Implementation

In terms of implementation, we address two main issues:

1. Implementation using floating point arithmetic? What are likely sources of error or inconsistent arithmetic?
2. Implementation using integer point aritmetic? Suppose the input is given as integer coordinates, we would like to avoid any floating point arithmetic. In particular, the computation of angles (for sorting) involves computing the or function. Its input is a double precision number, so it involves converting from int to double. This could be inaccurate if the machine allocates more bits to the int type than it does to the mantissa of the double type. Furthermore, the function only computes an approximation to the irrational number. Instead of using , we can use the slopes. For that we need to make sure, that the lines are in appropriate quadrants. More details are given in Section 1.5.2 of O'Rourke's book.

Implementation of Left: Given 3 points, The point is left of , if

is collinear with , if D = 0.

Optimal Convex Hull Algorithm: The most optimal algorithm for convex hulls is due to Seidel & Kirkpatrick (1981). Its complexity is , where H is the number of extreme points in the input. It is output sensitive.