In mathematics, two-center bipolar coordinates is a coordinate system based on two coordinates which give distances from two fixed centers and .[1] This system is very useful in some scientific applications (e.g. calculating the electric field of a dipole on a plane).[2][3]
Transformation to Cartesian coordinates
editWhen the centers are at and , the transformation to Cartesian coordinates from two-center bipolar coordinates is
Transformation to polar coordinates
editWhen x > 0, the transformation to polar coordinates from two-center bipolar coordinates is
where is the distance between the poles (coordinate system centers).
Applications
editPolar plotters use two-center bipolar coordinates to describe the drawing paths required to draw a target image.
See also
editReferences
edit