Calculating ellipse overlap areas
Abstract
We present a general algorithm for finding the overlap area between two ellipses. The algorithm is based on finding a segment area (the area between an ellipse and a secant line) given two points on the ellipse. The GaussGreen formula is used to determine the ellipse sector area between two points, and a triangular area is added or subtracted to give the segment area. For two ellipses, overlap area is calculated by adding the areas of appropriate sectors and polygons. Intersection points for two general ellipses are found using Ferrari's quartic formula to solve the polynomial that results from combining the two ellipse equations. All cases for the number of intersection points (0, 1, 2, 3, 4) are handled. The algorithm is implemented in ccode, and has been tested with a range of input ellipses. The code is efficient enough for use in simulations that require many overlap area calculations.
 Publication:

arXiv eprints
 Pub Date:
 June 2011
 DOI:
 10.48550/arXiv.1106.3787
 arXiv:
 arXiv:1106.3787
 Bibcode:
 2011arXiv1106.3787H
 Keywords:

 Physics  Computational Physics;
 Computer Science  Computational Geometry
 EPrint:
 85 pages, 10 figures, code in c