obtainVrep

 creates a polytope object in V-representation (vertices)

 Syntax: obtainVRep(object, param, dim)
 
 obtainPolytope(object, ..) generates the specified object. Possible 
 definitions are given as follows, where brackets denote special bodies:
   1D - line
   2D - square, circle, polygon, (4-polygon-par)
   3D - cube, sphere, cone, pyramid, bicone, bipyramid, prism, 
        (ikosaprism), (mixCubeOctahedron)
 More details below.

 obtainPolytope(.., param, ..) provides an additional parameter for the
 specified object. For example, the number of corners of a polygon. The
 parameter can be optional (e.g.  number of corners to approximate a
 circle) or not defined at all (e.g. for a square). Use param = [], if the
 parameter is not required, but one of the following options is required.

 obtainPolytope(.., dim, ..) Specifies the dimension of the object. If not 
 specified or dim = [] is used, the dimension of the object is dim = 3. If 
 dim is higher than the native dimension of the object (e.g. a 3D line), 
 the object is stretched with a very small size into this dimension(s).
 See the following option for detail.

 Comments on available objects:

   CIRCLES and POLYGONES: Polygones are approximations of circles.
   And polygones are created exactly in this manner from which follows that
   polygones fit exactly in the unit-circle.

   LINE, SQUARE and CUBE: These objects fill the interval [0 1] in the
   appropriate coordinate directions.

   PRISMS, ANTIPRISM, CONE, PYRAMID, BIPYRAMID and BICONE: These objects 
   are created starting with the two-dimensional basis and extended into 
   z-direction to span either the interval [0 1] (prism, antisprism, 
   pyramid, cone) or [-1 1] (bipyramid, bicone) on the z-axis.

 See also: polytope, identifyPolytope, viewPolytope,
           obtainHRep, stretchPolytope, movePolytope, convertPolytope

• obtainVrep1d This is a subfunction.
• obtainVrep2d This is a subfunction.
• obtainVrep3d This is a subfunction.

• findCurvature
• fitCTCrystalsHealpixRounded % fits the crystals from the folder chosen by clicking
• testCTPotashHoughRounded
• testCTSalt get the file
• obtainDistributionDiscrete obtain a discrete probability distribution
• obtainHrep creates a polytope object in H-representation (halfspaces)

0001 function vrep = obtainVrep(object, param, dim)
0002 % creates a polytope object in V-representation (vertices)
0003 %
0004 % Syntax: obtainVRep(object, param, dim)
0005 %
0006 % obtainPolytope(object, ..) generates the specified object. Possible
0007 % definitions are given as follows, where brackets denote special bodies:
0008 %   1D - line
0009 %   2D - square, circle, polygon, (4-polygon-par)
0010 %   3D - cube, sphere, cone, pyramid, bicone, bipyramid, prism,
0011 %        (ikosaprism), (mixCubeOctahedron)
0012 % More details below.
0013 %
0014 % obtainPolytope(.., param, ..) provides an additional parameter for the
0015 % specified object. For example, the number of corners of a polygon. The
0016 % parameter can be optional (e.g.  number of corners to approximate a
0017 % circle) or not defined at all (e.g. for a square). Use param = [], if the
0018 % parameter is not required, but one of the following options is required.
0019 %
0020 % obtainPolytope(.., dim, ..) Specifies the dimension of the object. If not
0021 % specified or dim = [] is used, the dimension of the object is dim = 3. If
0022 % dim is higher than the native dimension of the object (e.g. a 3D line),
0023 % the object is stretched with a very small size into this dimension(s).
0024 % See the following option for detail.
0025 %
0026 % Comments on available objects:
0027 %
0028 %   CIRCLES and POLYGONES: Polygones are approximations of circles.
0029 %   And polygones are created exactly in this manner from which follows that
0030 %   polygones fit exactly in the unit-circle.
0031 %
0032 %   LINE, SQUARE and CUBE: These objects fill the interval [0 1] in the
0033 %   appropriate coordinate directions.
0034 %
0035 %   PRISMS, ANTIPRISM, CONE, PYRAMID, BIPYRAMID and BICONE: These objects
0036 %   are created starting with the two-dimensional basis and extended into
0037 %   z-direction to span either the interval [0 1] (prism, antisprism,
0038 %   pyramid, cone) or [-1 1] (bipyramid, bicone) on the z-axis.
0039 %
0040 % See also: polytope, identifyPolytope, viewPolytope,
0041 %           obtainHRep, stretchPolytope, movePolytope, convertPolytope
0042 
0043 % The elk-library: convex geometry applied to crystallization modeling.
0044 %   Copyright (C) 2012 Alexander Reinhold
0045 %
0046 % This program is free software: you can redistribute it and/or modify it
0047 %   under the terms of the GNU General Public License as published by the
0048 %   Free Software Foundation, either version 3 of the License, or (at your
0049 %   option) any later version.
0050 %
0051 % This program is distributed in the hope that it will be useful, but
0052 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0053 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0054 %   General Public License for more details.
0055 %
0056 % You should have received a copy of the GNU General Public License along
0057 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0058 
0059 %% No object error
0060 if nargin < 1 || ~ischar(object)
0061     error('No object name is specified, try: help obtainPolytope');end
0062 
0063 %% default parameters
0064 if ~exist('param', 'var'), param = [];end
0065 if ~exist('dim', 'var'), dim = 3;end
0066 
0067 %% Generate object with specified dimension
0068 switch dim
0069     case 1
0070         vrep = obtainVrep1d(object);
0071     case 2
0072         vrep = obtainVrep2d(object, param);
0073     case 3
0074         vrep = obtainVrep3d(object, param);
0075     otherwise
0076         error(['I cannot obtain polytopes in dimension ' num2str(dim) '.'])
0077 end