sugr_construct_parallel_lx_Line_2D

% Construct 2D line parallel to line l through point x

 Line_2D = sugr_construct_parallel_lx_Line_2D(l,x)

 * l =  2D line struct {l.h,l.Crr}
 * x =  2D point struct {x.h,x.Crr}

 * Line_2D  =  2D line struct {l.h,l.Crr}

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

 See also sugr_Line_2D, sugr_construct_parallel_lO_Line_2D,
 sugr_construct_midline_Line_2D, sugr_construct_footpoint_Ol_Point_2D,
 sugr_construct_footpoint_xl_Point_2D,
 sugr_construct_join_Line_2D, sugr_construct_join_Line_3D

0001 %% Construct 2D line parallel to line l through point x
0002 %
0003 % Line_2D = sugr_construct_parallel_lx_Line_2D(l,x)
0004 %
0005 % * l =  2D line struct {l.h,l.Crr}
0006 % * x =  2D point struct {x.h,x.Crr}
0007 %
0008 % * Line_2D  =  2D line struct {l.h,l.Crr}
0009 %
0010 % Wolfgang Förstner 1/2011
0011 % wfoerstn@uni-bonn.de
0012 %
0013 % See also sugr_Line_2D, sugr_construct_parallel_lO_Line_2D,
0014 % sugr_construct_midline_Line_2D, sugr_construct_footpoint_Ol_Point_2D,
0015 % sugr_construct_footpoint_xl_Point_2D,
0016 % sugr_construct_join_Line_2D, sugr_construct_join_Line_3D
0017 
0018 function Line_2D = sugr_construct_parallel_lx_Line_2D(l,x)
0019 
0020         S3 = calc_S([0,0,1]');
0021         A = -calc_S(x.h)*S3;
0022         B =  calc_S(S3*l.h);
0023         h   = A * l.h;
0024         Cxhh = sugr_get_CovM_homogeneous_Vector(x);
0025         Clhh = sugr_get_CovM_homogeneous_Vector(l);
0026         Chh = A * Clhh * A' + B * Cxhh * B'; 
0027      
0028 % generate line
0029 Line_2D = sugr_Line_2D(h,Chh);