(ii));
end
end
% add the south pole
X(ncoo+1:end)=X(ncoo1:-1:1);
Y(ncoo+1:end)=-Y(ncoo1:-1:1);
Y=acos(Y);
gridName = 'HEALPix';
elseif (gridType == 3)
X = zeros(2+4*(floor((p(1)+1)/2))*floor(p(1)/2),1);
Y = zeros(2+4*(floor((p(1)+1)/2))*floor(p(1)/2),1);
X(1) = 0.0;
Y(1) = 0.0;
d = 2;
for k = 1:p(1)-1
thetai = (k*pi)/p(1);
if (k<=(p(1)/2))
gammai = 4*k;
else
gammai = 4*(p(1)-k);
end
for n = 1:gammai
Y(d) = thetai;
X(d) = ((n-0.5)*((2.0*pi)/gammai));
d = d+1;
end
end
Y(d) = pi;
X(d) = 0.0;
size(X)
gridName = 'Equidistribution Example 7.1.11';
else
error('Wrong grid type!');
end
figure;
plot(X,Y,'ko');
axis equal;
axis([-0.1 2*pi+0.1 -0.1 pi+0.1]);
xlabel('Phi');
ylabel('Theta');
title(gridName);
return;
function coeff=codd(k);
if fix(k/2)*2 == k, coeff=0.5;, else, coeff=0;, end
return
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