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## Copyright (C) 2024 David Legland
## 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 AUTHOR 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.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = fillSphericalTriangle(sphere, p1, p2, p3, varargin)
%FILLSPHERICALTRIANGLE Fill a triangle on a sphere.
%
% fillSphericalTriangle(SPHERE, PT1, PT2, PT3);
%
%
% See also
% fillSphericalPolygon, drawSphericalTriangle, drawSphere
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-22
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% extract data of the sphere
ori = sphere(:, 1:3);
r = sphere(4);
% extract direction vectors for each point
v1 = normalizeVector3d(p1 - ori);
v2 = normalizeVector3d(p2 - ori);
v3 = normalizeVector3d(p3 - ori);
% create a plane tangent to the sphere containing first point
plane = createPlane(v1, v1);
% position on the plane of the direction vectors
pp2 = planePosition(intersectLinePlane([ori v2], plane), plane);
pp3 = planePosition(intersectLinePlane([ori v3], plane), plane);
% create rough parametrization with 2 variables
nTri = 5;
s = linspace(0, 1, nTri);
t = linspace(0, 1, nTri);
ns = length(s);
nt = length(t);
s = repmat(s, [nt, 1]);
t = repmat(t', [1, ns]);
% convert to plane coordinates
xp = s * pp2(1) + t .* (1-s) * pp3(1);
yp = s * pp2(2) + t .* (1-s) * pp3(2);
% convert to 3D coordinates (still on the 3D plane)
x = plane(1) * ones(size(xp)) + plane(4) * xp + plane(7) * yp - ori(1);
y = plane(2) * ones(size(xp)) + plane(5) * xp + plane(8) * yp - ori(2);
z = plane(3) * ones(size(xp)) + plane(6) * xp + plane(9) * yp - ori(3);
% project on the sphere
norm = hypot(hypot(x, y), z);
xn = x ./ norm * r + ori(1);
yn = y ./ norm * r + ori(2);
zn = z ./ norm * r + ori(3);
if nargout == 0
% simply display the patch
surf(xn, yn, zn, 'FaceColor', 'g', 'EdgeColor', 'none', varargin{:});
elseif nargout == 1
% display the patch and return a handle
h = surf(xn, yn, zn, 'FaceColor', 'g', 'EdgeColor', 'none', varargin{:});
varargout = {h};
elseif nargout == 3
% If 3 outputs are required, return patch vertex coordinates
varargout = {x, y, z};
end
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