I'm trying to build some jewellery in a 3D cad package. I found this:
The function that draws a figure eight
But I don't understand the equation (I only got to A' level :)
Is there a way of calculating cartesian [x, y] positions from this?
Any help much appreciated.
The curve is defined by this function.
$$t\in(-\tfrac12\pi,\tfrac32\pi)\mapsto(\cos t,\sin t\cos t)\in\mathbb R^2.$$
More specifically, the curve is the image of this function.
I assume you want some way to get a finite list of consecutive points on the curve so you can draw an approximation of it in your program. To do that, you can set the value of $t$ to $-\pi/2$. Then, compute $(\cos t, \sin t\cos t)$. This is your first point on the curve. Next, increment $t$ by some small positive amount. How small should depend on how accurate of an approximation you want. Then compute $(\cos t, \sin t\cos t)$ again with the new value of $t$. This is the second point. Repeat this process all the way until $t=3\pi/2$, and you will have finitely many points on the curve neatly in a list so you can draw a line between consecutive points and it will resemble the curve.