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How can i connect 2 points in the plane by rectilinear lines instead of straight lines??

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Hello People,
my aim is to visualize the rectilinear steiner tree problem, e.g. as it is presented here:
So i have to find the intersection points of the vertical and horizontal lines crossing the respective points in the x/y - plane.
Does anybody have a hint for me of how to get this grid as basic for my lines or how to connect my lines in a rectilinear way??
best greetz, John

Accepted Answer

Image Analyst
Image Analyst on 10 May 2013
Edited: Image Analyst on 10 May 2013
There is a built-in function for that in the Image Processing Toolbox: bwdistgeodesic().
Or, you can try "Pick of the week", John D'Errico's arclength:

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