Concepts6
Pick's Theorem
Pick's Theorem connects area and lattice-point counts for any simple polygon with integer-coordinate vertices.
Polygon Area and Centroid
The signed area of a simple polygon can be computed in O(n) using the shoelace formula, which sums cross products of consecutive vertices.
Convex Hull
The convex hull is the smallest convex polygon that contains all given points, like a rubber band snapped around nails on a board.
Orientation and CCW
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.
Basic Geometry - Points and Vectors
A 2D point can be treated as a vector from the origin, so vector math (addition, scaling, dot, cross) applies directly to points.
Determinant
The determinant of a square matrix measures how a linear transformation scales volume and whether it flips orientation.