Types

Point

A point is a pair of coordinates in the plane.

type Point = { x: number; y: number }

Line

A line is the implicit equation ax + by + c = 0.

type Line = { a: number; b: number; c: number }

The three coefficients cover all line orientations without special-casing verticals. A few common forms:

Equation	a	b	c
y = x	1	−1	0
y = 2x + 1	2	−1	1
x = 3	1	0	−3
y = 4	0	1	−4

The direction vector of the line is (−b, a) and the normal is (a, b).

Partial declarations

A line's coefficients can be partly known while solving — a direction known from parallel but no position yet, say. The missing coefficients are null and filled in as constraints are applied or canonical defaults are chosen.