added missing back_project_1c.m from gigatrack repo

core/pinhole/back_project_1c.m

+function [gl_pos] = back_project_1c(cam, M, ij_pos, b_distort)
+	% Given a camera model and the equation of a plane
+	% back project a set of points in image space to object space
+	%
+	% Input:
+	%	cam			camera model structure
+	%	M				equation of plane. M(1:3).x + M(4) = 0
+	%	ij_pos		points in image space, pixels
+	%	b_distort	flag, if true, correct for radial distortion first
+	
+	%% correct image coords for distortion
+	if nargin < 4
+		b_distort	= true;
+	end
+	if b_distort
+		ic				= cam.ic;
+		kr				= cam.kr;
+		ij_pos		= inverse_radial_distortion(ij_pos, ic, kr);
+	end
+	
+	%% back project to find object space coords
+	% we simultaneously solve
+	% P*[X;Y;Z;1] = lambda * [x;y;1]
+	% M*[X;Y;Z;1] = 0
+	% so we form a matrix T = [P;M]
+	% and solve for x~ / lambda = T^-1 * [x;y;1;0]
+	
+	P					= cam.P;
+	T					= [P; M(:)'];
+	N					= size(ij_pos, 2);
+	ytilde			= [ij_pos; ones(1,N); zeros(1,N)];
+	xtilde			= T \ ytilde;
+	lambda			= xtilde(4,:);
+	gl_pos			= bsxfun(@rdivide, xtilde(1:3,:), lambda);
+end
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