Expert: Paul Klarreich - 2/9/2007

Question
Hi!
Thanks for your quick reply.
We can make a spiral end by bounding the value of the 'r' in your polar equation. So the parametric eqn of a simple spiral is:
x(t)=a*t*cos(t)
y(t)=a*t*sin(t), t=[0,2*Pi] for 1 full rotation.
Multiples of 2*Pi bound the number of rotations.

By "line width" I mean the width of the generating line. The above eqn assumes a 0-width line, with the pitch growing at 'a*t' every full rotation.

I was wondering if you knew the parametric eqns when the line width is a non-zero constant, say 'b'. And also when the line-width varies from 'b' at t=0, to 'c' at t=t_end?
Also somehow I would like to maintain a constant pitch (spacing between adjacent arms) while doing all this.

A Fermat spiral replaces the 'a*t' with 'a*(plus/minus sqrt(t))'.

Thanks!

Answer
Hi, Raj,

If the width of the spiral is not zero, then you are no longer looking at a spiral, but instead at an area.  The concept of parametric equations doesn't really apply in that case, as far as I can see.

Sorry I can't provide anything better than that.