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Let $P_1, P_2, P_3, P_4$ be four 2-dimensional points (in $\mathbb{R}^2$, that is), with coordinates $x_i,y_i$. Is there a formula for the area of their convex-hull?

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  • $\begingroup$ I think first you have to find the ordering of vertices on the convex hull boundary, and then you can apply the shoelace formula. $\endgroup$ – Rahul Sep 7 '16 at 14:21
  • $\begingroup$ @Rahul How can I compute the ordering? $\endgroup$ – becko Sep 7 '16 at 14:33
  • $\begingroup$ There are lots of convex hull algorithms, the simplest ones being gift wrapping and Graham scan. $\endgroup$ – Rahul Sep 7 '16 at 15:12

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