ellipsoidMesh

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

0001 function varargout = ellipsoidMesh(elli, varargin)
0002 %ELLIPSOIDMESH Convert a 3D ellipsoid to face-vertex mesh representation.
0003 %
0004 %   [V, F] = ellipsoidMesh(ELLI)
0005 %   ELLI is given by:
0006 %   [XC YC ZC  A B C  PHI THETA PSI],
0007 %   where (XC, YC, ZC) is the ellipsoid center, A, B and C are the half
0008 %   lengths of the ellipsoid main axes, and PHI THETA PSI are Euler angles
0009 %   representing ellipsoid orientation, in degrees.
0010 %
0011 %   Example
0012 %     % compute mesh of an ellongated ellipsoid
0013 %     elli = [50 50 50   50 30 10   30 20 10];
0014 %     [v, f] = ellipsoidMesh(elli);
0015 %     figure; hold on; axis equal; axis([0 100 0 100 0 100]); view(3);
0016 %     drawMesh(v, f);
0017 %
0018 %   See also
0019 %   meshes3d, drawEllipsoid, sphereMesh, equivalentEllipsoid
0020 %
0021 
0022 % ------
0023 % Author: David Legland
0024 % E-mail: david.legland@inrae.fr
0025 % Created: 2011-03-12, using Matlab 7.9.0.529 (R2009b)
0026 % Copyright 2011-2024 INRA - Cepia Software Platform
0027 
0028 %% Default values
0029 
0030 % number of meridians
0031 nPhi    = 32;
0032 
0033 % number of parallels
0034 nTheta  = 16;
0035 
0036 
0037 %% Extract input arguments
0038 
0039 % Parse the input (try to extract center coordinates and radius)
0040 if nargin == 0
0041     % no input: assumes ellipsoid with default shape
0042     elli = [0 0 0 5 4 3 0 0 0];
0043 end
0044 
0045 % default set of options for drawing meshes
0046 options = {'FaceColor', 'g', 'linestyle', 'none'};
0047 
0048 while length(varargin) > 1
0049     switch lower(varargin{1})
0050         case 'nphi'
0051             nPhi = varargin{2};
0052             
0053         case 'ntheta'
0054             nTheta = varargin{2};
0055 
0056         otherwise
0057             % assumes this is drawing option
0058             options = [options varargin(1:2)]; %#ok<AGROW>
0059     end
0060 
0061     varargin(1:2) = [];
0062 end
0063 
0064 
0065 %% Parse numerical inputs
0066 
0067 % Extract ellipsoid parameters
0068 xc  = elli(:,1);
0069 yc  = elli(:,2);
0070 zc  = elli(:,3);
0071 a   = elli(:,4);
0072 b   = elli(:,5);
0073 c   = elli(:,6);
0074 k   = pi / 180;
0075 ellPhi   = elli(:,7) * k;
0076 ellTheta = elli(:,8) * k;
0077 ellPsi   = elli(:,9) * k;
0078 
0079 
0080 %% Coordinates computation
0081 
0082 % convert unit basis to ellipsoid basis
0083 sca     = createScaling3d(a, b, c);
0084 rotZ    = createRotationOz(ellPhi);
0085 rotY    = createRotationOy(ellTheta);
0086 rotX    = createRotationOx(ellPsi);
0087 tra     = createTranslation3d([xc yc zc]);
0088 
0089 % concatenate transforms
0090 trans   = tra * rotZ * rotY * rotX * sca;
0091 
0092 
0093 %% parametrisation of ellipsoid
0094 
0095 % spherical coordinates
0096 theta   = linspace(0, pi, nTheta+1);
0097 phi     = linspace(0, 2*pi, nPhi+1);
0098 
0099 % convert to cartesian coordinates
0100 sintheta = sin(theta);
0101 x = cos(phi') * sintheta;
0102 y = sin(phi') * sintheta;
0103 z = ones(length(phi),1) * cos(theta);
0104 
0105 % transform mesh vertices
0106 [x, y, z] = transformPoint3d(x, y, z, trans);
0107 
0108 % convert to FV mesh
0109 [vertices, faces] = surfToMesh(x, y, z, 'xPeriodic', false, 'yPeriodic', true);
0110 
0111 % format output
0112 varargout = formatMeshOutput(nargout, vertices, faces);