sugr_Point_2D

% Create 2D point

 Usage:
    Point_2D = sugr_Point_2D(xe)
         Euclidean vector, CovM = 0

    Point_2D = sugr_Point_2D(xh)
         homogeneous vector, CovM = 0

    Point_2D = sugr_Point_2D(x,y)
         Euclidean coordinates, CovM = 0

   Point_2D = sugr_Point_2D(xe,Cee)
         Euclidean vector with Cov.matrix

    Point_2D = sugr_Point_2D(xh,Chh)
          homgeneous vector with Cov.matrix

    Point_2D = sugr_Point_2D(u,v,w)
         homogeneous coordinates, CovM = 0

    Point_2D = sugr_Point_2D(x,y,Cee)
         Euclidean coordinates with Euclidean Cov.matrix

    Point_2D = sugr_Point_2D(x,y,sx,sy)
         independent Euclidean coordinates with standard deviations

    Point_2D = sugr_Point_2D(u,v,w,Chh)
         homogeneous coordinates with homogeneous Cov.matrix
 
  * Point_2D = structure 
        .h    = spherically normalized homogeneous coordinates
        .Crr  = reducedcovariance matrix
        .Jr   = null space of .h'
        .type = 1

 Wolfgang Förstner 1/2011
 wfoerstn@uni-bonn.de

 See also sugr_Line_2D, sugr_Line_3D, sugr_Plane_3D, sugr_Point_3D

0001 %% Create 2D point
0002 %
0003 % Usage:
0004 %    Point_2D = sugr_Point_2D(xe)
0005 %         Euclidean vector, CovM = 0
0006 %
0007 %    Point_2D = sugr_Point_2D(xh)
0008 %         homogeneous vector, CovM = 0
0009 %
0010 %    Point_2D = sugr_Point_2D(x,y)
0011 %         Euclidean coordinates, CovM = 0
0012 %
0013 %   Point_2D = sugr_Point_2D(xe,Cee)
0014 %         Euclidean vector with Cov.matrix
0015 %
0016 %    Point_2D = sugr_Point_2D(xh,Chh)
0017 %          homgeneous vector with Cov.matrix
0018 %
0019 %    Point_2D = sugr_Point_2D(u,v,w)
0020 %         homogeneous coordinates, CovM = 0
0021 %
0022 %    Point_2D = sugr_Point_2D(x,y,Cee)
0023 %         Euclidean coordinates with Euclidean Cov.matrix
0024 %
0025 %    Point_2D = sugr_Point_2D(x,y,sx,sy)
0026 %         independent Euclidean coordinates with standard deviations
0027 %
0028 %    Point_2D = sugr_Point_2D(u,v,w,Chh)
0029 %         homogeneous coordinates with homogeneous Cov.matrix
0030 %
0031 %  * Point_2D = structure
0032 %        .h    = spherically normalized homogeneous coordinates
0033 %        .Crr  = reducedcovariance matrix
0034 %        .Jr   = null space of .h'
0035 %        .type = 1
0036 %
0037 % Wolfgang Förstner 1/2011
0038 % wfoerstn@uni-bonn.de
0039 %
0040 % See also sugr_Line_2D, sugr_Line_3D, sugr_Plane_3D, sugr_Point_3D
0041 
0042 function Point_2D = sugr_Point_2D(a1,a2,a3,a4)
0043 
0044 % default
0045 Chh  = zeros(3);
0046 
0047 switch nargin
0048     case 0
0049     case 1 % 2- or 3-vector
0050         size_a1 = size(a1,1);
0051         switch size_a1
0052             case 2 
0053 %% (1) Euclidean vector, CovM == 0
0054                 % spherically normalized
0055                 Point_2D = sugr_minimal_vector([a1;1],Chh);
0056                 
0057             case 3 
0058 %% (1) homogeneous vector, CovM == 0
0059                 Point_2D = sugr_minimal_vector(a1,Chh);
0060                 
0061         end
0062     case 2
0063 
0064         size_a2 = size(a1,1);
0065         switch size_a2
0066             case 1 
0067 %% (2) Euclidean coordinates, CovM == 0
0068                 Point_2D = sugr_minimal_vector([a1;a2;1],Chh);
0069                 
0070             case 2
0071 %% (2) Euclidean vector
0072                 % spehrically normalized
0073                 Point_2D = sugr_minimal_vector([a1;1],[a2 zeros(2,1); zeros(1,3)]);
0074 
0075             case 3
0076 %% (3) uncertain homogeneous coordinates
0077                 Point_2D   = sugr_minimal_vector(a1,a2);
0078         end
0079     case 3
0080         size_a3 = size(a3,1);
0081         switch size_a3
0082             case 1 
0083 %% (3) homogeneous vector, CovM == 0
0084                  % spehrically normalized
0085                 Point_2D = sugr_minimal_vector([a1;a2;a3],Chh);
0086                 
0087             case 2
0088 %% (3) Euclidean coordinates
0089                 % spehrically normalized
0090                 Point_2D = sugr_minimal_vector([a1;a2;1],[a3 zeros(2,1); zeros(1,3)]);
0091         end
0092         
0093     case 4
0094         size_a4 = size(a4,1);
0095         switch size_a4
0096             case 1 
0097 %% (4) Euclidean vector, independent coordinates
0098                 % spehrically normalized
0099                 Point_2D = sugr_minimal_vector([a1;a2;1],...
0100                            [ a3^2, 0, 0; 0, a4^2, 0; zeros(1,3)]);
0101                 
0102             case 3
0103 %% (4) homogeneous coordinates
0104                 % spehrically normalized
0105                 Point_2D = sugr_minimal_vector([a1;a2;a3],a4);
0106         end
0107         
0108 end
0109 
0110 Point_2D.Jr = null(Point_2D.h');
0111 Point_2D.type=1;
0112