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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

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

$\displaystyle \frac{x^2}{a^2}+ \frac{y^2}{b^2}= \frac{1}{4}$

Solving for x, $\displaystyle \frac{x^2}{a^2}= \frac{1}{4}- \frac{y^2}{b^2}= \frac{b^2- 4y^2}{4b^2}$

$\displaystyle x= \pm a\frac{\sqrt{b^2- 4y^2}}{2b}$

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!).