{"version":3,"file":"ConvexHull.cjs","sources":["../../src/math/ConvexHull.js"],"sourcesContent":["import { Line3, Plane, Triangle, Vector3 } from 'three'\n\n/**\n * Ported from: https://github.com/maurizzzio/quickhull3d/ by Mauricio Poppe (https://github.com/maurizzzio)\n */\n\nconst Visible = 0\nconst Deleted = 1\n\nconst _v1 = /* @__PURE__ */ new Vector3()\nconst _line3 = /* @__PURE__ */ new Line3()\nconst _plane = /* @__PURE__ */ new Plane()\nconst _closestPoint = /* @__PURE__ */ new Vector3()\nconst _triangle = /* @__PURE__ */ new Triangle()\n\nclass ConvexHull {\n  constructor() {\n    this.tolerance = -1\n\n    this.faces = [] // the generated faces of the convex hull\n    this.newFaces = [] // this array holds the faces that are generated within a single iteration\n\n    // the vertex lists work as follows:\n    //\n    // let 'a' and 'b' be 'Face' instances\n    // let 'v' be points wrapped as instance of 'Vertex'\n    //\n    //     [v, v, ..., v, v, v, ...]\n    //      ^             ^\n    //      |             |\n    //  a.outside     b.outside\n    //\n    this.assigned = new VertexList()\n    this.unassigned = new VertexList()\n\n    this.vertices = [] // vertices of the hull (internal representation of given geometry data)\n  }\n\n  setFromPoints(points) {\n    // The algorithm needs at least four points.\n\n    if (points.length >= 4) {\n      this.makeEmpty()\n\n      for (let i = 0, l = points.length; i < l; i++) {\n        this.vertices.push(new VertexNode(points[i]))\n      }\n\n      this.compute()\n    }\n\n    return this\n  }\n\n  setFromObject(object) {\n    const points = []\n\n    object.updateMatrixWorld(true)\n\n    object.traverse(function (node) {\n      const geometry = node.geometry\n\n      if (geometry !== undefined) {\n        const attribute = geometry.attributes.position\n\n        if (attribute !== undefined) {\n          for (let i = 0, l = attribute.count; i < l; i++) {\n            const point = new Vector3()\n\n            point.fromBufferAttribute(attribute, i).applyMatrix4(node.matrixWorld)\n\n            points.push(point)\n          }\n        }\n      }\n    })\n\n    return this.setFromPoints(points)\n  }\n\n  containsPoint(point) {\n    const faces = this.faces\n\n    for (let i = 0, l = faces.length; i < l; i++) {\n      const face = faces[i]\n\n      // compute signed distance and check on what half space the point lies\n\n      if (face.distanceToPoint(point) > this.tolerance) return false\n    }\n\n    return true\n  }\n\n  intersectRay(ray, target) {\n    // based on \"Fast Ray-Convex Polyhedron Intersection\" by Eric Haines, GRAPHICS GEMS II\n\n    const faces = this.faces\n\n    let tNear = -Infinity\n    let tFar = Infinity\n\n    for (let i = 0, l = faces.length; i < l; i++) {\n      const face = faces[i]\n\n      // interpret faces as planes for the further computation\n\n      const vN = face.distanceToPoint(ray.origin)\n      const vD = face.normal.dot(ray.direction)\n\n      // if the origin is on the positive side of a plane (so the plane can \"see\" the origin) and\n      // the ray is turned away or parallel to the plane, there is no intersection\n\n      if (vN > 0 && vD >= 0) return null\n\n      // compute the distance from the ray’s origin to the intersection with the plane\n\n      const t = vD !== 0 ? -vN / vD : 0\n\n      // only proceed if the distance is positive. a negative distance means the intersection point\n      // lies \"behind\" the origin\n\n      if (t <= 0) continue\n\n      // now categorized plane as front-facing or back-facing\n\n      if (vD > 0) {\n        // plane faces away from the ray, so this plane is a back-face\n\n        tFar = Math.min(t, tFar)\n      } else {\n        // front-face\n\n        tNear = Math.max(t, tNear)\n      }\n\n      if (tNear > tFar) {\n        // if tNear ever is greater than tFar, the ray must miss the convex hull\n\n        return null\n      }\n    }\n\n    // evaluate intersection point\n\n    // always try tNear first since its the closer intersection point\n\n    if (tNear !== -Infinity) {\n      ray.at(tNear, target)\n    } else {\n      ray.at(tFar, target)\n    }\n\n    return target\n  }\n\n  intersectsRay(ray) {\n    return this.intersectRay(ray, _v1) !== null\n  }\n\n  makeEmpty() {\n    this.faces = []\n    this.vertices = []\n\n    return this\n  }\n\n  // Adds a vertex to the 'assigned' list of vertices and assigns it to the given face\n\n  addVertexToFace(vertex, face) {\n    vertex.face = face\n\n    if (face.outside === null) {\n      this.assigned.append(vertex)\n    } else {\n      this.assigned.insertBefore(face.outside, vertex)\n    }\n\n    face.outside = vertex\n\n    return this\n  }\n\n  // Removes a vertex from the 'assigned' list of vertices and from the given face\n\n  removeVertexFromFace(vertex, face) {\n    if (vertex === face.outside) {\n      // fix face.outside link\n\n      if (vertex.next !== null && vertex.next.face === face) {\n        // face has at least 2 outside vertices, move the 'outside' reference\n\n        face.outside = vertex.next\n      } else {\n        // vertex was the only outside vertex that face had\n\n        face.outside = null\n      }\n    }\n\n    this.assigned.remove(vertex)\n\n    return this\n  }\n\n  // Removes all the visible vertices that a given face is able to see which are stored in the 'assigned' vertex list\n\n  removeAllVerticesFromFace(face) {\n    if (face.outside !== null) {\n      // reference to the first and last vertex of this face\n\n      const start = face.outside\n      let end = face.outside\n\n      while (end.next !== null && end.next.face === face) {\n        end = end.next\n      }\n\n      this.assigned.removeSubList(start, end)\n\n      // fix references\n\n      start.prev = end.next = null\n      face.outside = null\n\n      return start\n    }\n  }\n\n  // Removes all the visible vertices that 'face' is able to see\n\n  deleteFaceVertices(face, absorbingFace) {\n    const faceVertices = this.removeAllVerticesFromFace(face)\n\n    if (faceVertices !== undefined) {\n      if (absorbingFace === undefined) {\n        // mark the vertices to be reassigned to some other face\n\n        this.unassigned.appendChain(faceVertices)\n      } else {\n        // if there's an absorbing face try to assign as many vertices as possible to it\n\n        let vertex = faceVertices\n\n        do {\n          // we need to buffer the subsequent vertex at this point because the 'vertex.next' reference\n          // will be changed by upcoming method calls\n\n          const nextVertex = vertex.next\n\n          const distance = absorbingFace.distanceToPoint(vertex.point)\n\n          // check if 'vertex' is able to see 'absorbingFace'\n\n          if (distance > this.tolerance) {\n            this.addVertexToFace(vertex, absorbingFace)\n          } else {\n            this.unassigned.append(vertex)\n          }\n\n          // now assign next vertex\n\n          vertex = nextVertex\n        } while (vertex !== null)\n      }\n    }\n\n    return this\n  }\n\n  // Reassigns as many vertices as possible from the unassigned list to the new faces\n\n  resolveUnassignedPoints(newFaces) {\n    if (this.unassigned.isEmpty() === false) {\n      let vertex = this.unassigned.first()\n\n      do {\n        // buffer 'next' reference, see .deleteFaceVertices()\n\n        const nextVertex = vertex.next\n\n        let maxDistance = this.tolerance\n\n        let maxFace = null\n\n        for (let i = 0; i < newFaces.length; i++) {\n          const face = newFaces[i]\n\n          if (face.mark === Visible) {\n            const distance = face.distanceToPoint(vertex.point)\n\n            if (distance > maxDistance) {\n              maxDistance = distance\n              maxFace = face\n            }\n\n            if (maxDistance > 1000 * this.tolerance) break\n          }\n        }\n\n        // 'maxFace' can be null e.g. if there are identical vertices\n\n        if (maxFace !== null) {\n          this.addVertexToFace(vertex, maxFace)\n        }\n\n        vertex = nextVertex\n      } while (vertex !== null)\n    }\n\n    return this\n  }\n\n  // Computes the extremes of a simplex which will be the initial hull\n\n  computeExtremes() {\n    const min = new Vector3()\n    const max = new Vector3()\n\n    const minVertices = []\n    const maxVertices = []\n\n    // initially assume that the first vertex is the min/max\n\n    for (let i = 0; i < 3; i++) {\n      minVertices[i] = maxVertices[i] = this.vertices[0]\n    }\n\n    min.copy(this.vertices[0].point)\n    max.copy(this.vertices[0].point)\n\n    // compute the min/max vertex on all six directions\n\n    for (let i = 0, l = this.vertices.length; i < l; i++) {\n      const vertex = this.vertices[i]\n      const point = vertex.point\n\n      // update the min coordinates\n\n      for (let j = 0; j < 3; j++) {\n        if (point.getComponent(j) < min.getComponent(j)) {\n          min.setComponent(j, point.getComponent(j))\n          minVertices[j] = vertex\n        }\n      }\n\n      // update the max coordinates\n\n      for (let j = 0; j < 3; j++) {\n        if (point.getComponent(j) > max.getComponent(j)) {\n          max.setComponent(j, point.getComponent(j))\n          maxVertices[j] = vertex\n        }\n      }\n    }\n\n    // use min/max vectors to compute an optimal epsilon\n\n    this.tolerance =\n      3 *\n      Number.EPSILON *\n      (Math.max(Math.abs(min.x), Math.abs(max.x)) +\n        Math.max(Math.abs(min.y), Math.abs(max.y)) +\n        Math.max(Math.abs(min.z), Math.abs(max.z)))\n\n    return { min: minVertices, max: maxVertices }\n  }\n\n  // Computes the initial simplex assigning to its faces all the points\n  // that are candidates to form part of the hull\n\n  computeInitialHull() {\n    const vertices = this.vertices\n    const extremes = this.computeExtremes()\n    const min = extremes.min\n    const max = extremes.max\n\n    // 1. Find the two vertices 'v0' and 'v1' with the greatest 1d separation\n    // (max.x - min.x)\n    // (max.y - min.y)\n    // (max.z - min.z)\n\n    let maxDistance = 0\n    let index = 0\n\n    for (let i = 0; i < 3; i++) {\n      const distance = max[i].point.getComponent(i) - min[i].point.getComponent(i)\n\n      if (distance > maxDistance) {\n        maxDistance = distance\n        index = i\n      }\n    }\n\n    const v0 = min[index]\n    const v1 = max[index]\n    let v2\n    let v3\n\n    // 2. The next vertex 'v2' is the one farthest to the line formed by 'v0' and 'v1'\n\n    maxDistance = 0\n    _line3.set(v0.point, v1.point)\n\n    for (let i = 0, l = this.vertices.length; i < l; i++) {\n      const vertex = vertices[i]\n\n      if (vertex !== v0 && vertex !== v1) {\n        _line3.closestPointToPoint(vertex.point, true, _closestPoint)\n\n        const distance = _closestPoint.distanceToSquared(vertex.point)\n\n        if (distance > maxDistance) {\n          maxDistance = distance\n          v2 = vertex\n        }\n      }\n    }\n\n    // 3. The next vertex 'v3' is the one farthest to the plane 'v0', 'v1', 'v2'\n\n    maxDistance = -1\n    _plane.setFromCoplanarPoints(v0.point, v1.point, v2.point)\n\n    for (let i = 0, l = this.vertices.length; i < l; i++) {\n      const vertex = vertices[i]\n\n      if (vertex !== v0 && vertex !== v1 && vertex !== v2) {\n        const distance = Math.abs(_plane.distanceToPoint(vertex.point))\n\n        if (distance > maxDistance) {\n          maxDistance = distance\n          v3 = vertex\n        }\n      }\n    }\n\n    const faces = []\n\n    if (_plane.distanceToPoint(v3.point) < 0) {\n      // the face is not able to see the point so 'plane.normal' is pointing outside the tetrahedron\n\n      faces.push(Face.create(v0, v1, v2), Face.create(v3, v1, v0), Face.create(v3, v2, v1), Face.create(v3, v0, v2))\n\n      // set the twin edge\n\n      for (let i = 0; i < 3; i++) {\n        const j = (i + 1) % 3\n\n        // join face[ i ] i > 0, with the first face\n\n        faces[i + 1].getEdge(2).setTwin(faces[0].getEdge(j))\n\n        // join face[ i ] with face[ i + 1 ], 1 <= i <= 3\n\n        faces[i + 1].getEdge(1).setTwin(faces[j + 1].getEdge(0))\n      }\n    } else {\n      // the face is able to see the point so 'plane.normal' is pointing inside the tetrahedron\n\n      faces.push(Face.create(v0, v2, v1), Face.create(v3, v0, v1), Face.create(v3, v1, v2), Face.create(v3, v2, v0))\n\n      // set the twin edge\n\n      for (let i = 0; i < 3; i++) {\n        const j = (i + 1) % 3\n\n        // join face[ i ] i > 0, with the first face\n\n        faces[i + 1].getEdge(2).setTwin(faces[0].getEdge((3 - i) % 3))\n\n        // join face[ i ] with face[ i + 1 ]\n\n        faces[i + 1].getEdge(0).setTwin(faces[j + 1].getEdge(1))\n      }\n    }\n\n    // the initial hull is the tetrahedron\n\n    for (let i = 0; i < 4; i++) {\n      this.faces.push(faces[i])\n    }\n\n    // initial assignment of vertices to the faces of the tetrahedron\n\n    for (let i = 0, l = vertices.length; i < l; i++) {\n      const vertex = vertices[i]\n\n      if (vertex !== v0 && vertex !== v1 && vertex !== v2 && vertex !== v3) {\n        maxDistance = this.tolerance\n        let maxFace = null\n\n        for (let j = 0; j < 4; j++) {\n          const distance = this.faces[j].distanceToPoint(vertex.point)\n\n          if (distance > maxDistance) {\n            maxDistance = distance\n            maxFace = this.faces[j]\n          }\n        }\n\n        if (maxFace !== null) {\n          this.addVertexToFace(vertex, maxFace)\n        }\n      }\n    }\n\n    return this\n  }\n\n  // Removes inactive faces\n\n  reindexFaces() {\n    const activeFaces = []\n\n    for (let i = 0; i < this.faces.length; i++) {\n      const face = this.faces[i]\n\n      if (face.mark === Visible) {\n        activeFaces.push(face)\n      }\n    }\n\n    this.faces = activeFaces\n\n    return this\n  }\n\n  // Finds the next vertex to create faces with the current hull\n\n  nextVertexToAdd() {\n    // if the 'assigned' list of vertices is empty, no vertices are left. return with 'undefined'\n\n    if (this.assigned.isEmpty() === false) {\n      let eyeVertex,\n        maxDistance = 0\n\n      // grap the first available face and start with the first visible vertex of that face\n\n      const eyeFace = this.assigned.first().face\n      let vertex = eyeFace.outside\n\n      // now calculate the farthest vertex that face can see\n\n      do {\n        const distance = eyeFace.distanceToPoint(vertex.point)\n\n        if (distance > maxDistance) {\n          maxDistance = distance\n          eyeVertex = vertex\n        }\n\n        vertex = vertex.next\n      } while (vertex !== null && vertex.face === eyeFace)\n\n      return eyeVertex\n    }\n  }\n\n  // Computes a chain of half edges in CCW order called the 'horizon'.\n  // For an edge to be part of the horizon it must join a face that can see\n  // 'eyePoint' and a face that cannot see 'eyePoint'.\n\n  computeHorizon(eyePoint, crossEdge, face, horizon) {\n    // moves face's vertices to the 'unassigned' vertex list\n\n    this.deleteFaceVertices(face)\n\n    face.mark = Deleted\n\n    let edge\n\n    if (crossEdge === null) {\n      edge = crossEdge = face.getEdge(0)\n    } else {\n      // start from the next edge since 'crossEdge' was already analyzed\n      // (actually 'crossEdge.twin' was the edge who called this method recursively)\n\n      edge = crossEdge.next\n    }\n\n    do {\n      const twinEdge = edge.twin\n      const oppositeFace = twinEdge.face\n\n      if (oppositeFace.mark === Visible) {\n        if (oppositeFace.distanceToPoint(eyePoint) > this.tolerance) {\n          // the opposite face can see the vertex, so proceed with next edge\n\n          this.computeHorizon(eyePoint, twinEdge, oppositeFace, horizon)\n        } else {\n          // the opposite face can't see the vertex, so this edge is part of the horizon\n\n          horizon.push(edge)\n        }\n      }\n\n      edge = edge.next\n    } while (edge !== crossEdge)\n\n    return this\n  }\n\n  // Creates a face with the vertices 'eyeVertex.point', 'horizonEdge.tail' and 'horizonEdge.head' in CCW order\n\n  addAdjoiningFace(eyeVertex, horizonEdge) {\n    // all the half edges are created in ccw order thus the face is always pointing outside the hull\n\n    const face = Face.create(eyeVertex, horizonEdge.tail(), horizonEdge.head())\n\n    this.faces.push(face)\n\n    // join face.getEdge( - 1 ) with the horizon's opposite edge face.getEdge( - 1 ) = face.getEdge( 2 )\n\n    face.getEdge(-1).setTwin(horizonEdge.twin)\n\n    return face.getEdge(0) // the half edge whose vertex is the eyeVertex\n  }\n\n  //  Adds 'horizon.length' faces to the hull, each face will be linked with the\n  //  horizon opposite face and the face on the left/right\n\n  addNewFaces(eyeVertex, horizon) {\n    this.newFaces = []\n\n    let firstSideEdge = null\n    let previousSideEdge = null\n\n    for (let i = 0; i < horizon.length; i++) {\n      const horizonEdge = horizon[i]\n\n      // returns the right side edge\n\n      const sideEdge = this.addAdjoiningFace(eyeVertex, horizonEdge)\n\n      if (firstSideEdge === null) {\n        firstSideEdge = sideEdge\n      } else {\n        // joins face.getEdge( 1 ) with previousFace.getEdge( 0 )\n\n        sideEdge.next.setTwin(previousSideEdge)\n      }\n\n      this.newFaces.push(sideEdge.face)\n      previousSideEdge = sideEdge\n    }\n\n    // perform final join of new faces\n\n    firstSideEdge.next.setTwin(previousSideEdge)\n\n    return this\n  }\n\n  // Adds a vertex to the hull\n\n  addVertexToHull(eyeVertex) {\n    const horizon = []\n\n    this.unassigned.clear()\n\n    // remove 'eyeVertex' from 'eyeVertex.face' so that it can't be added to the 'unassigned' vertex list\n\n    this.removeVertexFromFace(eyeVertex, eyeVertex.face)\n\n    this.computeHorizon(eyeVertex.point, null, eyeVertex.face, horizon)\n\n    this.addNewFaces(eyeVertex, horizon)\n\n    // reassign 'unassigned' vertices to the new faces\n\n    this.resolveUnassignedPoints(this.newFaces)\n\n    return this\n  }\n\n  cleanup() {\n    this.assigned.clear()\n    this.unassigned.clear()\n    this.newFaces = []\n\n    return this\n  }\n\n  compute() {\n    let vertex\n\n    this.computeInitialHull()\n\n    // add all available vertices gradually to the hull\n\n    while ((vertex = this.nextVertexToAdd()) !== undefined) {\n      this.addVertexToHull(vertex)\n    }\n\n    this.reindexFaces()\n\n    this.cleanup()\n\n    return this\n  }\n}\n\n//\n\nconst Face = /* @__PURE__ */ (() => {\n  class Face {\n    constructor() {\n      this.normal = new Vector3()\n      this.midpoint = new Vector3()\n      this.area = 0\n\n      this.constant = 0 // signed distance from face to the origin\n      this.outside = null // reference to a vertex in a vertex list this face can see\n      this.mark = Visible\n      this.edge = null\n    }\n\n    static create(a, b, c) {\n      const face = new Face()\n\n      const e0 = new HalfEdge(a, face)\n      const e1 = new HalfEdge(b, face)\n      const e2 = new HalfEdge(c, face)\n\n      // join edges\n\n      e0.next = e2.prev = e1\n      e1.next = e0.prev = e2\n      e2.next = e1.prev = e0\n\n      // main half edge reference\n\n      face.edge = e0\n\n      return face.compute()\n    }\n\n    getEdge(i) {\n      let edge = this.edge\n\n      while (i > 0) {\n        edge = edge.next\n        i--\n      }\n\n      while (i < 0) {\n        edge = edge.prev\n        i++\n      }\n\n      return edge\n    }\n\n    compute() {\n      const a = this.edge.tail()\n      const b = this.edge.head()\n      const c = this.edge.next.head()\n\n      _triangle.set(a.point, b.point, c.point)\n\n      _triangle.getNormal(this.normal)\n      _triangle.getMidpoint(this.midpoint)\n      this.area = _triangle.getArea()\n\n      this.constant = this.normal.dot(this.midpoint)\n\n      return this\n    }\n\n    distanceToPoint(point) {\n      return this.normal.dot(point) - this.constant\n    }\n  }\n\n  return Face\n})()\n\n// Entity for a Doubly-Connected Edge List (DCEL).\n\nclass HalfEdge {\n  constructor(vertex, face) {\n    this.vertex = vertex\n    this.prev = null\n    this.next = null\n    this.twin = null\n    this.face = face\n  }\n\n  head() {\n    return this.vertex\n  }\n\n  tail() {\n    return this.prev ? this.prev.vertex : null\n  }\n\n  length() {\n    const head = this.head()\n    const tail = this.tail()\n\n    if (tail !== null) {\n      return tail.point.distanceTo(head.point)\n    }\n\n    return -1\n  }\n\n  lengthSquared() {\n    const head = this.head()\n    const tail = this.tail()\n\n    if (tail !== null) {\n      return tail.point.distanceToSquared(head.point)\n    }\n\n    return -1\n  }\n\n  setTwin(edge) {\n    this.twin = edge\n    edge.twin = this\n\n    return this\n  }\n}\n\n// A vertex as a double linked list node.\n\nclass VertexNode {\n  constructor(point) {\n    this.point = point\n    this.prev = null\n    this.next = null\n    this.face = null // the face that is able to see this vertex\n  }\n}\n\n// A double linked list that contains vertex nodes.\n\nclass VertexList {\n  constructor() {\n    this.head = null\n    this.tail = null\n  }\n\n  first() {\n    return this.head\n  }\n\n  last() {\n    return this.tail\n  }\n\n  clear() {\n    this.head = this.tail = null\n\n    return this\n  }\n\n  // Inserts a vertex before the target vertex\n\n  insertBefore(target, vertex) {\n    vertex.prev = target.prev\n    vertex.next = target\n\n    if (vertex.prev === null) {\n      this.head = vertex\n    } else {\n      vertex.prev.next = vertex\n    }\n\n    target.prev = vertex\n\n    return this\n  }\n\n  // Inserts a vertex after the target vertex\n\n  insertAfter(target, vertex) {\n    vertex.prev = target\n    vertex.next = target.next\n\n    if (vertex.next === null) {\n      this.tail = vertex\n    } else {\n      vertex.next.prev = vertex\n    }\n\n    target.next = vertex\n\n    return this\n  }\n\n  // Appends a vertex to the end of the linked list\n\n  append(vertex) {\n    if (this.head === null) {\n      this.head = vertex\n    } else {\n      this.tail.next = vertex\n    }\n\n    vertex.prev = this.tail\n    vertex.next = null // the tail has no subsequent vertex\n\n    this.tail = vertex\n\n    return this\n  }\n\n  // Appends a chain of vertices where 'vertex' is the head.\n\n  appendChain(vertex) {\n    if (this.head === null) {\n      this.head = vertex\n    } else {\n      this.tail.next = vertex\n    }\n\n    vertex.prev = this.tail\n\n    // ensure that the 'tail' reference points to the last vertex of the chain\n\n    while (vertex.next !== null) {\n      vertex = vertex.next\n    }\n\n    this.tail = vertex\n\n    return this\n  }\n\n  // Removes a vertex from the linked list\n\n  remove(vertex) {\n    if (vertex.prev === null) {\n      this.head = vertex.next\n    } else {\n      vertex.prev.next = vertex.next\n    }\n\n    if (vertex.next === null) {\n      this.tail = vertex.prev\n    } else {\n      vertex.next.prev = vertex.prev\n    }\n\n    return this\n  }\n\n  // Removes a list of vertices whose 'head' is 'a' and whose 'tail' is b\n\n  removeSubList(a, b) {\n    if (a.prev === null) {\n      this.head = b.next\n    } else {\n      a.prev.next = b.next\n    }\n\n    if (b.next === null) {\n      this.tail = a.prev\n    } else {\n      b.next.prev = a.prev\n    }\n\n    return this\n  }\n\n  isEmpty() {\n    return this.head === null\n  }\n}\n\nexport { ConvexHull, Face, HalfEdge, VertexNode, VertexList 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