Points within an EllipseDate: 06/03/2003 at 06:32:27 From: Elly Subject: Ellipse My task is to generate points within an ellipse. I did it within a circle but I couldn't determine a condition for a point to be inside an ellipse. Date: 06/03/2003 at 08:15:52 From: Doctor George Subject: Re: Ellipse Hi Elly, Thanks for writing to Doctor Math. There are a couple of ways to determine whether a point is inside an ellipse. If the ellipse is in standard position, a point is inside it if x^2 y^2 --- + --- < 1 a^2 b^2 This is similar to determining whether a point is inside a circle. If the ellipse is not in standard position, or is in 3D space, then it may be easiest to go back to the definition of an ellipse. An ellipse is the locus of points such that the sum of the distances from each point to the two foci equals 2a. Remember that 2a is the length of the major axis. If the sum of the distances is less than 2a, then the point is inside the ellipse. Let's call the foci vectors C1 and C2. A point P is inside the ellipse if |P - C1| + |P - C2| < 2a Does this make sense? Write again if you need more help. - Doctor George, The Math Forum http://mathforum.org/dr.math/ Date: 06/04/2003 at 09:07:48 From: Elly Subject: Thank you (Ellipse) I did it! :) Thank you very much. |
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