Points within an Ellipse

Date: 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.