Computer Science
# Computational Geometry

The following text file contains a set, $P$, of one thousand 2d Cartesian points.

Your task is to compute the convex hulls of $P$. Let $V$ be the set of vertices of the convex hulls of the point $P$. How many elements does $V$ contain?

Suppose we are given three coordinate points $a=(x_0,y_0)$, $b=(x_1,y_1)$ and $c=(x_2,y_2)$. Your task is to devise a routine that tests whether point $c$ lies to the right of the directed line which goes from point $a$ to point $b$. If so, the angle formed by sweeping from $a$ to $c$ in a counterclokwise manner around $b$ is acute.

Each line of the following text file contains the three points arranged like the following:

`[x0,y0,x1,y1,x2,y2]`

How many of the triples satisfy the test described above?