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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 = ellipsoidMesh(elli, varargin)
%ELLIPSOIDMESH Convert a 3D ellipsoid to face-vertex mesh representation.
%
% [V, F] = ellipsoidMesh(ELLI)
% ELLI is given by:
% [XC YC ZC A B C PHI THETA PSI],
% where (XC, YC, ZC) is the ellipsoid center, A, B and C are the half
% lengths of the ellipsoid main axes, and PHI THETA PSI are Euler angles
% representing ellipsoid orientation, in degrees.
%
% Example
% % compute mesh of an ellongated ellipsoid
% elli = [50 50 50 50 30 10 30 20 10];
% [v, f] = ellipsoidMesh(elli);
% figure; hold on; axis equal; axis([0 100 0 100 0 100]); view(3);
% drawMesh(v, f);
%
% See also
% meshes3d, drawEllipsoid, sphereMesh, equivalentEllipsoid
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-03-12, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
%% Default values
% number of meridians
nPhi = 32;
% number of parallels
nTheta = 16;
%% Extract input arguments
% Parse the input (try to extract center coordinates and radius)
if nargin == 0
% no input: assumes ellipsoid with default shape
elli = [0 0 0 5 4 3 0 0 0];
end
% default set of options for drawing meshes
options = {'FaceColor', 'g', 'linestyle', 'none'};
while length(varargin) > 1
switch lower(varargin{1})
case 'nphi'
nPhi = varargin{2};
case 'ntheta'
nTheta = varargin{2};
otherwise
% assumes this is drawing option
options = [options varargin(1:2)]; %#ok<AGROW>
end
varargin(1:2) = [];
end
%% Parse numerical inputs
% Extract ellipsoid parameters
xc = elli(:,1);
yc = elli(:,2);
zc = elli(:,3);
a = elli(:,4);
b = elli(:,5);
c = elli(:,6);
k = pi / 180;
ellPhi = elli(:,7) * k;
ellTheta = elli(:,8) * k;
ellPsi = elli(:,9) * k;
%% Coordinates computation
% convert unit basis to ellipsoid basis
sca = createScaling3d(a, b, c);
rotZ = createRotationOz(ellPhi);
rotY = createRotationOy(ellTheta);
rotX = createRotationOx(ellPsi);
tra = createTranslation3d([xc yc zc]);
% concatenate transforms
trans = tra * rotZ * rotY * rotX * sca;
%% parametrisation of ellipsoid
% spherical coordinates
theta = linspace(0, pi, nTheta+1);
phi = linspace(0, 2*pi, nPhi+1);
% convert to cartesian coordinates
sintheta = sin(theta);
x = cos(phi') * sintheta;
y = sin(phi') * sintheta;
z = ones(length(phi),1) * cos(theta);
% transform mesh vertices
[x, y, z] = transformPoint3d(x, y, z, trans);
% convert to FV mesh
[vertices, faces] = surfToMesh(x, y, z, 'xPeriodic', false, 'yPeriodic', true);
% format output
varargout = formatMeshOutput(nargout, vertices, faces);
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