@edsilv/ami.js/examples/vr_crop/quickhull.js

<p align="center"> <img src="https://user-images.githubusercontent.com/214063/46479857-4cd66e80-c7f0-11e8-9585-5748409c9490.png" width="60%"> </p>

/**
 * @author Mugen87 / https://github.com/Mugen87
 *
 * Ported from: https://github.com/maurizzzio/quickhull3d/ by Mauricio Poppe (https://github.com/maurizzzio)
 *
 */

(function() {
  var Visible = 0;
  var Deleted = 1;

  function QuickHull() {
    this.tolerance = -1;

    this.faces = []; // the generated faces of the convex hull
    this.newFaces = []; // this array holds the faces that are generated within a single iteration

    // the vertex lists work as follows:
    //
    // let 'a' and 'b' be 'Face' instances
    // let 'v' be points wrapped as instance of 'Vertex'
    //
    //     [v, v, ..., v, v, v, ...]
    //      ^             ^
    //      |             |
    //  a.outside     b.outside
    //
    this.assigned = new VertexList();
    this.unassigned = new VertexList();

    this.vertices = []; // vertices of the hull (internal representation of given geometry data)
  }

  Object.assign(QuickHull.prototype, {
    setFromPoints: function(points) {
      if (Array.isArray(points) !== true) {
        console.error('THREE.QuickHull: Points parameter is not an array.');
      }

      if (points.length < 4) {
        console.error('THREE.QuickHull: The algorithm needs at least four points.');
      }

      this.makeEmpty();

      for (var i = 0, l = points.length; i < l; i++) {
        this.vertices.push(new VertexNode(points[i]));
      }

      this.compute();

      return this;
    },

    setFromObject: function(object) {
      var points = [];

      object.updateMatrixWorld(true);

      object.traverse(function(node) {
        var i, l, point;

        var geometry = node.geometry;

        if (geometry !== undefined) {
          if (geometry.isGeometry) {
            var vertices = geometry.vertices;

            for (i = 0, l = vertices.length; i < l; i++) {
              point = vertices[i].clone();
              point.applyMatrix4(node.matrixWorld);

              points.push(point);
            }
          } else if (geometry.isBufferGeometry) {
            var attribute = geometry.attributes.position;

            if (attribute !== undefined) {
              for (i = 0, l = attribute.count; i < l; i++) {
                point = new THREE.Vector3();

                point.fromBufferAttribute(attribute, i).applyMatrix4(node.matrixWorld);

                points.push(point);
              }
            }
          }
        }
      });

      return this.setFromPoints(points);
    },

    makeEmpty: function() {
      this.faces = [];
      this.vertices = [];

      return this;
    },

    // Adds a vertex to the 'assigned' list of vertices and assigns it to the given face

    addVertexToFace: function(vertex, face) {
      vertex.face = face;

      if (face.outside === null) {
        this.assigned.append(vertex);
      } else {
        this.assigned.insertBefore(face.outside, vertex);
      }

      face.outside = vertex;

      return this;
    },

    // Removes a vertex from the 'assigned' list of vertices and from the given face

    removeVertexFromFace: function(vertex, face) {
      if (vertex === face.outside) {
        // fix face.outside link

        if (vertex.next !== null && vertex.next.face === face) {
          // face has at least 2 outside vertices, move the 'outside' reference

          face.outside = vertex.next;
        } else {
          // vertex was the only outside vertex that face had

          face.outside = null;
        }
      }

      this.assigned.remove(vertex);

      return this;
    },

    // Removes all the visible vertices that a given face is able to see which are stored in the 'assigned' vertext list

    removeAllVerticesFromFace: function(face) {
      if (face.outside !== null) {
        // reference to the first and last vertex of this face

        var start = face.outside;
        var end = face.outside;

        while (end.next !== null && end.next.face === face) {
          end = end.next;
        }

        this.assigned.removeSubList(start, end);

        // fix references

        start.prev = end.next = null;
        face.outside = null;

        return start;
      }
    },

    // Removes all the visible vertices that 'face' is able to see

    deleteFaceVertices: function(face, absorbingFace) {
      var faceVertices = this.removeAllVerticesFromFace(face);

      if (faceVertices !== undefined) {
        if (absorbingFace === undefined) {
          // mark the vertices to be reassigned to some other face

          this.unassigned.appendChain(faceVertices);
        } else {
          // if there's an absorbing face try to assign as many vertices as possible to it

          var vertex = faceVertices;

          do {
            // we need to buffer the subsequent vertex at this point because the 'vertex.next' reference
            // will be changed by upcoming method calls

            var nextVertex = vertex.next;

            var distance = absorbingFace.distanceToPoint(vertex.point);

            // check if 'vertex' is able to see 'absorbingFace'

            if (distance > this.tolerance) {
              this.addVertexToFace(vertex, absorbingFace);
            } else {
              this.unassigned.append(vertex);
            }

            // now assign next vertex

            vertex = nextVertex;
          } while (vertex !== null);
        }
      }

      return this;
    },

    // Reassigns as many vertices as possible from the unassigned list to the new faces

    resolveUnassignedPoints: function(newFaces) {
      if (this.unassigned.isEmpty() === false) {
        var vertex = this.unassigned.first();

        do {
          // buffer 'next' reference, see .deleteFaceVertices()

          var nextVertex = vertex.next;

          var maxDistance = this.tolerance;

          var maxFace = null;

          for (var i = 0; i < newFaces.length; i++) {
            var face = newFaces[i];

            if (face.mark === Visible) {
              var distance = face.distanceToPoint(vertex.point);

              if (distance > maxDistance) {
                maxDistance = distance;
                maxFace = face;
              }

              if (maxDistance > 1000 * this.tolerance) break;
            }
          }

          // 'maxFace' can be null e.g. if there are identical vertices

          if (maxFace !== null) {
            this.addVertexToFace(vertex, maxFace);
          }

          vertex = nextVertex;
        } while (vertex !== null);
      }

      return this;
    },

    // Computes the extremes of a simplex which will be the initial hull

    computeExtremes: function() {
      var min = new THREE.Vector3();
      var max = new THREE.Vector3();

      var minVertices = [];
      var maxVertices = [];

      var i, l, j;

      // initially assume that the first vertex is the min/max

      for (i = 0; i < 3; i++) {
        minVertices[i] = maxVertices[i] = this.vertices[0];
      }

      min.copy(this.vertices[0].point);
      max.copy(this.vertices[0].point);

      // compute the min/max vertex on all six directions

      for (i = 0, l = this.vertices.length; i < l; i++) {
        var vertex = this.vertices[i];
        var point = vertex.point;

        // update the min coordinates

        for (j = 0; j < 3; j++) {
          if (point.getComponent(j) < min.getComponent(j)) {
            min.setComponent(j, point.getComponent(j));
            minVertices[j] = vertex;
          }
        }

        // update the max coordinates

        for (j = 0; j < 3; j++) {
          if (point.getComponent(j) > max.getComponent(j)) {
            max.setComponent(j, point.getComponent(j));
            maxVertices[j] = vertex;
          }
        }
      }

      // use min/max vectors to compute an optimal epsilon

      this.tolerance =
        3 *
        Number.EPSILON *
        (Math.max(Math.abs(min.x), Math.abs(max.x)) +
          Math.max(Math.abs(min.y), Math.abs(max.y)) +
          Math.max(Math.abs(min.z), Math.abs(max.z)));

      return { min: minVertices, max: maxVertices };
    },

    // Computes the initial simplex assigning to its faces all the points
    // that are candidates to form part of the hull

    computeInitialHull: (function() {
      var line3, plane, closestPoint;

      return function computeInitialHull() {
        if (line3 === undefined) {
          line3 = new THREE.Line3();
          plane = new THREE.Plane();
          closestPoint = new THREE.Vector3();
        }

        var vertex,
          vertices = this.vertices;
        var extremes = this.computeExtremes();
        var min = extremes.min;
        var max = extremes.max;

        var v0, v1, v2, v3;
        var i, l, j;

        // 1. Find the two vertices 'v0' and 'v1' with the greatest 1d separation
        // (max.x - min.x)
        // (max.y - min.y)
        // (max.z - min.z)

        var distance,
          maxDistance = 0;
        var index = 0;

        for (i = 0; i < 3; i++) {
          distance = max[i].point.getComponent(i) - min[i].point.getComponent(i);

          if (distance > maxDistance) {
            maxDistance = distance;
            index = i;
          }
        }

        v0 = min[index];
        v1 = max[index];

        // 2. The next vertex 'v2' is the one farthest to the line formed by 'v0' and 'v1'

        maxDistance = 0;
        line3.set(v0.point, v1.point);

        for (i = 0, l = this.vertices.length; i < l; i++) {
          vertex = vertices[i];

          if (vertex !== v0 && vertex !== v1) {
            line3.closestPointToPoint(vertex.point, true, closestPoint);

            distance = closestPoint.distanceToSquared(vertex.point);

            if (distance > maxDistance) {
              maxDistance = distance;
              v2 = vertex;
            }
          }
        }

        // 3. The next vertex 'v3' is the one farthest to the plane 'v0', 'v1', 'v2'

        maxDistance = -1;
        plane.setFromCoplanarPoints(v0.point, v1.point, v2.point);

        for (i = 0, l = this.vertices.length; i < l; i++) {
          vertex = vertices[i];

          if (vertex !== v0 && vertex !== v1 && vertex !== v2) {
            distance = Math.abs(plane.distanceToPoint(vertex.point));

            if (distance > maxDistance) {
              maxDistance = distance;
              v3 = vertex;
            }
          }
        }

        var faces = [];

        if (plane.distanceToPoint(v3.point) < 0) {
          // the face is not able to see the point so 'plane.normal' is pointing outside the tetrahedron

          faces.push(
            Face.create(v0, v1, v2),
            Face.create(v3, v1, v0),
            Face.create(v3, v2, v1),
            Face.create(v3, v0, v2)
          );

          // set the twin edge

          for (i = 0; i < 3; i++) {
            j = (i + 1) % 3;

            // join face[ i ] i > 0, with the first face

            faces[i + 1].getEdge(2).setTwin(faces[0].getEdge(j));

            // join face[ i ] with face[ i + 1 ], 1 <= i <= 3

            faces[i + 1].getEdge(1).setTwin(faces[j + 1].getEdge(0));
          }
        } else {
          // the face is able to see the point so 'plane.normal' is pointing inside the tetrahedron

          faces.push(
            Face.create(v0, v2, v1),
            Face.create(v3, v0, v1),
            Face.create(v3, v1, v2),
            Face.create(v3, v2, v0)
          );

          // set the twin edge

          for (i = 0; i < 3; i++) {
            j = (i + 1) % 3;

            // join face[ i ] i > 0, with the first face

            faces[i + 1].getEdge(2).setTwin(faces[0].getEdge((3 - i) % 3));

            // join face[ i ] with face[ i + 1 ]

            faces[i + 1].getEdge(0).setTwin(faces[j + 1].getEdge(1));
          }
        }

        // the initial hull is the tetrahedron

        for (i = 0; i < 4; i++) {
          this.faces.push(faces[i]);
        }

        // initial assignment of vertices to the faces of the tetrahedron

        for (i = 0, l = vertices.length; i < l; i++) {
          vertex = vertices[i];

          if (vertex !== v0 && vertex !== v1 && vertex !== v2 && vertex !== v3) {
            maxDistance = this.tolerance;
            var maxFace = null;

            for (j = 0; j < 4; j++) {
              distance = this.faces[j].distanceToPoint(vertex.point);

              if (distance > maxDistance) {
                maxDistance = distance;
                maxFace = this.faces[j];
              }
            }

            if (maxFace !== null) {
              this.addVertexToFace(vertex, maxFace);
            }
          }
        }

        return this;
      };
    })(),

    // Removes inactive faces

    reindexFaces: function() {
      var activeFaces = [];

      for (var i = 0; i < this.faces.length; i++) {
        var face = this.faces[i];

        if (face.mark === Visible) {
          activeFaces.push(face);
        }
      }

      this.faces = activeFaces;

      return this;
    },

    // Finds the next vertex to create faces with the current hull

    nextVertexToAdd: function() {
      // if the 'assigned' list of vertices is empty, no vertices are left. return with 'undefined'

      if (this.assigned.isEmpty() === false) {
        var eyeVertex,
          maxDistance = 0;

        // grap the first available face and start with the first visible vertex of that face

        var eyeFace = this.assigned.first().face;
        var vertex = eyeFace.outside;

        // now calculate the farthest vertex that face can see

        do {
          var distance = eyeFace.distanceToPoint(vertex.point);

          if (distance > maxDistance) {
            maxDistance = distance;
            eyeVertex = vertex;
          }

          vertex = vertex.next;
        } while (vertex !== null && vertex.face === eyeFace);

        return eyeVertex;
      }
    },

    // Computes a chain of half edges in CCW order called the 'horizon'.
    // For an edge to be part of the horizon it must join a face that can see
    // 'eyePoint' and a face that cannot see 'eyePoint'.

    computeHorizon: function(eyePoint, crossEdge, face, horizon) {
      // moves face's vertices to the 'unassigned' vertex list

      this.deleteFaceVertices(face);

      face.mark = Deleted;

      var edge;

      if (crossEdge === null) {
        edge = crossEdge = face.getEdge(0);
      } else {
        // start from the next edge since 'crossEdge' was already analyzed
        // (actually 'crossEdge.twin' was the edge who called this method recursively)

        edge = crossEdge.next;
      }

      do {
        var twinEdge = edge.twin;
        var oppositeFace = twinEdge.face;

        if (oppositeFace.mark === Visible) {
          if (oppositeFace.distanceToPoint(eyePoint) > this.tolerance) {
            // the opposite face can see the vertex, so proceed with next edge

            this.computeHorizon(eyePoint, twinEdge, oppositeFace, horizon);
          } else {
            // the opposite face can't see the vertex, so this edge is part of the horizon

            horizon.push(edge);
          }
        }

        edge = edge.next;
      } while (edge !== crossEdge);

      return this;
    },

    // Creates a face with the vertices 'eyeVertex.point', 'horizonEdge.tail' and 'horizonEdge.head' in CCW order

    addAdjoiningFace: function(eyeVertex, horizonEdge) {
      // all the half edges are created in ccw order thus the face is always pointing outside the hull

      var face = Face.create(eyeVertex, horizonEdge.tail(), horizonEdge.head());

      this.faces.push(face);

      // join face.getEdge( - 1 ) with the horizon's opposite edge face.getEdge( - 1 ) = face.getEdge( 2 )

      face.getEdge(-1).setTwin(horizonEdge.twin);

      return face.getEdge(0); // the half edge whose vertex is the eyeVertex
    },

    //  Adds 'horizon.length' faces to the hull, each face will be linked with the
    //  horizon opposite face and the face on the left/right

    addNewFaces: function(eyeVertex, horizon) {
      this.newFaces = [];

      var firstSideEdge = null;
      var previousSideEdge = null;

      for (var i = 0; i < horizon.length; i++) {
        var horizonEdge = horizon[i];

        // returns the right side edge

        var sideEdge = this.addAdjoiningFace(eyeVertex, horizonEdge);

        if (firstSideEdge === null) {
          firstSideEdge = sideEdge;
        } else {
          // joins face.getEdge( 1 ) with previousFace.getEdge( 0 )

          sideEdge.next.setTwin(previousSideEdge);
        }

        this.newFaces.push(sideEdge.face);
        previousSideEdge = sideEdge;
      }

      // perform final join of new faces

      firstSideEdge.next.setTwin(previousSideEdge);

      return this;
    },

    // Adds a vertex to the hull

    addVertexToHull: function(eyeVertex) {
      var horizon = [];

      this.unassigned.clear();

      // remove 'eyeVertex' from 'eyeVertex.face' so that it can't be added to the 'unassigned' vertex list

      this.removeVertexFromFace(eyeVertex, eyeVertex.face);

      this.computeHorizon(eyeVertex.point, null, eyeVertex.face, horizon);

      this.addNewFaces(eyeVertex, horizon);

      // reassign 'unassigned' vertices to the new faces

      this.resolveUnassignedPoints(this.newFaces);

      return this;
    },

    cleanup: function() {
      this.assigned.clear();
      this.unassigned.clear();
      this.newFaces = [];

      return this;
    },

    compute: function() {
      var vertex;

      this.computeInitialHull();

      // add all available vertices gradually to the hull

      while ((vertex = this.nextVertexToAdd()) !== undefined) {
        this.addVertexToHull(vertex);
      }

      this.reindexFaces();

      this.cleanup();

      return this;
    },
  });

  //

  function Face() {
    this.normal = new THREE.Vector3();
    this.midpoint = new THREE.Vector3();
    this.area = 0;

    this.constant = 0; // signed distance from face to the origin
    this.outside = null; // reference to a vertex in a vertex list this face can see
    this.mark = Visible;
    this.edge = null;
  }

  Object.assign(Face, {
    create: function(a, b, c) {
      var face = new Face();

      var e0 = new HalfEdge(a, face);
      var e1 = new HalfEdge(b, face);
      var e2 = new HalfEdge(c, face);

      // join edges

      e0.next = e2.prev = e1;
      e1.next = e0.prev = e2;
      e2.next = e1.prev = e0;

      // main half edge reference

      face.edge = e0;

      return face.compute();
    },
  });

  Object.assign(Face.prototype, {
    getEdge: function(i) {
      var edge = this.edge;

      while (i > 0) {
        edge = edge.next;
        i--;
      }

      while (i < 0) {
        edge = edge.prev;
        i++;
      }

      return edge;
    },

    compute: (function() {
      var triangle;

      return function compute() {
        if (triangle === undefined) triangle = new THREE.Triangle();

        var a = this.edge.tail();
        var b = this.edge.head();
        var c = this.edge.next.head();

        triangle.set(a.point, b.point, c.point);

        triangle.normal(this.normal);
        triangle.midpoint(this.midpoint);
        this.area = triangle.area();

        this.constant = this.normal.dot(this.midpoint);

        return this;
      };
    })(),

    distanceToPoint: function(point) {
      return this.normal.dot(point) - this.constant;
    },
  });

  // Entity for a Doubly-Connected Edge List (DCEL).

  function HalfEdge(vertex, face) {
    this.vertex = vertex;
    this.prev = null;
    this.next = null;
    this.twin = null;
    this.face = face;
  }

  Object.assign(HalfEdge.prototype, {
    head: function() {
      return this.vertex;
    },

    tail: function() {
      return this.prev ? this.prev.vertex : null;
    },

    length: function() {
      var head = this.head();
      var tail = this.tail();

      if (tail !== null) {
        return tail.point.distanceTo(head.point);
      }

      return -1;
    },

    lengthSquared: function() {
      var head = this.head();
      var tail = this.tail();

      if (tail !== null) {
        return tail.point.distanceToSquared(head.point);
      }

      return -1;
    },

    setTwin: function(edge) {
      this.twin = edge;
      edge.twin = this;

      return this;
    },
  });

  // A vertex as a double linked list node.

  function VertexNode(point) {
    this.point = point;
    this.prev = null;
    this.next = null;
    this.face = null; // the face that is able to see this vertex
  }

  // A double linked list that contains vertex nodes.

  function VertexList() {
    this.head = null;
    this.tail = null;
  }

  Object.assign(VertexList.prototype, {
    first: function() {
      return this.head;
    },

    last: function() {
      return this.tail;
    },

    clear: function() {
      this.head = this.tail = null;

      return this;
    },

    // Inserts a vertex before the target vertex

    insertBefore: function(target, vertex) {
      vertex.prev = target.prev;
      vertex.next = target;

      if (vertex.prev === null) {
        this.head = vertex;
      } else {
        vertex.prev.next = vertex;
      }

      target.prev = vertex;

      return this;
    },

    // Inserts a vertex after the target vertex

    insertAfter: function(target, vertex) {
      vertex.prev = target;
      vertex.next = target.next;

      if (vertex.next === null) {
        this.tail = vertex;
      } else {
        vertex.next.prev = vertex;
      }

      target.next = vertex;

      return this;
    },

    // Appends a vertex to the end of the linked list

    append: function(vertex) {
      if (this.head === null) {
        this.head = vertex;
      } else {
        this.tail.next = vertex;
      }

      vertex.prev = this.tail;
      vertex.next = null; // the tail has no subsequent vertex

      this.tail = vertex;

      return this;
    },

    // Appends a chain of vertices where 'vertex' is the head.

    appendChain: function(vertex) {
      if (this.head === null) {
        this.head = vertex;
      } else {
        this.tail.next = vertex;
      }

      vertex.prev = this.tail;

      // ensure that the 'tail' reference points to the last vertex of the chain

      while (vertex.next !== null) {
        vertex = vertex.next;
      }

      this.tail = vertex;

      return this;
    },

    // Removes a vertex from the linked list

    remove: function(vertex) {
      if (vertex.prev === null) {
        this.head = vertex.next;
      } else {
        vertex.prev.next = vertex.next;
      }

      if (vertex.next === null) {
        this.tail = vertex.prev;
      } else {
        vertex.next.prev = vertex.prev;
      }

      return this;
    },

    // Removes a list of vertices whose 'head' is 'a' and whose 'tail' is b

    removeSubList: function(a, b) {
      if (a.prev === null) {
        this.head = b.next;
      } else {
        a.prev.next = b.next;
      }

      if (b.next === null) {
        this.tail = a.prev;
      } else {
        b.next.prev = a.prev;
      }

      return this;
    },

    isEmpty: function() {
      return this.head === null;
    },
  });

  // export

  THREE.QuickHull = QuickHull;
})();