An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set

Step Find a point Pin the plane w%ch is in &he In&$x of Cl-l(s). At worst, this can be done in clfl sQp9 by te dting 3 element subsets of S for collineti@, discarding middle p&n& of collinear rets ar5b bq@rig when the fust noncollinear set (if there i# or&j. &y X, y arrcf z, is found. P can be chosen to I&E the centroid oC the triangle formed by X, y and z. Sfq 2: Express each si E S in polar coordinates th origin P and 8 = 0 in the direction of zu~ arhitnry fixed half-line L from P. This canversion can be done in c2n operations ior some rimed constant