Circumference of an ellipse

[Causus Deli]

approximate

Circumference = 2 * pi * sqrt((a^2+b^2)/2)

[wendigo100]

Breshenham's Algorithm indeed...

Was he the one who went mad?

[wendigo100]

dunno.

But he drew circles using only integers which is probably enough to make you mad...

Oh I see. Big, boxy ones I suppose. Picasso geometry.

[OwlHoot]

Does anyone have a formula for the circumference of an ellipse please?

Thanks

Unlike the area, which is PI.a.b (where a and b are the semiaxes major and minor), the circumference can't in general be expressed finitely in terms of elementary functions and constants. But it can be in terms of elliptic functions, e.g. 4.a.F(e) in which e is the eccentricity (= SQRT(1 - (b/a)^2) and F is the Complete Elliptic Integral of the Second Kind

As usual, Wikipedia has a good writeup

Also David Cantrell posted some references to good approximations here

[Churchill]

dunno.

But he drew circles using only integers which is probably enough to make you mad...

His line drawing algorithm was a beaut!

All because of his work on Plotters and pixel based displays.

A clever chap indeed.

Circles is easy. They're symetrical in all axes so you only have to calculate 1/8 of one anyway.

Now, rotating Ellipses are very pretty.

[Paddy]

Did you have to calculate their circumference?

I was circumferenced when I was six years old.

[Churchill]

I was circumferenced when I was six years old.

Have you still got the bit they chopped off?