Polar Coordinates Basics

In this tutorial we'll look at basic effects you can produce with the Polar Coordinates effect set to Rectangular to polar.

Horizontal Lines to Circles

First, let's look at an example image made up of a series of horizontal lines:

Now choose Effects > Distortion Effects > Polar Coordinates and select Rectangular to polar:

After you click OK, the result looks like this:

This illustrates several things about Rectangular to Polar:

The rectangular plane is converted to polar coordinates. In part, what this does is wrap the rectangular image around in a circle so that its sides meet. In the case of our example here, where we started out with horizontal lines, this produces a series of concentric circles.
The bottom of the original image becomes the outermost part of the circular result. In the example here, the blue line at the bottom of the original becomes the outer blue circle in the result.
The top of the original image becomes the center of the resulting image. In the example here, the blue line at the top of the original becomes the blue circle in the middle of the result.

Vertical Lines to Wedges

Now let's look at what we get if we start with vertical lines:

After using Rectangular to Polar on this image, you get this:

Here each of the lines is converted to a wedge. Note that the lines at the sides of the original meet at the top of the resulting image.

Circular Text

A variation on using horizontal lines to produce circles is to start with a horizontal string of text:

Applying Polar Coordinates (with Rectangular to Polar selected) produces this result:

Remember that the closer to the bottom the original line is, the farther from the center the results appear. So if you wanted your circular text to appear farther from the center, you'd start with something like this:

In this case, applying Polar Coordinates (with Rectangular to Polar selected) produces this result:

Filled Circles

Something else you can do with Polar Coordinates is create a filled circle from something like this:

After applying Polar Coordinates with Rectangular to Polar selected, you get results like this:

The top of the original pattern is pulled into the middle of the circle. The horizontal parts of the pattern become centric circles, while the vertical parts of the pattern become wedges. The white line at the bottom of the original becomes the white background surrounding the circle.

I hope you have fun experimenting with Polar Coordinates. To help get yourself started, grab the image below and use it with Polar Coordinates with Rectangular to Polar selected.