torusMesh

 Create a 3D mesh representing a torus.

   [V, F] = torusMesh(TORUS)
   Converts the torus in TORUS into a face-vertex quadrangular mesh.
   TORUS is given by [XC YC ZY R1 R2 THETA PHI]
   where (XC YZ ZC) is the center of the torus, R1 is the main radius, R2
   is the radius of the torus section, and (THETA PHI) is the angle of the
   torus normal vector (both in degrees).

   [V, F] = torusMesh(TORUS, 'nTheta', NT, 'nPhi', NP)
   Creates a mesh using NP circles, each circle being discretized with NT
   vertices. Default are 60 for both parameters.

   [V, F] = torusMesh()
   Creates a mesh representing a default torus.

   Example
     [v, f] = torusMesh([50 50 50  30 10  30 45]);
     figure; drawMesh(v, f, 'linestyle', 'none');
     view(3); axis equal; 
     lighting gouraud; light;


   See also
     meshes3d, drawTorus, revolutionSurface, cylinderMesh, sphereMesh
     drawMesh

0001 function varargout = torusMesh(torus, varargin)
0002 % Create a 3D mesh representing a torus.
0003 %
0004 %   [V, F] = torusMesh(TORUS)
0005 %   Converts the torus in TORUS into a face-vertex quadrangular mesh.
0006 %   TORUS is given by [XC YC ZY R1 R2 THETA PHI]
0007 %   where (XC YZ ZC) is the center of the torus, R1 is the main radius, R2
0008 %   is the radius of the torus section, and (THETA PHI) is the angle of the
0009 %   torus normal vector (both in degrees).
0010 %
0011 %   [V, F] = torusMesh(TORUS, 'nTheta', NT, 'nPhi', NP)
0012 %   Creates a mesh using NP circles, each circle being discretized with NT
0013 %   vertices. Default are 60 for both parameters.
0014 %
0015 %   [V, F] = torusMesh()
0016 %   Creates a mesh representing a default torus.
0017 %
0018 %   Example
0019 %     [v, f] = torusMesh([50 50 50  30 10  30 45]);
0020 %     figure; drawMesh(v, f, 'linestyle', 'none');
0021 %     view(3); axis equal;
0022 %     lighting gouraud; light;
0023 %
0024 %
0025 %   See also
0026 %     meshes3d, drawTorus, revolutionSurface, cylinderMesh, sphereMesh
0027 %     drawMesh
0028 
0029 % ------
0030 % Author: David Legland
0031 % e-mail: david.legland@inrae.fr
0032 % Created: 2012-10-25,    using Matlab 7.9.0.529 (R2009b)
0033 % Copyright 2012 INRA - Cepia Software Platform.
0034 
0035 %   HISTORY
0036 %   2013-04-30 add support for empty argument
0037 
0038 
0039 %% Extract data for torus
0040 
0041 % check input number
0042 if nargin == 0
0043     torus = [0 0 0  30 10  0 0];
0044 elseif ischar(torus)
0045     varargin = [{torus} varargin];
0046     torus = [0 0 0  30 10  0 0];
0047 end
0048 
0049 if isnumeric(torus) && size(torus, 2) ~= 7
0050     error('First argument must be a numeric row vector with 7 elements');
0051 end
0052 
0053 center = torus(1:3);
0054 r1 = torus(4);
0055 r2 = torus(5);
0056 
0057 if size(torus, 2) >= 7
0058     normal = torus(6:7);
0059 end
0060 
0061 
0062 %% Extract data for discretisation
0063 
0064 % number
0065 nTheta = 60;
0066 nPhi = 60;
0067 while length(varargin) > 1
0068     argName = varargin{1};
0069     switch lower(argName)
0070         case 'ntheta'
0071             nTheta = varargin{2};
0072         case 'nphi'
0073             nPhi = varargin{2};
0074         otherwise
0075             error('Unknown optional argument: %s', argName);
0076     end
0077     
0078     varargin(1:2) = [];
0079 end
0080 
0081 
0082 %% Discretize torus
0083 
0084 % create base circle (duplicate last vertex to manage mesh periodicity)
0085 circle = circleToPolygon([r1 0 r2], nTheta);
0086 circle = circle([1:end 1], :);
0087 % create rotation angle list (duplicate last one to manage mesh periodicity)
0088 phiList = linspace(0, 2*pi, nPhi + 1);
0089 [x, y, z] = revolutionSurface(circle, phiList);
0090 
0091 % transform torus
0092 trans = localToGlobal3d([center normal]);
0093 [x, y, z] = transformPoint3d(x, y, z, trans);
0094 
0095 % convert to FV mesh
0096 [vertices, faces] = surfToMesh(x, y, z, 'xPeriodic', true, 'yPeriodic', true);
0097 
0098 % format output
0099 varargout = formatMeshOutput(nargout, vertices, faces);