Calculating ellipse overlap areas View Full Text


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Article Info

DATE

2012-10

AUTHORS

Gary B. Hughes, Mohcine Chraibi

ABSTRACT

We present an approach for finding the overlap area between two ellipses that does not rely on proxy curves. The Gauss-Green formula is used to determine a segment area between two points on an ellipse. Overlap between two ellipses is calculated by combining the areas of appropriate segments and polygons in each ellipse. For four of the ten possible orientations of two ellipses, the method requires numerical determination of transverse intersection points. Approximate intersection points can be determined by solving the two implicit ellipse equations simultaneously. Alternative approaches for finding transverse intersection points are available using tools from algebraic geometry, e.g., based on solving an Eigen-problem that is related to companion matrices of the two implicit ellipse curves. Implementations in C of several algorithm options are analyzed for accuracy, precision and robustness with a range of input ellipses. More... »

PAGES

291-301

References to SciGraph publications

  • 2005. Resultant-Based Methods for Plane Curves Intersection Problems in COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING
  • 2005-01-01. Symbolic-numeric methods for solving polynomial equations and applications in SOLVING POLYNOMIAL EQUATIONS
  • 1994-10. Asymptotic approximation of convex curves in ARCHIV DER MATHEMATIK
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00791-013-0214-3

    DOI

    http://dx.doi.org/10.1007/s00791-013-0214-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1021311985


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