0

Is there a way to describe any 2D shape from a set of independent parameters $p_0$, $p_1$, ... such that it is always convex no matter what the parameters are? The parameters can be limited to a fixed range $[{min}_i, {max}_i]$.

For example, you could say: $$x=p_0 \cos(\theta), y=p_1 \sin(\theta)$$ which would always give you a convex shape, but is limited to ellipses.

Or you could say: $$r=p_0 \sin(\theta + p_1) + p_2 \sin(2\theta + p_3) + ...$$

which should allow you to make any convex shape but it would also allow non-convex shapes.

Is there some parameterisation that ticks both boxes - allows all shapes (or at least a wide variety) but doesn't allow non-convex shapes?

Timmmm
  • 244
  • What is meant by independent parameters here? You might look at intersection of half spaces as a representation of convex shapes. – Jürgen Sukumaran Oct 17 '21 at 11:37
  • I mean changing one parameter doesn't affect the valid domain of other parameters. Nice idea about half spaces - I will have a think, thanks. – Timmmm Oct 17 '21 at 14:08

0 Answers0