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+// Copyright 2006 The Closure Library Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//      http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS-IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+/**
+ * @fileoverview A utility class for representing two-dimensional positions.
+ */
+
+
+goog.provide('goog.math.Coordinate');
+
+goog.require('goog.math');
+
+
+
+/**
+ * Class for representing coordinates and positions.
+ * @param {number=} opt_x Left, defaults to 0.
+ * @param {number=} opt_y Top, defaults to 0.
+ * @struct
+ * @constructor
+ */
+goog.math.Coordinate = function(opt_x, opt_y) {
+  /**
+   * X-value
+   * @type {number}
+   */
+  this.x = goog.isDef(opt_x) ? opt_x : 0;
+
+  /**
+   * Y-value
+   * @type {number}
+   */
+  this.y = goog.isDef(opt_y) ? opt_y : 0;
+};
+
+
+/**
+ * Returns a new copy of the coordinate.
+ * @return {!goog.math.Coordinate} A clone of this coordinate.
+ */
+goog.math.Coordinate.prototype.clone = function() {
+  return new goog.math.Coordinate(this.x, this.y);
+};
+
+
+if (goog.DEBUG) {
+  /**
+   * Returns a nice string representing the coordinate.
+   * @return {string} In the form (50, 73).
+   * @override
+   */
+  goog.math.Coordinate.prototype.toString = function() {
+    return '(' + this.x + ', ' + this.y + ')';
+  };
+}
+
+
+/**
+ * Compares coordinates for equality.
+ * @param {goog.math.Coordinate} a A Coordinate.
+ * @param {goog.math.Coordinate} b A Coordinate.
+ * @return {boolean} True iff the coordinates are equal, or if both are null.
+ */
+goog.math.Coordinate.equals = function(a, b) {
+  if (a == b) {
+    return true;
+  }
+  if (!a || !b) {
+    return false;
+  }
+  return a.x == b.x && a.y == b.y;
+};
+
+
+/**
+ * Returns the distance between two coordinates.
+ * @param {!goog.math.Coordinate} a A Coordinate.
+ * @param {!goog.math.Coordinate} b A Coordinate.
+ * @return {number} The distance between {@code a} and {@code b}.
+ */
+goog.math.Coordinate.distance = function(a, b) {
+  var dx = a.x - b.x;
+  var dy = a.y - b.y;
+  return Math.sqrt(dx * dx + dy * dy);
+};
+
+
+/**
+ * Returns the magnitude of a coordinate.
+ * @param {!goog.math.Coordinate} a A Coordinate.
+ * @return {number} The distance between the origin and {@code a}.
+ */
+goog.math.Coordinate.magnitude = function(a) {
+  return Math.sqrt(a.x * a.x + a.y * a.y);
+};
+
+
+/**
+ * Returns the angle from the origin to a coordinate.
+ * @param {!goog.math.Coordinate} a A Coordinate.
+ * @return {number} The angle, in degrees, clockwise from the positive X
+ *     axis to {@code a}.
+ */
+goog.math.Coordinate.azimuth = function(a) {
+  return goog.math.angle(0, 0, a.x, a.y);
+};
+
+
+/**
+ * Returns the squared distance between two coordinates. Squared distances can
+ * be used for comparisons when the actual value is not required.
+ *
+ * Performance note: eliminating the square root is an optimization often used
+ * in lower-level languages, but the speed difference is not nearly as
+ * pronounced in JavaScript (only a few percent.)
+ *
+ * @param {!goog.math.Coordinate} a A Coordinate.
+ * @param {!goog.math.Coordinate} b A Coordinate.
+ * @return {number} The squared distance between {@code a} and {@code b}.
+ */
+goog.math.Coordinate.squaredDistance = function(a, b) {
+  var dx = a.x - b.x;
+  var dy = a.y - b.y;
+  return dx * dx + dy * dy;
+};
+
+
+/**
+ * Returns the difference between two coordinates as a new
+ * goog.math.Coordinate.
+ * @param {!goog.math.Coordinate} a A Coordinate.
+ * @param {!goog.math.Coordinate} b A Coordinate.
+ * @return {!goog.math.Coordinate} A Coordinate representing the difference
+ *     between {@code a} and {@code b}.
+ */
+goog.math.Coordinate.difference = function(a, b) {
+  return new goog.math.Coordinate(a.x - b.x, a.y - b.y);
+};
+
+
+/**
+ * Returns the sum of two coordinates as a new goog.math.Coordinate.
+ * @param {!goog.math.Coordinate} a A Coordinate.
+ * @param {!goog.math.Coordinate} b A Coordinate.
+ * @return {!goog.math.Coordinate} A Coordinate representing the sum of the two
+ *     coordinates.
+ */
+goog.math.Coordinate.sum = function(a, b) {
+  return new goog.math.Coordinate(a.x + b.x, a.y + b.y);
+};
+
+
+/**
+ * Rounds the x and y fields to the next larger integer values.
+ * @return {!goog.math.Coordinate} This coordinate with ceil'd fields.
+ */
+goog.math.Coordinate.prototype.ceil = function() {
+  this.x = Math.ceil(this.x);
+  this.y = Math.ceil(this.y);
+  return this;
+};
+
+
+/**
+ * Rounds the x and y fields to the next smaller integer values.
+ * @return {!goog.math.Coordinate} This coordinate with floored fields.
+ */
+goog.math.Coordinate.prototype.floor = function() {
+  this.x = Math.floor(this.x);
+  this.y = Math.floor(this.y);
+  return this;
+};
+
+
+/**
+ * Rounds the x and y fields to the nearest integer values.
+ * @return {!goog.math.Coordinate} This coordinate with rounded fields.
+ */
+goog.math.Coordinate.prototype.round = function() {
+  this.x = Math.round(this.x);
+  this.y = Math.round(this.y);
+  return this;
+};
+
+
+/**
+ * Translates this box by the given offsets. If a {@code goog.math.Coordinate}
+ * is given, then the x and y values are translated by the coordinate's x and y.
+ * Otherwise, x and y are translated by {@code tx} and {@code opt_ty}
+ * respectively.
+ * @param {number|goog.math.Coordinate} tx The value to translate x by or the
+ *     the coordinate to translate this coordinate by.
+ * @param {number=} opt_ty The value to translate y by.
+ * @return {!goog.math.Coordinate} This coordinate after translating.
+ */
+goog.math.Coordinate.prototype.translate = function(tx, opt_ty) {
+  if (tx instanceof goog.math.Coordinate) {
+    this.x += tx.x;
+    this.y += tx.y;
+  } else {
+    this.x += Number(tx);
+    if (goog.isNumber(opt_ty)) {
+      this.y += opt_ty;
+    }
+  }
+  return this;
+};
+
+
+/**
+ * Scales this coordinate by the given scale factors. The x and y values are
+ * scaled by {@code sx} and {@code opt_sy} respectively.  If {@code opt_sy}
+ * is not given, then {@code sx} is used for both x and y.
+ * @param {number} sx The scale factor to use for the x dimension.
+ * @param {number=} opt_sy The scale factor to use for the y dimension.
+ * @return {!goog.math.Coordinate} This coordinate after scaling.
+ */
+goog.math.Coordinate.prototype.scale = function(sx, opt_sy) {
+  var sy = goog.isNumber(opt_sy) ? opt_sy : sx;
+  this.x *= sx;
+  this.y *= sy;
+  return this;
+};
+
+
+/**
+ * Rotates this coordinate clockwise about the origin (or, optionally, the given
+ * center) by the given angle, in radians.
+ * @param {number} radians The angle by which to rotate this coordinate
+ *     clockwise about the given center, in radians.
+ * @param {!goog.math.Coordinate=} opt_center The center of rotation. Defaults
+ *     to (0, 0) if not given.
+ */
+goog.math.Coordinate.prototype.rotateRadians = function(radians, opt_center) {
+  var center = opt_center || new goog.math.Coordinate(0, 0);
+
+  var x = this.x;
+  var y = this.y;
+  var cos = Math.cos(radians);
+  var sin = Math.sin(radians);
+
+  this.x = (x - center.x) * cos - (y - center.y) * sin + center.x;
+  this.y = (x - center.x) * sin + (y - center.y) * cos + center.y;
+};
+
+
+/**
+ * Rotates this coordinate clockwise about the origin (or, optionally, the given
+ * center) by the given angle, in degrees.
+ * @param {number} degrees The angle by which to rotate this coordinate
+ *     clockwise about the given center, in degrees.
+ * @param {!goog.math.Coordinate=} opt_center The center of rotation. Defaults
+ *     to (0, 0) if not given.
+ */
+goog.math.Coordinate.prototype.rotateDegrees = function(degrees, opt_center) {
+  this.rotateRadians(goog.math.toRadians(degrees), opt_center);
+};