Reply to: Circumference of an ellipse

[Churchill]

I was circumferenced when I was six years old.

Have you still got the bit they chopped off?

[Paddy]

Did you have to calculate their circumference?

I was circumferenced when I was six years old.

[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.

[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

[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.

[wendigo100]

Breshenham's Algorithm indeed...

Was he the one who went mad?

[Causus Deli]

approximate

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

[wobbegong]

This contains formulae and some Java code to plot it

wobb in <not something I've ever had to do (thank God)> mode.

[BrilloPad]

Let me rephrase the question. If a and b are the minor and major radius, can anyone integrate (over theta from 0 to 2*pi) :-

srqt( (a*sin(theta)) ^2 + (b*cos(theta)) ^2 )

[richard-af]

Ellipse: The fleshy mouth parts covering the teeth of an eel.

[richard-af]

What's the diameter of an ellipse?

The sum of the squares on the other two sides?

[wendigo100]

Define an ellipse.

[AlfredJPruffock]

What's the diameter of an ellipse?

The same as the Width Of A Circle ...


In the corner of the morning in the past -
I would sit and blame The Master first and last

All the roads were straight and narrow
And the prayers were small and yellow
And the rumour spread that I was aging fast

Then I ran across a monster who was sleeping by a tree.
And I looked and frowned and the monster was me

So I cried for all the others till the day was nearly through
For I realized that God's a young man too

So I said "So long" and I waved "Bye-bye"
And I smashed my soul and traded my mind

And the moral of this magic spell
Negotiates my hide
When God did take my logic for a ride

[King Cnvt]

What's the diameter of an ellipse?

[richard-af]

Pi x diameter.

I did get a "D" for maths.