| Walt Mankowski on Wed, 8 May 2002 02:30:15 +0200 |
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On Tue, May 07, 2002 at 07:09:26PM -0400, Darxus@chaosreigns.com wrote: > http://www.chaosreigns.com/code/springgraph/diagram.jpg > > The axes of the ellipse are paralel to the coordinate axes. > > I know the x,y coordinates of the center of the ellipse. > > I know the height and width of the ellipse. > > I know angle A (it can be anything) > > I am trying to find either the length of line B (radius of the ellipse > at the given angle), or the x,y coordinates of the intersection of line > B with the edge of the ellipse (from this I can easily calculate the length). > > Ian suggested finding the coordinates of the two foci, using the line > between them as a base of a triangle, and the intersection of line B > with the edge of the ellipse as the opposite point of the triangle. Since you have the angle and are trying to find the radius, it's a lot easier if you use the polar coordinates version of the equation of an ellipse. You can find it derived at http://mathworld.wolfram.com/Ellipse.html (and undoubtedly lots of other places). Simplifying a bit what's written there, the equation you want is r = sqrt( (b^2 * a^2) / ( (b^2 * cos(theta)) + (a^2 * sin(theta)) ) ) where... b is the height of the ellipse above its center (x,y) a is the width of the ellipse from its center (x,y) theta is the angle you call A in your diagram r is the distance from the center of the ellipse to the edge Note that a and b are measured from the *center*, and not from top-to-bottom or left-to-right. Have fun! Walt Attachment:
pgpGPiio3Vtg9.pgp
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