Get the minimum distance between a point and a line. Get the nearest point on a line to a second point.

point-to-line.ts

/**
 * Get the minimum distance from a point P to a line with a segment AB.
 * @param A The start of the line.
 * @param B The end of the line.
 * @param P A point.
 * @returns 
 */
export function distanceToLine(A: number[], B: number[], P: number[]) {
  const delta = sub(B, A)
  const angle = Math.atan2(delta[1], delta[0])
  const dir = rot(sub(P, A), -angle)
  return dir[1]
}

/**
 * Get the nearest point on a line segment AB.
 * @param A The start of the line.
 * @param B The end of the line.
 * @param P A point.
 * @param clamp Whether to clamp the resulting point to the segment.
 * @returns
 */
export function nearestPointOnLine(
  A: number[],
  B: number[],
  P: number[],
  clamp = true
) {  
  const delta = sub(B, A)
  const angle = Math.atan2(delta[1], delta[0])
  const length = len(delta)
  const dir = rot(sub(P, A), -angle)

  if (clamp) {
    if (dir[0] < 0) return A
    if (dir[0] > length) return B
  }

  return add(A, div(mul(delta, dir[0]), length))
}

// Vector utilities

export function add(A: number[], B: number[]) {
  return [A[0] + B[0], A[1] + B[1]]
}

export function sub(A: number[], B: number[]) {
  return [A[0] - B[0], A[1] - B[1]]
}

export function div(A: number[], n: number) {
  return [A[0] / n, A[1] / n]
}

export function mul(A: number[], n: number) {
  return [A[0] * n, A[1] * n]
}

export function dpr(A: number[], B: number[]) {
  return A[0] * B[0] + A[1] * B[1]
}

export function cpr(A: number[], B: number[]) {
  return A[0] * B[1] - B[0] * A[1]
}

export function len(A: number[]) {
  return Math.hypot(A[0], A[1])
}

export function rot(A: number[], r: number) {
  return [
    A[0] * Math.cos(r) - A[1] * Math.sin(r),
    A[1] * Math.cos(r) + A[0] * Math.sin(r),
  ]
}

// Thanks to https://observablehq.com/@tomktjemsland/distance-from-point-to-line