📄 vgg_line3d_pv_from_xy.m
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% L = vgg_line3d_pv_from_XY(X,Y) Pluecker vector 3d line from two 3d points.
%
% Syntax: L = vgg_line3d_pv_from_XY(X,Y) or
% L = vgg_line3d_pv_from_XY(XY)
%
% X, Y ... size (4,N), 3D points
% XY ... size (4,2*N), XY stacked as XY = [X1 Y1 ... XN YN].
% L ... size (N,6), Pluecker vector(s) of 3D line(s).
%
% It is vectorized for N>1.
%
% See vgg_line3d_*
% T.Werner
function L = vgg_line3d_pv_from_XY(X,Y)
if nargin == 1
Y = X(:,2:2:end);
X = X(:,1:2:end);
end
if size(X,2) == 1
L = [(X(1:3)*Y(4)-Y(1:3)*X(4))' vgg_wedge([X(1:3) Y(1:3)])];
else % vectorized version
L = [(X(1:3,:).*([1;1;1]*Y(4,:))-Y(1:3,:).*([1;1;1]*X(4,:)))' vgg_wedge(X(1:3,:),Y(1:3,:))];
end
return
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