SAT.js

/** @preserve SAT.js - Version 0.7.0 - Copyright 2012 - 2018 - Jim Riecken <jimr@jimr.ca> - released under the MIT License. https://github.com/jriecken/sat-js */

/*global define: false, module: false*/
/*jshint shadow:true, sub:true, forin:true, noarg:true, noempty:true,
  eqeqeq:true, bitwise:true, strict:true, undef:true,
  curly:true, browser:true */

/**
 * @param {*} root - The global scope
 * @param {Function} factory - Factory that creates SAT module
 */
(function (root, factory) {
  "use strict";
  if (typeof define === 'function' && define['amd']) {
    define(factory);
  } else if (typeof exports === 'object') {
    module['exports'] = factory();
  } else {
    root['SAT'] = factory();
  }
}(this, function () {
  "use strict";

  var SAT = {};

  /**
   * @param {?number=} x The x position.
   * @param {?number=} y The y position.
   * @constructor
   */
  function Vector(x, y) {
    this['x'] = x || 0;
    this['y'] = y || 0;
  }
  SAT['Vector'] = Vector;

  SAT['V'] = Vector;

  /**
   * @param {Vector} other The other Vector.
   * @return {Vector} This for chaining.
   */
  Vector.prototype['copy'] = Vector.prototype.copy = function(other) {
    this['x'] = other['x'];
    this['y'] = other['y'];
    return this;
  };

  /**
   * @return {Vector} The new cloned vector
   */
  Vector.prototype['clone'] = Vector.prototype.clone = function() {
    return new Vector(this['x'], this['y']);
  };

  /**
   * @return {Vector} This for chaining.
   */
  Vector.prototype['perp'] = Vector.prototype.perp = function() {
    var x = this['x'];
    this['x'] = this['y'];
    this['y'] = -x;
    return this;
  };

  /**
   * @param {number} angle The angle to rotate (in radians)
   * @return {Vector} This for chaining.
   */
  Vector.prototype['rotate'] = Vector.prototype.rotate = function (angle) {
    var x = this['x'];
    var y = this['y'];
    this['x'] = x * Math.cos(angle) - y * Math.sin(angle);
    this['y'] = x * Math.sin(angle) + y * Math.cos(angle);
    return this;
  };

  /**
   * @return {Vector} This for chaining.
   */
  Vector.prototype['reverse'] = Vector.prototype.reverse = function() {
    this['x'] = -this['x'];
    this['y'] = -this['y'];
    return this;
  };

  /**
   * @return {Vector} This for chaining.
   */
  Vector.prototype['normalize'] = Vector.prototype.normalize = function() {
    var d = this.len();
    if(d > 0) {
      this['x'] = this['x'] / d;
      this['y'] = this['y'] / d;
    }
    return this;
  };

  /**
   * @param {Vector} other The other Vector.
   * @return {Vector} This for chaining.
   */
  Vector.prototype['add'] = Vector.prototype.add = function(other) {
    this['x'] += other['x'];
    this['y'] += other['y'];
    return this;
  };

  /**
   * @param {Vector} other The other Vector.
   * @return {Vector} This for chaiing.
   */
  Vector.prototype['sub'] = Vector.prototype.sub = function(other) {
    this['x'] -= other['x'];
    this['y'] -= other['y'];
    return this;
  };

  /**
   * @param {number} x The scaling factor in the x direction.
   * @param {?number=} y The scaling factor in the y direction.  If this
   *   is not specified, the x scaling factor will be used.
   * @return {Vector} This for chaining.
   */
  Vector.prototype['scale'] = Vector.prototype.scale = function(x,y) {
    this['x'] *= x;
    this['y'] *= y || x;
    return this;
  };

  /**
   * @param {Vector} other The vector to project onto.
   * @return {Vector} This for chaining.
   */
  Vector.prototype['project'] = Vector.prototype.project = function(other) {
    var amt = this.dot(other) / other.len2();
    this['x'] = amt * other['x'];
    this['y'] = amt * other['y'];
    return this;
  };

  /**
   * @param {Vector} other The unit vector to project onto.
   * @return {Vector} This for chaining.
   */
  Vector.prototype['projectN'] = Vector.prototype.projectN = function(other) {
    var amt = this.dot(other);
    this['x'] = amt * other['x'];
    this['y'] = amt * other['y'];
    return this;
  };

  /**
   * @param {Vector} axis The vector representing the axis.
   * @return {Vector} This for chaining.
   */
  Vector.prototype['reflect'] = Vector.prototype.reflect = function(axis) {
    var x = this['x'];
    var y = this['y'];
    this.project(axis).scale(2);
    this['x'] -= x;
    this['y'] -= y;
    return this;
  };

  /**
   * @param {Vector} axis The unit vector representing the axis.
   * @return {Vector} This for chaining.
   */
  Vector.prototype['reflectN'] = Vector.prototype.reflectN = function(axis) {
    var x = this['x'];
    var y = this['y'];
    this.projectN(axis).scale(2);
    this['x'] -= x;
    this['y'] -= y;
    return this;
  };

  /**
   * @param {Vector}  other The vector to dot this one against.
   * @return {number} The dot product.
   */
  Vector.prototype['dot'] = Vector.prototype.dot = function(other) {
    return this['x'] * other['x'] + this['y'] * other['y'];
  };

  /**
   * @return {number} The length^2 of this vector.
   */
  Vector.prototype['len2'] = Vector.prototype.len2 = function() {
    return this.dot(this);
  };

  /**
   * @return {number} The length of this vector.
   */
  Vector.prototype['len'] = Vector.prototype.len = function() {
    return Math.sqrt(this.len2());
  };

  /**
   * @param {Vector=} pos A vector representing the position of the center of the circle
   * @param {?number=} r The radius of the circle
   * @constructor
   */
  function Circle(pos, r) {
    this['pos'] = pos || new Vector();
    this['r'] = r || 0;
  }
  SAT['Circle'] = Circle;

  /**
   * @return {Polygon} The AABB
   */
  Circle.prototype['getAABB'] = Circle.prototype.getAABB = function() {
    var r = this['r'];
    var corner = this["pos"].clone().sub(new Vector(r, r));
    return new Box(corner, r*2, r*2).toPolygon();
  };

  /**
   * @param {Vector=} pos A vector representing the origin of the polygon. (all other
   *   points are relative to this one)
   * @param {Array.<Vector>=} points An array of vectors representing the points in the polygon,
   *   in counter-clockwise order.
   * @constructor
   */
  function Polygon(pos, points) {
    this['pos'] = pos || new Vector();
    this['angle'] = 0;
    this['offset'] = new Vector();
    this.setPoints(points || []);
  }
  SAT['Polygon'] = Polygon;

  /**
   * @param {Array.<Vector>=} points An array of vectors representing the points in the polygon,
   *   in counter-clockwise order.
   * @return {Polygon} This for chaining.
   */
  Polygon.prototype['setPoints'] = Polygon.prototype.setPoints = function(points) {

    var lengthChanged = !this['points'] || this['points'].length !== points.length;
    if (lengthChanged) {
      var i;
      var calcPoints = this['calcPoints'] = [];
      var edges = this['edges'] = [];
      var normals = this['normals'] = [];

      for (i = 0; i < points.length; i++) {
        calcPoints.push(new Vector());
        edges.push(new Vector());
        normals.push(new Vector());
      }
    }
    this['points'] = points;
    this._recalc();
    return this;
  };

  /**
   * @param {number} angle The current rotation angle (in radians).
   * @return {Polygon} This for chaining.
   */
  Polygon.prototype['setAngle'] = Polygon.prototype.setAngle = function(angle) {
    this['angle'] = angle;
    this._recalc();
    return this;
  };

  /**
   * @param {Vector} offset The new offset vector.
   * @return {Polygon} This for chaining.
   */
  Polygon.prototype['setOffset'] = Polygon.prototype.setOffset = function(offset) {
    this['offset'] = offset;
    this._recalc();
    return this;
  };

  /**
   * @param {number} angle The angle to rotate (in radians)
   * @return {Polygon} This for chaining.
   */
  Polygon.prototype['rotate'] = Polygon.prototype.rotate = function(angle) {
    var points = this['points'];
    var len = points.length;
    for (var i = 0; i < len; i++) {
      points[i].rotate(angle);
    }
    this._recalc();
    return this;
  };

  /**
   * @param {number} x The horizontal amount to translate.
   * @param {number} y The vertical amount to translate.
   * @return {Polygon} This for chaining.
   */
  Polygon.prototype['translate'] = Polygon.prototype.translate = function (x, y) {
    var points = this['points'];
    var len = points.length;
    for (var i = 0; i < len; i++) {
      points[i]["x"] += x;
      points[i]["y"] += y;
    }
    this._recalc();
    return this;
  };

  /**
   * @return {Polygon} This for chaining.
   */
  Polygon.prototype._recalc = function() {

    var calcPoints = this['calcPoints'];

    var edges = this['edges'];

    var normals = this['normals'];

    var points = this['points'];
    var offset = this['offset'];
    var angle = this['angle'];
    var len = points.length;
    var i;
    for (i = 0; i < len; i++) {
      var calcPoint = calcPoints[i].copy(points[i]);
      calcPoint["x"] += offset["x"];
      calcPoint["y"] += offset["y"];
      if (angle !== 0) {
        calcPoint.rotate(angle);
      }
    }

    for (i = 0; i < len; i++) {
      var p1 = calcPoints[i];
      var p2 = i < len - 1 ? calcPoints[i + 1] : calcPoints[0];
      var e = edges[i].copy(p2).sub(p1);
      normals[i].copy(e).perp().normalize();
    }
    return this;
  };

  /**
   * @return {Polygon} The AABB
   */
  Polygon.prototype["getAABB"] = Polygon.prototype.getAABB = function() {
    var points = this["calcPoints"];
    var len = points.length;
    var xMin = points[0]["x"];
    var yMin = points[0]["y"];
    var xMax = points[0]["x"];
    var yMax = points[0]["y"];
    for (var i = 1; i < len; i++) {
      var point = points[i];
      if (point["x"] < xMin) {
        xMin = point["x"];
      }
      else if (point["x"] > xMax) {
        xMax = point["x"];
      }
      if (point["y"] < yMin) {
        yMin = point["y"];
      }
      else if (point["y"] > yMax) {
        yMax = point["y"];
      }
    }
    return new Box(this["pos"].clone().add(new Vector(xMin, yMin)), xMax - xMin, yMax - yMin).toPolygon();
  };

  Polygon.prototype["getCentroid"] = Polygon.prototype.getCentroid = function() {
    var points = this["calcPoints"];
    var len = points.length;
    var cx = 0;
    var cy = 0;
    var ar = 0;
    for (var i = 0; i < len; i++) {
      var p1 = points[i];
      var p2 = i === len - 1 ? points[0] : points[i+1]; // Loop around if last point
      var a = p1["x"] * p2["y"] - p2["x"] * p1["y"];
      cx += (p1["x"] + p2["x"]) * a;
      cy += (p1["y"] + p2["y"]) * a;
      ar += a;
    }
    ar = ar * 3; // we want 1 / 6 the area and we currently hae 2*area
    cx = cx / ar;
    cy = cy / ar;
    return new Vector(cx, cy);
  };

  /**
   * @param {Vector=} pos A vector representing the bottom-left of the box (i.e. the smallest x and smallest y value).
   * @param {?number=} w The width of the box.
   * @param {?number=} h The height of the box.
   * @constructor
   */
  function Box(pos, w, h) {
    this['pos'] = pos || new Vector();
    this['w'] = w || 0;
    this['h'] = h || 0;
  }
  SAT['Box'] = Box;

  /**
   * @return {Polygon} A new Polygon that represents this box.
   */
  Box.prototype['toPolygon'] = Box.prototype.toPolygon = function() {
    var pos = this['pos'];
    var w = this['w'];
    var h = this['h'];
    return new Polygon(new Vector(pos['x'], pos['y']), [
     new Vector(), new Vector(w, 0),
     new Vector(w,h), new Vector(0,h)
    ]);
  };

  /**
   * @constructor
   */
  function Response() {
    this['a'] = null;
    this['b'] = null;
    this['overlapN'] = new Vector();
    this['overlapV'] = new Vector();
    this.clear();
  }
  SAT['Response'] = Response;

  /**
   * @return {Response} This for chaining
   */
  Response.prototype['clear'] = Response.prototype.clear = function() {
    this['aInB'] = true;
    this['bInA'] = true;
    this['overlap'] = Number.MAX_VALUE;
    return this;
  };

  /**
   * @type {Array.<Vector>}
   */
  var T_VECTORS = [];
  for (var i = 0; i < 10; i++) { T_VECTORS.push(new Vector()); }

  /**
   * @type {Array.<Array.<number>>}
   */
  var T_ARRAYS = [];
  for (var i = 0; i < 5; i++) { T_ARRAYS.push([]); }

  /**
   * @type {Response}
   */
  var T_RESPONSE = new Response();

  /**
   * @type {Polygon}
   */
  var TEST_POINT = new Box(new Vector(), 0.000001, 0.000001).toPolygon();

  /**
   * @param {Array.<Vector>} points The points to flatten.
   * @param {Vector} normal The unit vector axis to flatten on.
   * @param {Array.<number>} result An array.  After calling this function,
   *   result[0] will be the minimum value,
   *   result[1] will be the maximum value.
   */
  function flattenPointsOn(points, normal, result) {
    var min = Number.MAX_VALUE;
    var max = -Number.MAX_VALUE;
    var len = points.length;
    for (var i = 0; i < len; i++ ) {

      var dot = points[i].dot(normal);
      if (dot < min) { min = dot; }
      if (dot > max) { max = dot; }
    }
    result[0] = min; result[1] = max;
  }

  /**
   * @param {Vector} aPos The position of the first polygon.
   * @param {Vector} bPos The position of the second polygon.
   * @param {Array.<Vector>} aPoints The points in the first polygon.
   * @param {Array.<Vector>} bPoints The points in the second polygon.
   * @param {Vector} axis The axis (unit sized) to test against.  The points of both polygons
   *   will be projected onto this axis.
   * @param {Response=} response A Response object (optional) which will be populated
   *   if the axis is not a separating axis.
   * @return {boolean} true if it is a separating axis, false otherwise.  If false,
   *   and a response is passed in, information about how much overlap and
   *   the direction of the overlap will be populated.
   */
  function isSeparatingAxis(aPos, bPos, aPoints, bPoints, axis, response) {
    var rangeA = T_ARRAYS.pop();
    var rangeB = T_ARRAYS.pop();

    var offsetV = T_VECTORS.pop().copy(bPos).sub(aPos);
    var projectedOffset = offsetV.dot(axis);

    flattenPointsOn(aPoints, axis, rangeA);
    flattenPointsOn(bPoints, axis, rangeB);

    rangeB[0] += projectedOffset;
    rangeB[1] += projectedOffset;

    if (rangeA[0] > rangeB[1] || rangeB[0] > rangeA[1]) {
      T_VECTORS.push(offsetV);
      T_ARRAYS.push(rangeA);
      T_ARRAYS.push(rangeB);
      return true;
    }

    if (response) {
      var overlap = 0;

      if (rangeA[0] < rangeB[0]) {
        response['aInB'] = false;

        if (rangeA[1] < rangeB[1]) {
          overlap = rangeA[1] - rangeB[0];
          response['bInA'] = false;

        } else {
          var option1 = rangeA[1] - rangeB[0];
          var option2 = rangeB[1] - rangeA[0];
          overlap = option1 < option2 ? option1 : -option2;
        }

      } else {
        response['bInA'] = false;

        if (rangeA[1] > rangeB[1]) {
          overlap = rangeA[0] - rangeB[1];
          response['aInB'] = false;

        } else {
          var option1 = rangeA[1] - rangeB[0];
          var option2 = rangeB[1] - rangeA[0];
          overlap = option1 < option2 ? option1 : -option2;
        }
      }

      var absOverlap = Math.abs(overlap);
      if (absOverlap < response['overlap']) {
        response['overlap'] = absOverlap;
        response['overlapN'].copy(axis);
        if (overlap < 0) {
          response['overlapN'].reverse();
        }
      }
    }
    T_VECTORS.push(offsetV);
    T_ARRAYS.push(rangeA);
    T_ARRAYS.push(rangeB);
    return false;
  }
  SAT['isSeparatingAxis'] = isSeparatingAxis;

  /**
   * @param {Vector} line The line segment.
   * @param {Vector} point The point.
   * @return  {number} LEFT_VORONOI_REGION (-1) if it is the left region,
   *          MIDDLE_VORONOI_REGION (0) if it is the middle region,
   *          RIGHT_VORONOI_REGION (1) if it is the right region.
   */
  function voronoiRegion(line, point) {
    var len2 = line.len2();
    var dp = point.dot(line);

    if (dp < 0) { return LEFT_VORONOI_REGION; }

    else if (dp > len2) { return RIGHT_VORONOI_REGION; }

    else { return MIDDLE_VORONOI_REGION; }
  }

  /**
   * @const
   */
  var LEFT_VORONOI_REGION = -1;
  /**
   * @const
   */
  var MIDDLE_VORONOI_REGION = 0;
  /**
   * @const
   */
  var RIGHT_VORONOI_REGION = 1;

  /**
   * @param {Vector} p The point to test.
   * @param {Circle} c The circle to test.
   * @return {boolean} true if the point is inside the circle, false if it is not.
   */
  function pointInCircle(p, c) {
    var differenceV = T_VECTORS.pop().copy(p).sub(c['pos']);
    var radiusSq = c['r'] * c['r'];
    var distanceSq = differenceV.len2();
    T_VECTORS.push(differenceV);

    return distanceSq <= radiusSq;
  }
  SAT['pointInCircle'] = pointInCircle;

  /**
   * @param {Vector} p The point to test.
   * @param {Polygon} poly The polygon to test.
   * @return {boolean} true if the point is inside the polygon, false if it is not.
   */
  function pointInPolygon(p, poly) {
    TEST_POINT['pos'].copy(p);
    T_RESPONSE.clear();
    var result = testPolygonPolygon(TEST_POINT, poly, T_RESPONSE);
    if (result) {
      result = T_RESPONSE['aInB'];
    }
    return result;
  }
  SAT['pointInPolygon'] = pointInPolygon;

  /**
   * @param {Circle} a The first circle.
   * @param {Circle} b The second circle.
   * @param {Response=} response Response object (optional) that will be populated if
   *   the circles intersect.
   * @return {boolean} true if the circles intersect, false if they don't.
   */
  function testCircleCircle(a, b, response) {

    var differenceV = T_VECTORS.pop().copy(b['pos']).sub(a['pos']);
    var totalRadius = a['r'] + b['r'];
    var totalRadiusSq = totalRadius * totalRadius;
    var distanceSq = differenceV.len2();

    if (distanceSq > totalRadiusSq) {
      T_VECTORS.push(differenceV);
      return false;
    }

    if (response) {
      var dist = Math.sqrt(distanceSq);
      response['a'] = a;
      response['b'] = b;
      response['overlap'] = totalRadius - dist;
      response['overlapN'].copy(differenceV.normalize());
      response['overlapV'].copy(differenceV).scale(response['overlap']);
      response['aInB']= a['r'] <= b['r'] && dist <= b['r'] - a['r'];
      response['bInA'] = b['r'] <= a['r'] && dist <= a['r'] - b['r'];
    }
    T_VECTORS.push(differenceV);
    return true;
  }
  SAT['testCircleCircle'] = testCircleCircle;

  /**
   * @param {Polygon} polygon The polygon.
   * @param {Circle} circle The circle.
   * @param {Response=} response Response object (optional) that will be populated if
   *   they interset.
   * @return {boolean} true if they intersect, false if they don't.
   */
  function testPolygonCircle(polygon, circle, response) {

    var circlePos = T_VECTORS.pop().copy(circle['pos']).sub(polygon['pos']);
    var radius = circle['r'];
    var radius2 = radius * radius;
    var points = polygon['calcPoints'];
    var len = points.length;
    var edge = T_VECTORS.pop();
    var point = T_VECTORS.pop();

    for (var i = 0; i < len; i++) {
      var next = i === len - 1 ? 0 : i + 1;
      var prev = i === 0 ? len - 1 : i - 1;
      var overlap = 0;
      var overlapN = null;

      edge.copy(polygon['edges'][i]);

      point.copy(circlePos).sub(points[i]);

      if (response && point.len2() > radius2) {
        response['aInB'] = false;
      }

      var region = voronoiRegion(edge, point);

      if (region === LEFT_VORONOI_REGION) {

        edge.copy(polygon['edges'][prev]);

        var point2 = T_VECTORS.pop().copy(circlePos).sub(points[prev]);
        region = voronoiRegion(edge, point2);
        if (region === RIGHT_VORONOI_REGION) {

          var dist = point.len();
          if (dist > radius) {

            T_VECTORS.push(circlePos);
            T_VECTORS.push(edge);
            T_VECTORS.push(point);
            T_VECTORS.push(point2);
            return false;
          } else if (response) {

            response['bInA'] = false;
            overlapN = point.normalize();
            overlap = radius - dist;
          }
        }
        T_VECTORS.push(point2);

      } else if (region === RIGHT_VORONOI_REGION) {

        edge.copy(polygon['edges'][next]);

        point.copy(circlePos).sub(points[next]);
        region = voronoiRegion(edge, point);
        if (region === LEFT_VORONOI_REGION) {

          var dist = point.len();
          if (dist > radius) {

            T_VECTORS.push(circlePos);
            T_VECTORS.push(edge);
            T_VECTORS.push(point);
            return false;
          } else if (response) {

            response['bInA'] = false;
            overlapN = point.normalize();
            overlap = radius - dist;
          }
        }

      } else {

        var normal = edge.perp().normalize();

        var dist = point.dot(normal);
        var distAbs = Math.abs(dist);

        if (dist > 0 && distAbs > radius) {

          T_VECTORS.push(circlePos);
          T_VECTORS.push(normal);
          T_VECTORS.push(point);
          return false;
        } else if (response) {

          overlapN = normal;
          overlap = radius - dist;

          if (dist >= 0 || overlap < 2 * radius) {
            response['bInA'] = false;
          }
        }
      }

      if (overlapN && response && Math.abs(overlap) < Math.abs(response['overlap'])) {
        response['overlap'] = overlap;
        response['overlapN'].copy(overlapN);
      }
    }

    if (response) {
      response['a'] = polygon;
      response['b'] = circle;
      response['overlapV'].copy(response['overlapN']).scale(response['overlap']);
    }
    T_VECTORS.push(circlePos);
    T_VECTORS.push(edge);
    T_VECTORS.push(point);
    return true;
  }
  SAT['testPolygonCircle'] = testPolygonCircle;

  /**
   * @param {Circle} circle The circle.
   * @param {Polygon} polygon The polygon.
   * @param {Response=} response Response object (optional) that will be populated if
   *   they interset.
   * @return {boolean} true if they intersect, false if they don't.
   */
  function testCirclePolygon(circle, polygon, response) {

    var result = testPolygonCircle(polygon, circle, response);
    if (result && response) {

      var a = response['a'];
      var aInB = response['aInB'];
      response['overlapN'].reverse();
      response['overlapV'].reverse();
      response['a'] = response['b'];
      response['b'] = a;
      response['aInB'] = response['bInA'];
      response['bInA'] = aInB;
    }
    return result;
  }
  SAT['testCirclePolygon'] = testCirclePolygon;

  /**
   * @param {Polygon} a The first polygon.
   * @param {Polygon} b The second polygon.
   * @param {Response=} response Response object (optional) that will be populated if
   *   they interset.
   * @return {boolean} true if they intersect, false if they don't.
   */
  function testPolygonPolygon(a, b, response) {
    var aPoints = a['calcPoints'];
    var aLen = aPoints.length;
    var bPoints = b['calcPoints'];
    var bLen = bPoints.length;

    for (var i = 0; i < aLen; i++) {
      if (isSeparatingAxis(a['pos'], b['pos'], aPoints, bPoints, a['normals'][i], response)) {
        return false;
      }
    }

    for (var i = 0;i < bLen; i++) {
      if (isSeparatingAxis(a['pos'], b['pos'], aPoints, bPoints, b['normals'][i], response)) {
        return false;
      }
    }

    if (response) {
      response['a'] = a;
      response['b'] = b;
      response['overlapV'].copy(response['overlapN']).scale(response['overlap']);
    }
    return true;
  }
  SAT['testPolygonPolygon'] = testPolygonPolygon;

  return SAT;
}));