campinhole_LSfun.m

function F=campinhole_LSfun(a,data)
% F=campinhole_LSfun(a,data)
% solves the camera pinhole problem (linear), see Ng and Zhang, 2006, Exp. 
% Fluids., 34, pp. 484-493.  this solves equation 8 in that paper.  See 
% also Willert, exp. in fluids. (2006), n.41, pp.135., set the constraint 
% of a(12)=1, so the trivial solution is not solved for.
%
% This function is called by fitcameramodels.m
% 
% Inputs:
%    data:          Contains a file structure that holds the world and
%                   pixel corrdinates for the target markers.
%    data.allxdata: World coordinates for the target markers
%    data.allXdata: Pixel coordinates for the target markers
%    a:             Polynomial Coef.  There are only 11 coef. entered in
%                   because the 12th is set manually to 1.
% Output:
%    F:             Residual from the minimization on the pinhole camera 
%                   model equations. F(1) is camera 1, F(2) is camera 2.

% Writen by M. Brady
% Edited and Commented by S. Raben

%     This file is part of prana, an open-source GUI-driven program for
%     calculating velocity fields using PIV or PTV.
%
%     Copyright (C) 2014  Virginia Polytechnic Institute and State
%     University
% 
%     Copyright 2014.  Los Alamos National Security, LLC. This material was
%     produced under U.S. Government contract DE-AC52-06NA25396 for Los 
%     Alamos National Laboratory (LANL), which is operated by Los Alamos 
%     National Security, LLC for the U.S. Department of Energy. The U.S. 
%     Government has rights to use, reproduce, and distribute this software.
%     NEITHER THE GOVERNMENT NOR LOS ALAMOS NATIONAL SECURITY, LLC MAKES ANY
%     WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY LIABILITY FOR THE USE OF
%     THIS SOFTWARE.  If software is modified to produce derivative works,
%     such modified software should be clearly marked, so as not to confuse
%     it with the version available from LANL.
%
%     prana is free software: you can redistribute it and/or modify
%     it under the terms of the GNU General Public License as published by
%     the Free Software Foundation, either version 3 of the License, or
%     (at your option) any later version.
% 
%     This program is distributed in the hope that it will be useful,
%     but WITHOUT ANY WARRANTY; without even the implied warranty of
%     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%     GNU General Public License for more details.
% 
%     You should have received a copy of the GNU General Public License
%     along with this program.  If not, see <http://www.gnu.org/licenses/>.

%  World target coord. for X,Y, and Z, x1,x2,x3 respectively.
x1=data.allxdata(:,1);
x2=data.allxdata(:,2);
x3=data.allxdata(:,3);

% Pixel target coordinates in X and Y direction, X1,X3 respectively.
X1=data.allXdata(:,1);
X2=data.allXdata(:,2);

% This equation comes from Willert 2006 eqn (2).  
eqns1=(a(1).*x1+a(2).*x2+a(3).*x3+a(4))-X1.*(a(9).*x1+a(10).*x2+a(11).*x3+1);
eqns2=(a(5).*x1+a(6).*x2+a(7).*x3+a(8))-X2.*(a(9).*x1+a(10).*x2+a(11).*x3+1);

% F=[eqns1;eqns2;eqns3]
F=[eqns1;eqns2];