[comp.graphics] Intersecting ellipses

pwebb@yoyodyne.ncsa.uiuc.edu (Peter Webb) (05/17/91)

I am trying to draw the boundary of the union of two ellipses in 2D.  I know 
the following:

	- The major and minor axes of the ellipses are parallel to the 
	  coordinate axes.  

	- The ellipses are symmetric about the Y-Axis - both of the center
	  points lie on that axis.

	- A total of 4 points on the boundary curve.  Two of these points are
	  the ellipse intersection points, the other two are the y-intercepts
 	  of each ellipse. 

	- The eccentricity of each ellipse.  This is expressed as a ratio of
	  the major to the minor axis, rather than the e from the polar
	  coordinate equation.

This amouts to knowing 3 points on each ellipse and the eccentricity.  My
problem is to determine the coordinates of the center point and the length of
the major and minor axes.  I've been told that 3 points are enough to determine
an ellipse, but the method for doing so escapes me.  Any help would be 
appreciated - pointers to articles, actual equations, hints, etc. 

			Peter Webb (pwebb@ncsa.uiuc.edu)