Determine the intersection point of two line segments, but considering also colinear segments as intersection

segment-intersection.js

/**
 * Determine the intersection point of two line segments, but considering also
 * colinear segments as intersection
 * @see {@link http://paulbourke.net/geometry/pointlineplane/}
 */
function intersect(
  x1, y1, x2, y2,
  x3, y3, x4, y4
) {

  // Check if none of the lines are of length 0
	if ((x1 === x2 && y1 === y2) || (x3 === x4 && y3 === y4)) {
		return null
	}

	const denominator = ((y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1))
  const numera = ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3))
  const numerb = ((x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3))

  // Lines are parallel
	if (denominator === 0) {
    const isColinear = numera === 0 && numerb === 0;

		return isColinear ? Infinity : null
	}

	const ua = numera / denominator
	const ub = numerb / denominator

  // is the intersection along the segments
	if ((ua >= 0 && ua <= 1) && (ub >= 0 && ub <= 1) ) {
    // Intersection point
    const x = x1 + ua * (x2 - x1)
    const y = y1 + ua * (y2 - y1)
    
    return { x, y }
	}

  return null
}

const segmentIntersection = intersect(0, 0, 1, 1, 0, 1, 1, 0) // { x: 0.5, y: 0.5 }
const parallel = intersect(0, 0, 1, 0, 0, 1, 1, 1) // null
const lineIntersection = intersect(0, 0, 1, 1, 0, 3, 2, 2) // null
const edge = intersect(0, 0, 1, 1, 0, 3, 1, 1) // { x: 1, y: 1 } 
const colinear = intersect(0, 0, 2, 0, 1, 0, 2, 0) // true

console.log({
  segmentIntersection,
  parallel,
  lineIntersection,
  edge,
  colinear
})