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Filename : polygon.js
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// Copyright (c) 2011, Chris Umbel, James Coglan
// Polygon class - depends on Vector, Plane, Polygon.Vertex and LinkedList.

var Sylvester = require('./sylvester');

function Polygon() {}
Polygon.prototype = {

  // Returns the vertex at the given position on the vertex list, numbered from 1.
  v: function(i) {
    return this.vertices.at(i - 1).data;
  },

  // Returns the node in the vertices linked list that refers to the given vertex.
  nodeFor: function(vertex) {
    return this.vertices.withData(vertex);
  },

  // Returns a new polygon with the same vertices as the receiver. The vertices
  // will not be duplicates, they refer to the same objects as the vertices in this
  // polygon, but the linked list and nodes used to point to them are separate and
  // can be manipulated independently of this one.
  dup: function() {
    return Polygon.create(this.vertices, this.plane);
  },

  // Translates the polygon by the given vector and returns the polygon.
  translate: function(vector) {
    var P = vector.elements || vector;
    this.vertices.each(function(node) {
      var E = node.data.elements;
      node.data.setElements([E[0] + P[0], E[1] + P[1], E[2] + (P[2] || 0)]);
    });
    this.plane = this.plane.translate(vector);
    this.updateTrianglePlanes(function(plane) { return plane.translate(vector); });
    return this;
  },

  // Rotates the polygon about the given line and returns the polygon.
  rotate: function(t, line) {
    var R = Matrix.Rotation(t, line.direction);
    this.vertices.each(function(node) {
      node.data.setElements(node.data.rotate(R, line).elements);
    });
    this.plane = this.plane.rotate(R, line);
    this.updateTrianglePlanes(function(plane) { return plane.rotate(R, line); });
    return this;
  },

  // Scales the polygon relative to the given point and returns the polygon.
  scale: function(k, point) {
    var P = point.elements || point;
    this.vertices.each(function(node) {
      var E = node.data.elements;
      node.data.setElements([
        P[0] + k * (E[0] - P[0]),
        P[1] + k * (E[1] - P[1]),
        (P[2] || 0) + k * (E[2] - (P[2] || 0))
      ]);
    });
    var anchor = this.vertices.first.data;
    this.plane.anchor.setElements(anchor);
    this.updateTrianglePlanes(function(plane) { return Plane.create(anchor, plane.normal); });
    return this;
  },

  // Updates the plane properties of all the cached triangles belonging to
  // the polygon according to the given function. For example, suppose you
  // just rotated the polygon, you should call:
  //
  //   poly.updateTrianglePlanes(function(plane) { return plane.rotate(t, line); });
  //
  // This method is called automatically by Polygon.translate, Polygon.rotate
  // and Polygon.scale transformation methods.
  updateTrianglePlanes: function(fn) {
    var i;
    if (this.cached.triangles !== null) {
      i = this.cached.triangles.length;
      while (i--) {
        this.cached.triangles[i].plane = fn(this.cached.triangles[i].plane);
      }
    }
    if (this.cached.surfaceIntegralElements !== null) {
      i = this.cached.surfaceIntegralElements.length;
      while (i--) {
        this.cached.surfaceIntegralElements[i].plane = fn(this.cached.surfaceIntegralElements[i].plane);
      }
    }
  },

  // Returns true iff the polygon is a triangle
  isTriangle: function() {
    return this.vertices.length == 3;
  },

  // Returns a collection of triangles used for calculating area and center of mass.
  // Some of the triangles will not lie inside the polygon - this collection is essentially
  // a series of itervals in a surface integral, so some are 'negative'. If you want the
  // polygon broken into constituent triangles, use toTriangles(). This method is used
  // because it's much faster than toTriangles().
  // The triangles generated share vertices with the original polygon, so they transform
  // with the polygon. They are cached after first calculation and should remain in sync
  // with changes to the parent polygon.
  trianglesForSurfaceIntegral: function() {
    if (this.cached.surfaceIntegralElements !== null) { return this.cached.surfaceIntegralElements; }
    var triangles = [];
    var firstVertex = this.vertices.first.data;
    var plane = this.plane;
    this.vertices.each(function(node, i) {
      if (i < 2) { return; }
      var points = [firstVertex, node.prev.data, node.data];
      // If the vertices lie on a straigh line, give the polygon's own plane. If the
      // element has no area, it doesn't matter which way its normal faces.
      triangles.push(Polygon.create(points, Plane.fromPoints(points) || plane));
    });
    return this.setCache('surfaceIntegralElements', triangles);
  },

  // Returns the area of the polygon. Requires that the polygon
  // be converted to triangles, so use with caution.
  area: function() {
    if (this.isTriangle()) {
      // Area is half the modulus of the cross product of two sides
      var A = this.vertices.first, B = A.next, C = B.next;
      A = A.data.elements; B = B.data.elements; C = C.data.elements;
      return 0.5 * Vector.create([
        (A[1] - B[1]) * (C[2] - B[2]) - (A[2] - B[2]) * (C[1] - B[1]),
        (A[2] - B[2]) * (C[0] - B[0]) - (A[0] - B[0]) * (C[2] - B[2]),
        (A[0] - B[0]) * (C[1] - B[1]) - (A[1] - B[1]) * (C[0] - B[0])
      ]).modulus();
    } else {
      var trigs = this.trianglesForSurfaceIntegral(), area = 0;
      var i = trigs.length;
      while (i--) {
        area += trigs[i].area() * trigs[i].plane.normal.dot(this.plane.normal);
      }
      return area;
    }
  },

  // Returns the centroid of the polygon. Requires division into
  // triangles - use with caution
  centroid: function() {
    if (this.isTriangle()) {
      var A = this.v(1).elements, B = this.v(2).elements, C = this.v(3).elements;
      return Vector.create([(A[0] + B[0] + C[0])/3, (A[1] + B[1] + C[1])/3, (A[2] + B[2] + C[2])/3]);
    } else {
      var A, M = 0, V = Vector.Zero(3), P, C, trigs = this.trianglesForSurfaceIntegral();
      var i = trigs.length;
      while (i--) {
        A = trigs[i].area() * trigs[i].plane.normal.dot(this.plane.normal);
        M += A;
        P = V.elements;
        C = trigs[i].centroid().elements;
        V.setElements([P[0] + C[0] * A, P[1] + C[1] * A, P[2] + C[2] * A]);
      }
      return V.x(1/M);
    }
  },

  // Returns the polygon's projection on the given plane as another polygon
  projectionOn: function(plane) {
    var points = [];
    this.vertices.each(function(node) { points.push(plane.pointClosestTo(node.data)); });
    return Polygon.create(points);
  },

  // Removes the given vertex from the polygon as long as it's not triangular.
  removeVertex: function(vertex) {
    if (this.isTriangle()) { return; }
    var node = this.nodeFor(vertex);
    if (node === null) { return null; }
    this.clearCache();
    // Previous and next entries in the main vertex list
    var prev = node.prev, next = node.next;
    var prevWasConvex = prev.data.isConvex(this);
    var nextWasConvex = next.data.isConvex(this);
    if (node.data.isConvex(this)) {
      this.convexVertices.remove(this.convexVertices.withData(node.data));
    } else {
      this.reflexVertices.remove(this.reflexVertices.withData(node.data));
    }
    this.vertices.remove(node);
    // Deal with previous vertex's change of class
    if (prevWasConvex != prev.data.isConvex(this)) {
      if (prevWasConvex) {
        this.convexVertices.remove(this.convexVertices.withData(prev.data));
        this.reflexVertices.append(new LinkedList.Node(prev.data));
      } else {
        this.reflexVertices.remove(this.reflexVertices.withData(prev.data));
        this.convexVertices.append(new LinkedList.Node(prev.data));
      }
    }
    // Deal with next vertex's change of class
    if (nextWasConvex != next.data.isConvex(this)) {
      if (nextWasConvex) {
        this.convexVertices.remove(this.convexVertices.withData(next.data));
        this.reflexVertices.append(new LinkedList.Node(next.data));
      } else {
        this.reflexVertices.remove(this.reflexVertices.withData(next.data));
        this.convexVertices.append(new LinkedList.Node(next.data));
      }
    }
    return this;
  },

  // Returns true iff the point is strictly inside the polygon
  contains: function(point) {
    return this.containsByWindingNumber(point);
  },

  // Returns true iff the given point is strictly inside the polygon using the winding number method
  containsByWindingNumber: function(point) {
    var P = point.elements || point;
    if (!this.plane.contains(P)) { return false; }
    if (this.hasEdgeContaining(P)) { return false; }
    var V, W, A, B, theta = 0, dt, loops = 0, self = this;
    this.vertices.each(function(node) {
      V = node.data.elements;
      W = node.next.data.elements;
      A = Vector.create([V[0] - P[0], V[1] - P[1], V[2] - (P[2] || 0)]);
      B = Vector.create([W[0] - P[0], W[1] - P[1], W[2] - (P[2] || 0)]);
      dt = A.angleFrom(B);
      if (dt === null || dt === 0) { return; }
      theta += (A.cross(B).isParallelTo(self.plane.normal) ? 1 : -1) * dt;
      if (theta >= 2 * Math.PI - Sylvester.precision) { loops++; theta -= 2 * Math.PI; }
      if (theta <= -2 * Math.PI + Sylvester.precision) { loops--; theta += 2 * Math.PI; }
    });
    return loops != 0;
  },

  // Returns true if the given point lies on an edge of the polygon
  // May cause problems with 'hole-joining' edges
  hasEdgeContaining: function(point) {
    var P = (point.elements || point);
    var success = false;
    this.vertices.each(function(node) {
      if (Line.Segment.create(node.data, node.next.data).contains(P)) { success = true; }
    });
    return success;
  },

  // Returns an array of 3-vertex polygons that the original has been split into
  // Stores the first calculation for faster retrieval later on
  toTriangles: function() {
    if (this.cached.triangles !== null) { return this.cached.triangles; }
    return this.setCache('triangles', this.triangulateByEarClipping());
  },

  // Implementation of ear clipping algorithm
  // Found in 'Triangulation by ear clipping', by David Eberly
  // at http://www.geometrictools.com
  // This will not deal with overlapping sections - contruct your polygons sensibly
  triangulateByEarClipping: function() {
    var poly = this.dup(), triangles = [], success, convexNode, mainNode, trig;
    while (!poly.isTriangle()) {
      success = false;
      while (!success) {
        success = true;
        // Ear tips must be convex vertices - let's pick one at random
        convexNode = poly.convexVertices.randomNode();
        mainNode = poly.vertices.withData(convexNode.data);
        // For convex vertices, this order will always be anticlockwise
        trig = Polygon.create([mainNode.data, mainNode.next.data, mainNode.prev.data], this.plane);
        // Now test whether any reflex vertices lie within the ear
        poly.reflexVertices.each(function(node) {
          // Don't test points belonging to this triangle. node won't be
          // equal to convexNode as node is reflex and vertex is convex.
          if (node.data != mainNode.prev.data && node.data != mainNode.next.data) {
            if (trig.contains(node.data) || trig.hasEdgeContaining(node.data)) { success = false; }
          }
        });
      }
      triangles.push(trig);
      poly.removeVertex(mainNode.data);
    }
    // Need to do this to renumber the remaining vertices
    triangles.push(Polygon.create(poly.vertices, this.plane));
    return triangles;
  },

  // Sets the polygon's vertices
  setVertices: function(points, plane) {
    var pointSet = points.toArray ? points.toArray() : points;
    this.plane = (plane && plane.normal) ? plane.dup() : Plane.fromPoints(pointSet);
    if (this.plane === null) { return null; }
    this.vertices = new LinkedList.Circular();
    // Construct linked list of vertices. If each point is already a polygon
    // vertex, we reference it rather than creating a new vertex.
    var i = pointSet.length, newVertex;
    while (i--) {
      newVertex = pointSet[i].isConvex ? pointSet[i] : new Polygon.Vertex(pointSet[i]);
      this.vertices.prepend(new LinkedList.Node(newVertex));
    }
    this.clearCache();
    this.populateVertexTypeLists();
    return this;
  },

  // Constructs lists of convex and reflex vertices based on the main vertex list.
  populateVertexTypeLists: function() {
    this.convexVertices = new LinkedList.Circular();
    this.reflexVertices = new LinkedList.Circular();
    var self = this;
    this.vertices.each(function(node) {
      // Split vertices into convex / reflex groups
      // The LinkedList.Node class wraps each vertex so it can belong to many linked lists.
      self[node.data.type(self) + 'Vertices'].append(new LinkedList.Node(node.data));
    });
  },

  // Gives the polygon its own local set of vertex points, allowing it to be
  // transformed independently of polygons it may be sharing vertices with.
  copyVertices: function() {
    this.clearCache();
    this.vertices.each(function(node) {
      node.data = new Polygon.Vertex(node.data);
    });
    this.populateVertexTypeLists();
  },

  // Clear any cached properties
  clearCache: function() {
    this.cached = {
      triangles: null,
      surfaceIntegralElements: null
    };
  },

  // Set cached value and return the value
  setCache: function(key, value) {
    this.cached[key] = value;
    return value;
  },

  // Returns a string representation of the polygon's vertices.
  inspect: function() {
    var points = [];
    this.vertices.each(function(node) { points.push(node.data.inspect()); });
    return points.join(' -> ');
  }
};

// Constructor function
Polygon.create = function(points, plane) {
  var P = new Polygon();
  return P.setVertices(points, plane);
};

module.exports = Polygon;