fix(modeling): added fromNoisyPoints() to plane

packages/modeling/src/maths/plane/fromNoisyPoints.d.ts

@@ -0,0 +1,6 @@
+import Plane from './type'
+import Vec3 from '../vec3/type'
+
+export default fromNoisyPoints
+
+declare function fromNoisyPoints(out: Plane, ...vertices: Array<Vec3>): Plane

packages/modeling/src/maths/plane/fromNoisyPoints.js

@@ -0,0 +1,106 @@
+const vec3 = require('../vec3')
+const fromNormalAndPoint = require('./fromNormalAndPoint')
+
+/**
+ * Create a best-fit plane from the given noisy vertices.
+ *
+ * NOTE: There are two possible orientations for every plane.
+ *       This function always produces positive orientations.
+ *
+ * See http://www.ilikebigbits.com for the original discussion
+ *
+ * @param {Plane} out - receiving plane
+ * @param {Array} vertices - list of vertices in any order or position
+ * @returns {Plane} out
+ * @alias module:modeling/maths/plane.fromNoisyPoints
+ */
+const fromNoisyPoints = (out, ...vertices) => {
+  out[0] = 0.0
+  out[1] = 0.0
+  out[2] = 0.0
+  out[3] = 0.0
+
+  // calculate the centroid of the vertices
+  // NOTE: out is the centriod
+  const n = vertices.length
+  vertices.forEach((v) => {
+    vec3.add(out, out, v)
+  })
+  vec3.scale(out, out, 1.0 / n)
+
+  // Calculate full 3x3 covariance matrix, excluding symmetries
+  let xx = 0.0
+  let xy = 0.0
+  let xz = 0.0
+  let yy = 0.0
+  let yz = 0.0
+  let zz = 0.0
+
+  const vn = vec3.create()
+  vertices.forEach((v) => {
+    // NOTE: out is the centriod
+    vec3.subtract(vn, v, out)
+    xx += vn[0] * vn[0]
+    xy += vn[0] * vn[1]
+    xz += vn[0] * vn[2]
+    yy += vn[1] * vn[1]
+    yz += vn[1] * vn[2]
+    zz += vn[2] * vn[2]
+  })
+
+  xx /= n
+  xy /= n
+  xz /= n
+  yy /= n
+  yz /= n
+  zz /= n
+
+  // Calculate the smallest Eigenvector of the covariance matrix
+  // which becomes the plane normal
+
+  vn[0] = 0.0
+  vn[1] = 0.0
+  vn[2] = 0.0
+
+  // weighted directional vector
+  const wdv = vec3.create()
+
+  // X axis
+  let det = yy * zz - yz * yz
+  wdv[0] = det
+  wdv[1] = xz * yz - xy * zz
+  wdv[2] = xy * yz - xz * yy
+
+  let weight = det * det
+  vec3.add(vn, vn, vec3.scale(wdv, wdv, weight))
+
+  // Y axis
+  det = xx * zz - xz * xz
+  wdv[0] = xz * yz - xy * zz
+  wdv[1] = det
+  wdv[2] = xy * xz - yz * xx
+
+  weight = det * det
+  if (vec3.dot(vn, wdv) < 0.0) {
+    weight = -weight
+  }
+  vec3.add(vn, vn, vec3.scale(wdv, wdv, weight))
+
+  // Z axis
+  det = xx * yy - xy * xy
+  wdv[0] = xy * yz - xz * yy
+  wdv[1] = xy * xz - yz * xx
+  wdv[2] = det
+
+  weight = det * det
+  if (vec3.dot(vn, wdv) < 0.0) {
+    weight = -weight
+  }
+  vec3.add(vn, vn, vec3.scale(wdv, wdv, weight))
+
+  // create the plane from normal and centriod
+  // NOTE: out is the centriod
+  return fromNormalAndPoint(out, vn, out)
+}
+
+module.exports = fromNoisyPoints

packages/modeling/src/maths/plane/fromNoisyPoints.test.js

@@ -0,0 +1,24 @@
+const test = require('ava')
+const { fromNoisyPoints, create } = require('./index')
+
+const { compareVectors } = require('../../../test/helpers/index')
+
+test('plane: fromNoisyPoints() should return a new plane with correct values', (t) => {
+  const obs1 = fromNoisyPoints(create(), [0, 0, 0], [1, 0, 0], [1, 1, 0])
+  t.true(compareVectors(obs1, [0, 0, 1, 0]))
+
+  const obs2 = fromNoisyPoints(obs1, [0, 6, 0], [0, 2, 2], [0, 6, 6])
+  t.true(compareVectors(obs2, [1, 0, 0, 0]))
+
+  // same vertices results in an invalid plane
+  const obs3 = fromNoisyPoints(obs1, [0, 6, 0], [0, 6, 0], [0, 6, 0])
+  t.true(compareVectors(obs3, [0 / 0, 0 / 0, 0 / 0, 0 / 0]))
+
+  // co-linear vertices
+  const obs4 = fromNoisyPoints(obs1, [0, 0, 0], [1, 0, 0], [2, 0, 0], [0, 1, 0])
+  t.true(compareVectors(obs4, [0, 0, 1, 0]))
+
+  // random vertices
+  const obs5 = fromNoisyPoints(obs1, [0, 0, 0], [5, 1, -2], [3, -2, 4], [1, 1, 0])
+  t.true(compareVectors(obs5, [0.08054818365229491, 0.8764542170444571, 0.47469990050062555, 0.4185833634679763]))
+})

packages/modeling/src/maths/plane/index.d.ts

@@ -5,6 +5,7 @@ export { default as equals } from './equals'
 export { default as flip } from './flip'
 export { default as fromNormalAndPoint } from './fromNormalAndPoint'
 export { default as fromValues } from './fromValues'
+export { default as fromNoisyPoints } from './fromNoisyPoints'
 export { default as fromPoints } from './fromPoints'
 export { default as fromPointsRandom } from './fromPointsRandom'
 export { default as signedDistanceToPoint } from './signedDistanceToPoint'

packages/modeling/src/maths/plane/index.js

@@ -32,6 +32,7 @@ module.exports = {
    * @function fromValues
    */
   fromValues: require('../vec4/fromValues'),
+  fromNoisyPoints: require('./fromNoisyPoints'),
   fromPoints: require('./fromPoints'),
   fromPointsRandom: require('./fromPointsRandom'),
   projectionOfPoint: require('./projectionOfPoint'),