# Calculate point on ellipse

• Jun 25th 2012, 09:35 AM
bigus
Calculate point on ellipse
Hi

If I have an ellipse like this (not very good) illustration below. I know the length of the major & minor axis's, I know the distance between A and B, A and C, etc. The angle of the red lines will always be 90 degrees.

Could someone tell me the formula for calculating points on the ellipse for the red lines?

Attachment 24158

Ultimately, I want to programmatically draw segments of the ellipse like in the second image. I figure I can do this using bezier curves once I know how to work out points on an ellipse.

Thanks
Bigus
• Jun 25th 2012, 10:18 AM
HallsofIvy
Re: Calculate point on ellipse
An ellipse with axis a in the x- direction and axis b in the y-direction can be written as
$\frac{x^2}{a^2}+ \frac{y^2}{b^2}= \frac{1}{4}$

Solving for x, $\frac{x^2}{a^2}= \frac{1}{4}- \frac{y^2}{b^2}= \frac{b^2- 4y^2}{4b^2}$
$x= \pm a\frac{\sqrt{b^2- 4y^2}}{2b}$
• Jun 26th 2012, 09:19 AM
bigus
Re: Calculate point on ellipse
Thank you for the reply. I think I've managed to interpret that into a suitable equation for the code (work in progress!).