torusMesh

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 %TORUSMESH 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 2012-2024 INRA - Cepia Software Platform
0034 
0035 %% Extract data for torus
0036 
0037 % check input number
0038 if nargin == 0
0039     torus = [0 0 0  30 10  0 0];
0040 elseif ischar(torus)
0041     varargin = [{torus} varargin];
0042     torus = [0 0 0  30 10  0 0];
0043 end
0044 
0045 if isnumeric(torus) && size(torus, 2) ~= 7
0046     error('First argument must be a numeric row vector with 7 elements');
0047 end
0048 
0049 center = torus(1:3);
0050 r1 = torus(4);
0051 r2 = torus(5);
0052 
0053 if size(torus, 2) >= 7
0054     normal = torus(6:7);
0055 end
0056 
0057 
0058 %% Extract data for discretisation
0059 
0060 % number
0061 nTheta = 60;
0062 nPhi = 60;
0063 while length(varargin) > 1
0064     argName = varargin{1};
0065     switch lower(argName)
0066         case 'ntheta'
0067             nTheta = varargin{2};
0068         case 'nphi'
0069             nPhi = varargin{2};
0070         otherwise
0071             error('Unknown optional argument: %s', argName);
0072     end
0073     
0074     varargin(1:2) = [];
0075 end
0076 
0077 
0078 %% Discretize torus
0079 
0080 % create base circle (duplicate last vertex to manage mesh periodicity)
0081 circle = circleToPolygon([r1 0 r2], nTheta);
0082 circle = circle([1:end 1], :);
0083 % create rotation angle list (duplicate last one to manage mesh periodicity)
0084 phiList = linspace(0, 2*pi, nPhi + 1);
0085 [x, y, z] = revolutionSurface(circle, phiList);
0086 
0087 % transform torus
0088 trans = localToGlobal3d([center normal]);
0089 [x, y, z] = transformPoint3d(x, y, z, trans);
0090 
0091 % convert to FV mesh
0092 [vertices, faces] = surfToMesh(x, y, z, 'xPeriodic', true, 'yPeriodic', true);
0093 
0094 % format output
0095 varargout = formatMeshOutput(nargout, vertices, faces);