You are given an array/list/vector of pairs of integers representing cartesian coordinates \$(x, y)\$ of points on a 2D Euclidean plane; all coordinates are between \$−10^4\$ and \$10^4\$, duplicates are allowed. Find the area of the convex hull of those points, rounded to the nearest integer; an exact midpoint should be rounded to the closest even integer. You may use floating-point numbers in intermediate computations, but only if you can guarantee that the final result will be always correct. This is code-golfcode-golf, so the shortest correct program wins.
The convex hull of a set of points \$P\$ is the smallest convex set that contains \$P\$. On the Euclidean plane, for any single point \$(x,y)\$, it is the point itself; for two distinct points, it is the line containing them, for three non-collinear points, it is the triangle that they form, and so forth.
A very briefgood visual explanation of what a convex hulls is, is best described byas imagining all the points as nails in a wooden undergroundboard, and puttingthen stretching a rubber band around itthem to enclose all the points:
Some test cases:
Input: [[50, -13]]
Result: 0
Input: [[-25, -26], [34, -27]]
Result: 0
Input: [[-6, -14], [-48, -45], [21, 25]]
Result: 400
Input: [[4, 30], [5, 37], [-18, 49], [-9, -2]]
Result: 562
Input: [[0, 16], [24, 18], [-43, 36], [39, -29], [3, -38]]
Result: 2978
Input: [[19, -19], [15, 5], [-16, -41], [6, -25], [-42, 1], [12, 19]]
Result: 2118
Input: [[-23, 13], [-13, 13], [-6, -7], [22, 41], [-26, 50], [12, -12], [-23, -7]]
Result: 2307
Input: [[31, -19], [-41, -41], [25, 34], [29, -1], [42, -42], [-34, 32], [19, 33], [40, 39]]
Result: 6037
Input: [[47, 1], [-22, 24], [36, 38], [-17, 4], [41, -3], [-13, 15], [-36, -40], [-13, 35], [-25, 22]]
Result: 3908
Input: [[29, -19], [18, 9], [30, -46], [15, 20], [24, -4], [5, 19], [-44, 4], [-20, -8], [-16, 34], [17, -36]]
Result: 2905
