2D Geometry Algorithms — Points, Lines, Angles

Why it matters

2D geometry underlies many practical problems. Understanding shapes geometry code.

The architecture

Points as (x, y). Vector operations: add, subtract, dot, cross.

Orientation: cross product sign.

How it works end to end

Cross product (b-a) × (c-a): positive = CCW, negative = CW, zero = collinear.

Polygon area: shoelace formula = ½|Σ x_i*(y_{i+1} - y_{i-1})|.

Line-line intersection: solve parametric equations.

Point in polygon: ray casting.