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I used the equations found on Paul Bourke's "Circles and spheres" page to calculate the intersection points of two circles:

Image of intersecting circles from Paul Bourke's page

$P_3$ is what I'm trying to get, except now I want to do the same with two ellipses.

Calculating $h$ is the tricky bit. With regular circles, it can be done with the Pythagorean Theorem $a^2 + b^2 = c^2$, since we already know $r_0$ (the radius): $$h = \sqrt{a^2 + r_0^2}.$$

With ellipses it seems much trickier. I don't know how to calculate $h$. There is not a single radius anymore: there are $\operatorname{radiusX}$ and $\operatorname{radiusY}$.

Given $\operatorname{radiusX}$, $\operatorname{radiusY}$, and the center points $(x,y)$ of each ellipse, how do I find the two intersecting points? (Note: the ellipses are guaranteed to have two intersecting points in my specific application.)

  • 3
    Should this not be a question for the Mathematics forum instead?2012-01-27
  • 2
    I don't understand - are the ellipses alligned, sharing a major axis?2012-01-27
  • 0
    Are the ellipse rotated? Have you considered the following equation of the ellipse sqr((cx-x)/radiusX) + sqr((cy-y)/radiusY) = 1.0 ? starting with this equation should help you find the solution right?2012-01-27
  • 1
    Have you seen these solutions? http://www.analyzemath.com/EllipseProblems/ellipse_intersection.html http://mathforum.org/library/drmath/view/66877.html http://www.math.niu.edu/~rusin/known-math/99/2ellipses2012-01-27

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