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cg_similarity_2D

PURPOSE ^

% determines constraint values and Jacobians for 2D similarity

SYNOPSIS ^

function [cg,At,Bt] = cg_similarity_2D(l,la,xa)

DESCRIPTION ^

% determines constraint values and Jacobians for 2D similarity

 Model:
 cg(x,l) = zr - s*zl - t = 0

 [l(3)]    - [x(1) -x(2)] [l(1)] - [x(3)] = [0]
 [l(4)]    - [x(2)  x(1)] [l(2)] - [x(4)]   [0]

 l         = 4x1-vector [xl yl,xr yr] = [zl, zr]
 x         = 4x1-vector [ a  b, c  d] = [ s,  t]

 Wolfgang Förstner
 wfoerstn@uni-bonn.de

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% determines constraint values and Jacobians for 2D similarity
0002 %
0003 % Model:
0004 % cg(x,l) = zr - s*zl - t = 0
0005 %
0006 % [l(3)]    - [x(1) -x(2)] [l(1)] - [x(3)] = [0]
0007 % [l(4)]    - [x(2)  x(1)] [l(2)] - [x(4)]   [0]
0008 %
0009 % l         = 4x1-vector [xl yl,xr yr] = [zl, zr]
0010 % x         = 4x1-vector [ a  b, c  d] = [ s,  t]
0011 %
0012 % Wolfgang Förstner
0013 % wfoerstn@uni-bonn.de
0014 
0015 function [cg,At,Bt] = cg_similarity_2D(l,la,xa)
0016 
0017 At  = [-la(1)  la(2) -1  0 ;...
0018     -la(2) -la(1)  0 -1];
0019 Bt  = [-xa(1)  xa(2) 1 0;...
0020     -xa(2) -xa(1) 0 1];
0021 
0022 cg = -( [la(3);...
0023     la(4)] - ...
0024     [xa(1) -xa(2);
0025     xa(2)  xa(1)] * ...
0026     [la(1);...
0027     la(2)] - ...
0028     [xa(3); ...
0029     xa(4)])...
0030     + Bt * (la-l);

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