📄 vgg_h_from_p_plane.m
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% vgg_H_from_P_plane Given 3D plane and camera, returns 4-by-3 matrix mapping image points to points on the plane.
%
% H = vgg_H_from_P_plane(A,P), where
% A ... size (4,1), scene plane
% P ... size (3,4), camera matrix
% H ... size (4,3), matrix such that X = x*H, where x (size (3,1)) is an image point
% and X is a scene point lying on the scene plane A.
% In other words, P*H = s*eye(3), where s is a scalar factor.
%
% The overall sign of H is chosen such that s*A*vgg_wedge(P) > 0.
% T. Werner, Oct 2001
function H = vgg_H_from_P_plane(A,P)
A = A';
p1 = P(1,:);
p2 = P(2,:);
p3 = P(3,:);
H = [vgg_contreps(p2'*p3 - p3'*p2)*A ...
vgg_contreps(p3'*p1 - p1'*p3)*A ...
vgg_contreps(p1'*p2 - p2'*p1)*A];
return
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