Parametric representation of a Spiral

1. Sep 22, 2010

DorumonSg

Propose a parametric representation of a spiral.
Hint: Use the parametric representation of a circle.

This is the parametric representation of a circle we are given :

x = r * Cos(Theta)
y = r * Sin (Theta)

0 <= Theta <= 2 Pi

Nope, we are not given anything background on spirals.

I am like super new at this graphics thingy. I've been searching around the net for 4 hours now, I did find a few answers but none taught me how to get the representation from a circle and I have no idea how they derive at the answer.

x and y are like coordinates.

And that t or Theta in this case is kinda like a path or timeline where decides when coordinates of x and y starts and ends.

I am thinking of making the radius a parameter and then slowly increasing it?

x = u * Cos(Theta)
y = u * Sin (Theta)

1 <= u <= 4

Something like that?

Thats all I know, so help please?

Last edited: Sep 22, 2010
2. Sep 22, 2010

lanedance

that would work as a 2D spiral, but you would want it all in terms of one parameter, so try starting with theta(u) = u

3. Sep 22, 2010

HallsofIvy

If u is fixed, that is a circle of radius u, not a spiral. If u is a variable, then you have two parameters and that is a surface, not a spiral.

To get a spiral in two dimensions, you need to make the radius variable but not introduce a new variable so something like x= theta*cos(theta), y= theta* sin(theta).

If the problem is, as lanedance suggests, a three dimensional spiral, a "helix", then you need to introduce a "z" component that increases, again not introducing a new parameter.

Something like x= Cos(Theta), y= Sin(Theta), z= Theta.