sugr_Point_3D

% Create 3D point

 Point_3D = sugr_Point_3D(a1,a2,a3,a4,a5,a6)

 Usage:
 (1)   Point_3D = sugr_Point_3D(Xe)
         Euclidean vector, CovM = 0

 (1)   Point_3D = sugr_Point_3D(Xh)
         homogeneous vector, CovM = 0

 (2)   Point_3D = sugr_Point_3D(Xe,Cee)
         Euclidean vector and CovM

 (2)   Point_3D = sugr_Point_3D(Xh,Chh)
         homgeneous vector and CovM

 (6)   Point_3D = sugr_Point_3D(X,Y,Z,sX,sY,sZ)
         independent Euclidean coordinates with standard dev

 * Point_3D = structure
      .h     = spherically normalized homogeneous coordinates
      .Crr   = reduced covariance matrix
      .Jr    = null space of .h'
      .type  = 3

 Bernhard Wrobel, Wolfgang Förstner 2/2013
 wfoerstn@uni-bonn.de

 See also sugr_Line_3D, sugr_Plane_3D, sugr_Point_2D

0001 %% Create 3D point
0002 %
0003 % Point_3D = sugr_Point_3D(a1,a2,a3,a4,a5,a6)
0004 %
0005 % Usage:
0006 % (1)   Point_3D = sugr_Point_3D(Xe)
0007 %         Euclidean vector, CovM = 0
0008 %
0009 % (1)   Point_3D = sugr_Point_3D(Xh)
0010 %         homogeneous vector, CovM = 0
0011 %
0012 % (2)   Point_3D = sugr_Point_3D(Xe,Cee)
0013 %         Euclidean vector and CovM
0014 %
0015 % (2)   Point_3D = sugr_Point_3D(Xh,Chh)
0016 %         homgeneous vector and CovM
0017 %
0018 % (6)   Point_3D = sugr_Point_3D(X,Y,Z,sX,sY,sZ)
0019 %         independent Euclidean coordinates with standard dev
0020 %
0021 % * Point_3D = structure
0022 %      .h     = spherically normalized homogeneous coordinates
0023 %      .Crr   = reduced covariance matrix
0024 %      .Jr    = null space of .h'
0025 %      .type  = 3
0026 %
0027 % Bernhard Wrobel, Wolfgang Förstner 2/2013
0028 % wfoerstn@uni-bonn.de
0029 %
0030 % See also sugr_Line_3D, sugr_Plane_3D, sugr_Point_2D
0031 
0032 
0033 function Point_3D = sugr_Point_3D(a1,a2,a3,a4,a5,a6)
0034 
0035 % default
0036 Chh  = zeros(4);
0037 
0038 switch nargin
0039     case 0
0040     case 1 % 3- or 4-vector
0041         size_a1 = size(a1,1);
0042         switch size_a1
0043             case 3
0044                 %% (1) Euclidean vector, CovM == 0
0045                 % spherically normalized
0046                 Point_3D = sugr_minimal_vector([a1;1],Chh);
0047                 
0048             case 4
0049                 %% (1) homogeneous vector, CovM == 0
0050                 Point_3D = sugr_minimal_vector(a1,Chh);
0051                 
0052         end
0053     case 2
0054         
0055         size_a2 = size(a1,1);
0056         switch size_a2
0057             case 1
0058                 Point_3D = sugr_minimal_vector([a1(:);1],[a2,zeros(3,1);zeros(1,4)]);
0059                 
0060             case 3
0061                 %% (2) Euclidean coordinates, CovM == 0
0062                 Point_3D = sugr_minimal_vector([a1;1],[a2,zeros(3,1);zeros(1,4)]);
0063                 
0064             case 4
0065                 %% (2) homogeneous vector
0066                 % spherically normalized
0067                 Point_3D = sugr_minimal_vector(a1,a2);
0068         end
0069     case 6
0070         %% (6) homogeneous coordinates
0071         % individual standard deviations
0072         Point_3D = sugr_minimal_vector(...
0073             [a1;a2;a3;1],...
0074             [diag([a4,a5,a6]).^2,zeros(3,1);[0,0,0,1]]);
0075         
0076         
0077 end
0078 
0079 Point_3D.Jr = null(Point_3D.h');
0080 
0081 Point_3D.type=3;
0082