Concepts5

Pick's Theorem connects area and lattice-point counts for any simple polygon with integer-coordinate vertices.

The signed area of a simple polygon can be computed in O(n) using the shoelace formula, which sums cross products of consecutive vertices.

The convex hull is the smallest convex polygon that contains all given points, like a rubber band snapped around nails on a board.

Orientation (CCW test) tells whether three points make a left turn, right turn, or are collinear by using the sign of a 2D cross product.

A 2D point can be treated as a vector from the origin, so vector math (addition, scaling, dot, cross) applies directly to points.