I saw the following sentence from Feature Extraction & Image Processing, 2nd Edition

$$ x = a_0 + a_x\cos(\theta)+b_x\sin(\theta) $$ $$ y = b_0 + a_y\cos(\theta)+b_y\sin(\theta) $$

This equation corresponds to the polar representation of an ellipse.

I don't know this meaning. If you need extra information, I'll add it.


1 Answer 1


It's a little mis-leading and confusing.

The usual way to describe an ellipse is using cartesian ($x,y$) coordinates. Another way to represent an ellipse is using polar coordinates ($r,\theta$) (where $r$ is the distance (radius) from the origin, and $\theta$ is the angle.

What the equation is saying is that the cartesian coordinates of the ellipse are parameterized by $\theta$ in the two equations. That is, as you change $\theta$ from 0 to $2\pi$, the values for $x$ and $y$ will lie on the ellipse, for constants ($a_0,b_0,a_x,b_x,a_y,b_y$).


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