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Say I have the lines shown in the image below, represented in polar coordinate format (rho and theta). These lines are the output of OpenCV's HoughLines function after some post processing. (Sorry I'm not allowed to embed images yet.)

enter image description here

What I want to do is, given any one line, find all of the lines that are perpendicular to that line, as shown in the second image below.

enter image description here

I understand how to do this with Cartesian lines, but I'm having trouble wrapping my mind around what properties of rho and theta the two lines would have to have to be perpendicular, although I understand how polar lines work at least fundamentally. Sorry if this is elementary stuff, but I'm having trouble finding any explanation of this online anywhere. Do I need to first convert the lines to Cartesian coordinates, or is there some simpler way to do this? Any help would be much appreciated, thanks!

Bart Kiers
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Michael Walker
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1 Answers1

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To get perpendicular lines in polar coordinates, you simply take the theta for the first line, and find all lines whose theta = +/- 90° of the first theta.

You have to normalize the angles to be within 0°-360° or some other range, when comparing them.

So if line 1 has a theta line1.Theta
Then the angle to another line is a = (line2.Theta - line1.Theta)
and you want all lines where a is close to -90°, 90°, 270°, -270°, ...
depending on how you normalize your angles

HugoRune
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