CODEWITHSUNDEEP
2dcoordinate-transformation
bob87
bob87

Reputation: 11

From line in cartesian coordinates to polar coordinates with youth style

I have line like in 2D defined by ax+by+c = 0 so (a,b,c). I need to compute a polar representation of this line like Hough approach with rho an theta.

How to do this?

Upvotes: 0

Views: 1215

Answers (1)

dognotdog
dognotdog

Reputation: 701

A line in cartesian coordinates is not as easily represented in polar coordinates.

You can simply substitute x,y with their respective polar equivalents, r*cos(theta), r*sin(theta), giving you

a*r*cos(theta) + b*r*sin(theta) + c = 0

This implicit equation is not as easy to figure out, however. But, if you first convert your implicit line equation to a parametric vector equation of the form (x,y) = R(t) = R0 + t*V, where R0,V are cartesian vectors which you can derive from a,b,c, you can then write

(r*cos(theta), r*sin(theta)) = R0 + t*V

and solve this system of equations for r and theta in terms of t.

However, polar coordinates are not the same as the Hough transform.

In the Hough system, the line is defined by the length rho of a perpendicular line that crosses (0,0) , which is theta = atan(b/a). Figuring out rho seems more difficult at first, but this tutorial explains it.

Upvotes: 2

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