Explore the circle inversion of six figures. Drag the locators to move and scale the red pre-image. The blue shape is the image after circle inversion in the dashed circle.

Inversion of a point in a circle with center and radius to a point is the nonlinear mapping of the plane (except for the point ) to itself defined by , where , , and are collinear. Inversion swaps the interior and exterior of , preserves angles, and maps generalized circles to generalized circles. (A generalized circle is either an ordinary circle or a straight line.)