Two-center bipolar coordinates


In mathematics, two-center bipolar coordinates is a coordinate system based on two coordinates which give distances from two fixed centers and. This system is very useful in some scientific applications.

Transformation to Cartesian coordinates

When the centers are at and, the transformation to Cartesian coordinates from two-center bipolar coordinates is

Transformation to polar coordinates

When x > 0, the transformation to polar coordinates from two-center bipolar coordinates is
where is the distance between the poles.

Applications

Polar plotters use two-center bipolar coordinates to describe the drawing paths required to draw a target image.