In mathematics, two-center bipolar coordinates is a coordinate system. This system is very useful in some scientific applications (e.g. calculating the electric field of a dipole on a plane).

Transformation to Cartesian coordinates

, the transformation to Cartesian coordinates is

Transformation to polar coordinates

When x > 0, the transformation to polar coordinates from two-center bipolar coordinates is

is the distance between the poles (coordinate system centers).

Applications

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

See also

• Bipolar coordinates

• Biangular coordinates

• Lemniscate of Bernoulli

• Oval of Cassini

• Cartesian oval

• Ellipse

References