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Copy pathgenerate_figure1a.m
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generate_figure1a.m
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%
% Copyright (c) 2014, Ross Adelman, Nail A. Gumerov, and Ramani Duraiswami
% All rights reserved.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are met:
%
% 1. Redistributions of source code must retain the above copyright notice,
% this list of conditions and the following disclaimer.
%
% 2. Redistributions in binary form must reproduce the above copyright notice,
% this list of conditions and the following disclaimer in the documentation
% and/or other materials provided with the distribution.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
% POSSIBILITY OF SUCH DAMAGE.
%
%
% Generate a figure showing the prolate spheroidal coordinate system.
%
function generate_figure1a()
w = 2.0;
nels = 100;
x = linspace(-w, w, nels);
y = linspace(-w, w, nels);
z = linspace(-w, w, nels);
[ ...
x, y, z ...
] = meshgrid(x, y, z);
x = reshape(x, 1, nels * nels * nels);
y = reshape(y, 1, nels * nels * nels);
z = reshape(z, 1, nels * nels * nels);
cart = [x; y; z];
pro = cart_to_pro(1.0, cart);
eta = pro(1, :);
xi = pro(2, :);
phi = pro(3, :);
x = reshape(x, nels, nels, nels);
y = reshape(y, nels, nels, nels);
z = reshape(z, nels, nels, nels);
eta = reshape(eta, nels, nels, nels);
xi = reshape(xi, nels, nels, nels);
phi = reshape(phi, nels, nels, nels);
fv = isosurface(x, y, z, eta, -0.5);
figure();
trisurf(fv.faces, fv.vertices(:, 1), fv.vertices(:, 2), fv.vertices(:, 3), 'edgecolor', 'none', 'facecolor', [1.0, 0.0, 0.0]);
hold('on');
fv = isosurface(x, y, z, eta, 0.5);
trisurf(fv.faces, fv.vertices(:, 1), fv.vertices(:, 2), fv.vertices(:, 3), 'edgecolor', 'none', 'facecolor', [1.0, 0.0, 0.0]);
fv = isosurface(x, y, z, xi, 1.5);
trisurf(fv.faces, fv.vertices(:, 1), fv.vertices(:, 2), fv.vertices(:, 3), 'edgecolor', 'none', 'facecolor', [0.0, 0.7, 0.0]);
x = linspace(0.0, w, nels);
y = linspace(-w, w, nels);
z = linspace(-w, w, nels);
[ ...
x, y, z ...
] = meshgrid(x, y, z);
x = reshape(x, 1, nels * nels * nels);
y = reshape(y, 1, nels * nels * nels);
z = reshape(z, 1, nels * nels * nels);
cart = [x; y; z];
pro = cart_to_pro(1.0, cart);
eta = pro(1, :);
xi = pro(2, :);
phi = pro(3, :);
x = reshape(x, nels, nels, nels);
y = reshape(y, nels, nels, nels);
z = reshape(z, nels, nels, nels);
eta = reshape(eta, nels, nels, nels);
xi = reshape(xi, nels, nels, nels);
phi = reshape(phi, nels, nels, nels);
fv = isosurface(x, y, z, phi, 0.0);
trisurf(fv.faces, fv.vertices(:, 1), fv.vertices(:, 2), fv.vertices(:, 3), 'edgecolor', 'none', 'facecolor', [0.0, 0.0, 1.0]);
alpha(0.5);
axis('equal');
xlim([-w, w]);
ylim([-w, w]);
zlim([-w, w]);
axis('off');
view(50.0, 10.0);
set(gcf, 'position', [100, 100, 800, 600]);
set(gcf, 'color', [1.0, 1.0, 1.0]);
export_fig(gcf, 'images/figure1a.png');
close();
end