TheAlgorithms/JavaScript · error · Error

Minimum of 3 points is required to form closed polygon!

Error message

Minimum of 3 points is required to form closed polygon!

What it means

Thrown by convexHull(points) (plain Error) when points.length <= 2. A convex hull requires at least three distinct points to bound a non-degenerate polygon; with 0, 1, or 2 points the algorithm cannot form a hull, so it refuses rather than returning an arbitrary segment.

Source

Thrown at Geometry/ConvexHullGraham.js:31

  return 1
}
function orientation(a, b, c) {
  // Check orientation of Line(a, b) and Line(b, c)
  const alpha = (b.y - a.y) / (b.x - a.x)
  const beta = (c.y - b.y) / (c.x - b.x)

  // Clockwise
  if (alpha > beta) return 1
  // Anticlockwise
  else if (beta > alpha) return -1
  // Colinear
  return 0
}

function convexHull(points) {
  const pointsLen = points.length
  if (pointsLen <= 2) {
    throw new Error('Minimum of 3 points is required to form closed polygon!')
  }

  points.sort(compare)
  const p1 = points[0]
  const p2 = points[pointsLen - 1]

  // Divide Hull in two halves
  const upperPoints = []
  const lowerPoints = []

  upperPoints.push(p1)
  lowerPoints.push(p1)

  for (let i = 1; i < pointsLen; i++) {
    if (i === pointsLen - 1 || orientation(p1, points[i], p2) !== -1) {
      let upLen = upperPoints.length

      while (

View on GitHub (pinned to 5c39e87a9a)

Solutions

1. Check points.length >= 3 before calling convexHull.
2. For small sets, return the points themselves as the 'hull' rather than invoking the algorithm.
3. Deduplicate points before counting, since duplicates can drop the effective count below 3.
4. Validate at the API boundary and surface a domain-specific 'not enough points' error.

Example fix

// before
const hull = convexHull(points) // throws when points.length <= 2

// after
if (points.length < 3) return points.slice()
const hull = convexHull(points)

function safeConvexHull(points) {
  if (!Array.isArray(points) || points.length < 3) return points.slice()
  return convexHull(points)
}

const canFormHull = (points) => Array.isArray(points) && points.length >= 3

try {
  return convexHull(points)
} catch (e) {
  if (e instanceof Error && /3 points/i.test(e.message)) return points.slice()
  throw e
}

When it happens

Trigger: convexHull([]); convexHull([{x:0,y:0}]); convexHull([p1, p2]).

Common situations: Spatial datasets filtered down to a handful of points; empty result from a failed query; degenerate clusters where nearly all points were deduplicated.

Related errors

• Cannot normalize vectors of length 0
• Triplet cannot exist with the given array
• Invalid Triangle sides.
• The ${paramName} only accepts non-negative values
• The ${noName} should be Number type

AI-assisted analysis of TheAlgorithms/JavaScript@5c39e87a9a (2026-08-13). Data as JSON: /api/errors/0abc3a9e561b4273. Report an issue: GitHub.