Convex hull
An interactive animation of an alogithm to find the convex hull of a group of points. You can try it out here: https://mrtimuk.github.io/convhull/
The algorithm has two steps:
1. Create a hull containing the points
A simple polygon containing all the points. The simplest way to do this is to join all the points in radial order.
2. Remove points which make the hull concave
Imagine travelling along the edge of the hull clockwise. If the hull is convex then at each vertex one must make a right-turn to continue clockwise. A left-turn indicates that the vertex is causing the polygon to be convex, so that vertex should be removed.
We need a function that shows whether a turn is to the right or left. The cross product serves this purpose as it can be defined as:
a × b = |a| . |b| . sin θ
Since |a| and |b| are non-negative, the sign of a × b is determined by the sign of sin θ, the internal angle of the polygon. sin θ is positive for 0° < θ < 180° and negative for 180° < θ < 360°, the latter being a reflex angle indicating concavity.