A robust quickhull implementation to find the convex hull of a set of 3d points in O(n log n) ported from John Lloyd implementation
Additional implementation material:
- Dirk Gregorius presentation: https://archive.org/details/GDC2014Gregorius
- Convex Hull Generation with Quick Hull by Randy Gaul (lost link)
This library was incorporated into ThreeJS!. Thanks to https://github.com/Mugen87 for his work to move the primitives to ThreeJS primitives, the quickhull3d library will always be library agnostic and will operate with raw arrays.
- Key functions are well documented (including ascii graphics)
- Faster than other JavaScript implementations of convex hull
Click on the image to see a demo!
<script type="module">
import qh from 'https://cdn.jsdelivr.net/npm/quickhull3d@<version>/+esm'
const points = [
[0, 1, 0],
[1, -1, 1],
[-1, -1, 1],
[0, -1, -1]
]
const faces = qh(points)
console.log(faces)
// output:
// [ [ 2, 1, 0 ], [ 3, 1, 2 ], [ 3, 0, 1 ], [ 3, 2, 0 ] ]
// 1st face:
// points[2] = [-1, -1, 1]
// points[1] = [1, -1, 1]
// points[0] = [0, 1, 0]
// normal = (points[1] - points[2]) x (points[0] - points[2])
</script>$ npm install --save quickhull3dimport qh from 'quickhull3d'params
points{Array<Array>} an array of 3d points whose convex hull needs to be computedoptions{Object} (optional)options.skipTriangulation{Boolean} True to skip the triangulation of the faces (returning n-vertex faces)
returns An array of 3 element arrays, each subarray has the indices of 3 points which form a face whose normal points outside the polyhedra
params
point{Array} The point that we want to check that it's a convex hull.points{Array<Array>} The array of 3d points whose convex hull was computedfaces{Array<Array>} An array of 3 element arrays, each subarray has the indices of 3 points which form a face whose normal points outside the polyhedra
returns true if the point point is inside the convex hull
example
import qh, { isPointInsideHull } from 'quickhull3d'
const points = [
[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1],
[1, 1, 0], [1, 0, 1], [0, 1, 1], [1, 1, 1]
]
const faces = qh(points)
expect(isPointInsideHull([0.5, 0.5, 0.5], points, faces)).toBe(true)
expect(isPointInsideHull([0, 0, -0.1], points, faces)).toBe(false)import QuickHull from 'quickhull3d/dist/QuickHull'params
points{Array} an array of 3d points whose convex hull needs to be computed
Computes the quickhull of all the points stored in the instance
time complexity O(n log n)
params
skipTriangulation{Boolean} (default: false) True to skip the triangulation and return n-vertices faces
returns
An array of 3-element arrays (or n-element arrays if skipTriangulation = true)
which are the faces of the convex hull
import qh from 'quickhull3d'
const points = [
[0, 1, 0],
[1, -1, 1],
[-1, -1, 1],
[0, -1, -1]
]
qh(points)
// output:
// [ [ 2, 0, 3 ], [ 0, 1, 3 ], [ 2, 1, 0 ], [ 2, 3, 1 ] ]
// 1st face:
// points[2] = [-1, -1, 1]
// points[0] = [0, 1, 0]
// points[3] = [0, -1, -1]
// normal = (points[0] - points[2]) x (points[3] - points[2])Using the constructor:
import { QuickHull } from 'quickhull3d'
const points = [
[0, 1, 0],
[1, -1, 1],
[-1, -1, 1],
[0, -1, -1]
];
const instance = new QuickHull(points)
instance.build()
instance.collectFaces() // returns an array of 3-element arraysSpecs:
MacBook Pro (Retina, Mid 2012)
2.3 GHz Intel Core i7
8 GB 1600 MHz DDR3
NVIDIA GeForce GT 650M 1024 MB
Versus convex-hull
// LEGEND: program:numberOfPoints
quickhull3d:100 x 6,212 ops/sec 1.24% (92 runs sampled)
convexhull:100 x 2,507 ops/sec 1.20% (89 runs sampled)
quickhull3d:1000 x 1,171 ops/sec 0.93% (97 runs sampled)
convexhull:1000 x 361 ops/sec 1.38% (88 runs sampled)
quickhull3d:10000 x 190 ops/sec 1.33% (87 runs sampled)
convexhull:10000 x 32.04 ops/sec 2.37% (56 runs sampled)
quickhull3d:100000 x 11.90 ops/sec 6.34% (34 runs sampled)
convexhull:100000 x 2.81 ops/sec 2.17% (11 runs sampled)
quickhull3d:200000 x 5.11 ops/sec 10.05% (18 runs sampled)
convexhull:200000 x 1.23 ops/sec 3.33% (8 runs sampled)
Mauricio Poppe. Licensed under the MIT license.
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