/* This file is automatically rebuilt by the Cesium build process. */
define(['exports', './Check-c23b5bd5', './when-9f8cafad', './Math-cf2f57e0'], function (exports, Check, when, _Math) { 'use strict';
/**
* A 3D Cartesian point.
* @alias Cartesian3
* @constructor
*
* @param {Number} [x=0.0] The X component.
* @param {Number} [y=0.0] The Y component.
* @param {Number} [z=0.0] The Z component.
*
* @see Cartesian2
* @see Cartesian4
* @see Packable
*/
function Cartesian3(x, y, z) {
/**
* The X component.
* @type {Number}
* @default 0.0
*/
this.x = when.defaultValue(x, 0.0);
/**
* The Y component.
* @type {Number}
* @default 0.0
*/
this.y = when.defaultValue(y, 0.0);
/**
* The Z component.
* @type {Number}
* @default 0.0
*/
this.z = when.defaultValue(z, 0.0);
}
/**
* Converts the provided Spherical into Cartesian3 coordinates.
*
* @param {Spherical} spherical The Spherical to be converted to Cartesian3.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.fromSpherical = function (spherical, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("spherical", spherical);
//>>includeEnd('debug');
if (!when.defined(result)) {
result = new Cartesian3();
}
var clock = spherical.clock;
var cone = spherical.cone;
var magnitude = when.defaultValue(spherical.magnitude, 1.0);
var radial = magnitude * Math.sin(cone);
result.x = radial * Math.cos(clock);
result.y = radial * Math.sin(clock);
result.z = magnitude * Math.cos(cone);
return result;
};
/**
* Creates a Cartesian3 instance from x, y and z coordinates.
*
* @param {Number} x The x coordinate.
* @param {Number} y The y coordinate.
* @param {Number} z The z coordinate.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.fromElements = function (x, y, z, result) {
if (!when.defined(result)) {
return new Cartesian3(x, y, z);
}
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Duplicates a Cartesian3 instance.
*
* @param {Cartesian3} cartesian The Cartesian to duplicate.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided. (Returns undefined if cartesian is undefined)
*/
Cartesian3.clone = function (cartesian, result) {
if (!when.defined(cartesian)) {
return undefined;
}
if (!when.defined(result)) {
return new Cartesian3(cartesian.x, cartesian.y, cartesian.z);
}
result.x = cartesian.x;
result.y = cartesian.y;
result.z = cartesian.z;
return result;
};
/**
* Creates a Cartesian3 instance from an existing Cartesian4. This simply takes the
* x, y, and z properties of the Cartesian4 and drops w.
* @function
*
* @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian3 instance from.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.fromCartesian4 = Cartesian3.clone;
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Cartesian3.packedLength = 3;
/**
* Stores the provided instance into the provided array.
*
* @param {Cartesian3} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Cartesian3.pack = function (value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("value", value);
Check.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = when.defaultValue(startingIndex, 0);
array[startingIndex++] = value.x;
array[startingIndex++] = value.y;
array[startingIndex] = value.z;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Cartesian3} [result] The object into which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.unpack = function (array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = when.defaultValue(startingIndex, 0);
if (!when.defined(result)) {
result = new Cartesian3();
}
result.x = array[startingIndex++];
result.y = array[startingIndex++];
result.z = array[startingIndex];
return result;
};
/**
* Flattens an array of Cartesian3s into an array of components.
*
* @param {Cartesian3[]} array The array of cartesians to pack.
* @param {Number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 3 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 3) elements.
* @returns {Number[]} The packed array.
*/
Cartesian3.packArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("array", array);
//>>includeEnd('debug');
var length = array.length;
var resultLength = length * 3;
if (!when.defined(result)) {
result = new Array(resultLength);
} else if (!Array.isArray(result) && result.length !== resultLength) {
throw new Check.DeveloperError(
"If result is a typed array, it must have exactly array.length * 3 elements"
);
} else if (result.length !== resultLength) {
result.length = resultLength;
}
for (var i = 0; i < length; ++i) {
Cartesian3.pack(array[i], result, i * 3);
}
return result;
};
/**
* Unpacks an array of cartesian components into an array of Cartesian3s.
*
* @param {Number[]} array The array of components to unpack.
* @param {Cartesian3[]} [result] The array onto which to store the result.
* @returns {Cartesian3[]} The unpacked array.
*/
Cartesian3.unpackArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("array", array);
Check.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 3);
if (array.length % 3 !== 0) {
throw new Check.DeveloperError("array length must be a multiple of 3.");
}
//>>includeEnd('debug');
var length = array.length;
if (!when.defined(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (var i = 0; i < length; i += 3) {
var index = i / 3;
result[index] = Cartesian3.unpack(array, i, result[index]);
}
return result;
};
/**
* Creates a Cartesian3 from three consecutive elements in an array.
* @function
*
* @param {Number[]} array The array whose three consecutive elements correspond to the x, y, and z components, respectively.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*
* @example
* // Create a Cartesian3 with (1.0, 2.0, 3.0)
* var v = [1.0, 2.0, 3.0];
* var p = Cesium.Cartesian3.fromArray(v);
*
* // Create a Cartesian3 with (1.0, 2.0, 3.0) using an offset into an array
* var v2 = [0.0, 0.0, 1.0, 2.0, 3.0];
* var p2 = Cesium.Cartesian3.fromArray(v2, 2);
*/
Cartesian3.fromArray = Cartesian3.unpack;
/**
* Computes the value of the maximum component for the supplied Cartesian.
*
* @param {Cartesian3} cartesian The cartesian to use.
* @returns {Number} The value of the maximum component.
*/
Cartesian3.maximumComponent = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return Math.max(cartesian.x, cartesian.y, cartesian.z);
};
/**
* Computes the value of the minimum component for the supplied Cartesian.
*
* @param {Cartesian3} cartesian The cartesian to use.
* @returns {Number} The value of the minimum component.
*/
Cartesian3.minimumComponent = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return Math.min(cartesian.x, cartesian.y, cartesian.z);
};
/**
* Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
*
* @param {Cartesian3} first A cartesian to compare.
* @param {Cartesian3} second A cartesian to compare.
* @param {Cartesian3} result The object into which to store the result.
* @returns {Cartesian3} A cartesian with the minimum components.
*/
Cartesian3.minimumByComponent = function (first, second, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("first", first);
Check.Check.typeOf.object("second", second);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.min(first.x, second.x);
result.y = Math.min(first.y, second.y);
result.z = Math.min(first.z, second.z);
return result;
};
/**
* Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
*
* @param {Cartesian3} first A cartesian to compare.
* @param {Cartesian3} second A cartesian to compare.
* @param {Cartesian3} result The object into which to store the result.
* @returns {Cartesian3} A cartesian with the maximum components.
*/
Cartesian3.maximumByComponent = function (first, second, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("first", first);
Check.Check.typeOf.object("second", second);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.max(first.x, second.x);
result.y = Math.max(first.y, second.y);
result.z = Math.max(first.z, second.z);
return result;
};
/**
* Computes the provided Cartesian's squared magnitude.
*
* @param {Cartesian3} cartesian The Cartesian instance whose squared magnitude is to be computed.
* @returns {Number} The squared magnitude.
*/
Cartesian3.magnitudeSquared = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return (
cartesian.x * cartesian.x +
cartesian.y * cartesian.y +
cartesian.z * cartesian.z
);
};
/**
* Computes the Cartesian's magnitude (length).
*
* @param {Cartesian3} cartesian The Cartesian instance whose magnitude is to be computed.
* @returns {Number} The magnitude.
*/
Cartesian3.magnitude = function (cartesian) {
return Math.sqrt(Cartesian3.magnitudeSquared(cartesian));
};
var distanceScratch$1 = new Cartesian3();
/**
* Computes the distance between two points.
*
* @param {Cartesian3} left The first point to compute the distance from.
* @param {Cartesian3} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 1.0
* var d = Cesium.Cartesian3.distance(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(2.0, 0.0, 0.0));
*/
Cartesian3.distance = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian3.subtract(left, right, distanceScratch$1);
return Cartesian3.magnitude(distanceScratch$1);
};
/**
* Computes the squared distance between two points. Comparing squared distances
* using this function is more efficient than comparing distances using {@link Cartesian3#distance}.
*
* @param {Cartesian3} left The first point to compute the distance from.
* @param {Cartesian3} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 4.0, not 2.0
* var d = Cesium.Cartesian3.distanceSquared(new Cesium.Cartesian3(1.0, 0.0, 0.0), new Cesium.Cartesian3(3.0, 0.0, 0.0));
*/
Cartesian3.distanceSquared = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian3.subtract(left, right, distanceScratch$1);
return Cartesian3.magnitudeSquared(distanceScratch$1);
};
/**
* Computes the normalized form of the supplied Cartesian.
*
* @param {Cartesian3} cartesian The Cartesian to be normalized.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.normalize = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
var magnitude = Cartesian3.magnitude(cartesian);
result.x = cartesian.x / magnitude;
result.y = cartesian.y / magnitude;
result.z = cartesian.z / magnitude;
//>>includeStart('debug', pragmas.debug);
if (isNaN(result.x) || isNaN(result.y) || isNaN(result.z)) {
throw new Check.DeveloperError("normalized result is not a number");
}
//>>includeEnd('debug');
return result;
};
/**
* Computes the dot (scalar) product of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @returns {Number} The dot product.
*/
Cartesian3.dot = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
//>>includeEnd('debug');
return left.x * right.x + left.y * right.y + left.z * right.z;
};
/**
* Computes the componentwise product of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.multiplyComponents = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x * right.x;
result.y = left.y * right.y;
result.z = left.z * right.z;
return result;
};
/**
* Computes the componentwise quotient of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.divideComponents = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x / right.x;
result.y = left.y / right.y;
result.z = left.z / right.z;
return result;
};
/**
* Computes the componentwise sum of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.add = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x + right.x;
result.y = left.y + right.y;
result.z = left.z + right.z;
return result;
};
/**
* Computes the componentwise difference of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.subtract = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x - right.x;
result.y = left.y - right.y;
result.z = left.z - right.z;
return result;
};
/**
* Multiplies the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian3} cartesian The Cartesian to be scaled.
* @param {Number} scalar The scalar to multiply with.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.multiplyByScalar = function (cartesian, scalar, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.number("scalar", scalar);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = cartesian.x * scalar;
result.y = cartesian.y * scalar;
result.z = cartesian.z * scalar;
return result;
};
/**
* Divides the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian3} cartesian The Cartesian to be divided.
* @param {Number} scalar The scalar to divide by.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.divideByScalar = function (cartesian, scalar, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.number("scalar", scalar);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = cartesian.x / scalar;
result.y = cartesian.y / scalar;
result.z = cartesian.z / scalar;
return result;
};
/**
* Negates the provided Cartesian.
*
* @param {Cartesian3} cartesian The Cartesian to be negated.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.negate = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = -cartesian.x;
result.y = -cartesian.y;
result.z = -cartesian.z;
return result;
};
/**
* Computes the absolute value of the provided Cartesian.
*
* @param {Cartesian3} cartesian The Cartesian whose absolute value is to be computed.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.abs = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.abs(cartesian.x);
result.y = Math.abs(cartesian.y);
result.z = Math.abs(cartesian.z);
return result;
};
var lerpScratch$1 = new Cartesian3();
/**
* Computes the linear interpolation or extrapolation at t using the provided cartesians.
*
* @param {Cartesian3} start The value corresponding to t at 0.0.
* @param {Cartesian3} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Cartesian3.lerp = function (start, end, t, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("start", start);
Check.Check.typeOf.object("end", end);
Check.Check.typeOf.number("t", t);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
Cartesian3.multiplyByScalar(end, t, lerpScratch$1);
result = Cartesian3.multiplyByScalar(start, 1.0 - t, result);
return Cartesian3.add(lerpScratch$1, result, result);
};
var angleBetweenScratch$1 = new Cartesian3();
var angleBetweenScratch2$1 = new Cartesian3();
/**
* Returns the angle, in radians, between the provided Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @returns {Number} The angle between the Cartesians.
*/
Cartesian3.angleBetween = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian3.normalize(left, angleBetweenScratch$1);
Cartesian3.normalize(right, angleBetweenScratch2$1);
var cosine = Cartesian3.dot(angleBetweenScratch$1, angleBetweenScratch2$1);
var sine = Cartesian3.magnitude(
Cartesian3.cross(
angleBetweenScratch$1,
angleBetweenScratch2$1,
angleBetweenScratch$1
)
);
return Math.atan2(sine, cosine);
};
var mostOrthogonalAxisScratch$1 = new Cartesian3();
/**
* Returns the axis that is most orthogonal to the provided Cartesian.
*
* @param {Cartesian3} cartesian The Cartesian on which to find the most orthogonal axis.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The most orthogonal axis.
*/
Cartesian3.mostOrthogonalAxis = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
var f = Cartesian3.normalize(cartesian, mostOrthogonalAxisScratch$1);
Cartesian3.abs(f, f);
if (f.x <= f.y) {
if (f.x <= f.z) {
result = Cartesian3.clone(Cartesian3.UNIT_X, result);
} else {
result = Cartesian3.clone(Cartesian3.UNIT_Z, result);
}
} else if (f.y <= f.z) {
result = Cartesian3.clone(Cartesian3.UNIT_Y, result);
} else {
result = Cartesian3.clone(Cartesian3.UNIT_Z, result);
}
return result;
};
/**
* Projects vector a onto vector b
* @param {Cartesian3} a The vector that needs projecting
* @param {Cartesian3} b The vector to project onto
* @param {Cartesian3} result The result cartesian
* @returns {Cartesian3} The modified result parameter
*/
Cartesian3.projectVector = function (a, b, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("a", a);
Check.Check.defined("b", b);
Check.Check.defined("result", result);
//>>includeEnd('debug');
var scalar = Cartesian3.dot(a, b) / Cartesian3.dot(b, b);
return Cartesian3.multiplyByScalar(b, scalar, result);
};
/**
* Compares the provided Cartesians componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Cartesian3} [left] The first Cartesian.
* @param {Cartesian3} [right] The second Cartesian.
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
*/
Cartesian3.equals = function (left, right) {
return (
left === right ||
(when.defined(left) &&
when.defined(right) &&
left.x === right.x &&
left.y === right.y &&
left.z === right.z)
);
};
/**
* @private
*/
Cartesian3.equalsArray = function (cartesian, array, offset) {
return (
cartesian.x === array[offset] &&
cartesian.y === array[offset + 1] &&
cartesian.z === array[offset + 2]
);
};
/**
* Compares the provided Cartesians componentwise and returns
* <code>true</code> if they pass an absolute or relative tolerance test,
* <code>false</code> otherwise.
*
* @param {Cartesian3} [left] The first Cartesian.
* @param {Cartesian3} [right] The second Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
*/
Cartesian3.equalsEpsilon = function (
left,
right,
relativeEpsilon,
absoluteEpsilon
) {
return (
left === right ||
(when.defined(left) &&
when.defined(right) &&
_Math.CesiumMath.equalsEpsilon(
left.x,
right.x,
relativeEpsilon,
absoluteEpsilon
) &&
_Math.CesiumMath.equalsEpsilon(
left.y,
right.y,
relativeEpsilon,
absoluteEpsilon
) &&
_Math.CesiumMath.equalsEpsilon(
left.z,
right.z,
relativeEpsilon,
absoluteEpsilon
))
);
};
/**
* Computes the cross (outer) product of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The cross product.
*/
Cartesian3.cross = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
var leftX = left.x;
var leftY = left.y;
var leftZ = left.z;
var rightX = right.x;
var rightY = right.y;
var rightZ = right.z;
var x = leftY * rightZ - leftZ * rightY;
var y = leftZ * rightX - leftX * rightZ;
var z = leftX * rightY - leftY * rightX;
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Computes the midpoint between the right and left Cartesian.
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The midpoint.
*/
Cartesian3.midpoint = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = (left.x + right.x) * 0.5;
result.y = (left.y + right.y) * 0.5;
result.z = (left.z + right.z) * 0.5;
return result;
};
/**
* Returns a Cartesian3 position from longitude and latitude values given in degrees.
*
* @param {Number} longitude The longitude, in degrees
* @param {Number} latitude The latitude, in degrees
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*
* @example
* var position = Cesium.Cartesian3.fromDegrees(-115.0, 37.0);
*/
Cartesian3.fromDegrees = function (
longitude,
latitude,
height,
ellipsoid,
result
) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.number("longitude", longitude);
Check.Check.typeOf.number("latitude", latitude);
//>>includeEnd('debug');
longitude = _Math.CesiumMath.toRadians(longitude);
latitude = _Math.CesiumMath.toRadians(latitude);
return Cartesian3.fromRadians(longitude, latitude, height, ellipsoid, result);
};
var scratchN = new Cartesian3();
var scratchK = new Cartesian3();
var wgs84RadiiSquared = new Cartesian3(
6378137.0 * 6378137.0,
6378137.0 * 6378137.0,
6356752.3142451793 * 6356752.3142451793
);
/**
* Returns a Cartesian3 position from longitude and latitude values given in radians.
*
* @param {Number} longitude The longitude, in radians
* @param {Number} latitude The latitude, in radians
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*
* @example
* var position = Cesium.Cartesian3.fromRadians(-2.007, 0.645);
*/
Cartesian3.fromRadians = function (
longitude,
latitude,
height,
ellipsoid,
result
) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.number("longitude", longitude);
Check.Check.typeOf.number("latitude", latitude);
//>>includeEnd('debug');
height = when.defaultValue(height, 0.0);
var radiiSquared = when.defined(ellipsoid)
? ellipsoid.radiiSquared
: wgs84RadiiSquared;
var cosLatitude = Math.cos(latitude);
scratchN.x = cosLatitude * Math.cos(longitude);
scratchN.y = cosLatitude * Math.sin(longitude);
scratchN.z = Math.sin(latitude);
scratchN = Cartesian3.normalize(scratchN, scratchN);
Cartesian3.multiplyComponents(radiiSquared, scratchN, scratchK);
var gamma = Math.sqrt(Cartesian3.dot(scratchN, scratchK));
scratchK = Cartesian3.divideByScalar(scratchK, gamma, scratchK);
scratchN = Cartesian3.multiplyByScalar(scratchN, height, scratchN);
if (!when.defined(result)) {
result = new Cartesian3();
}
return Cartesian3.add(scratchK, scratchN, result);
};
/**
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in degrees.
*
* @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* var positions = Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0, -107.0, 33.0]);
*/
Cartesian3.fromDegreesArray = function (coordinates, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("coordinates", coordinates);
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
throw new Check.DeveloperError(
"the number of coordinates must be a multiple of 2 and at least 2"
);
}
//>>includeEnd('debug');
var length = coordinates.length;
if (!when.defined(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (var i = 0; i < length; i += 2) {
var longitude = coordinates[i];
var latitude = coordinates[i + 1];
var index = i / 2;
result[index] = Cartesian3.fromDegrees(
longitude,
latitude,
0,
ellipsoid,
result[index]
);
}
return result;
};
/**
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in radians.
*
* @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* var positions = Cesium.Cartesian3.fromRadiansArray([-2.007, 0.645, -1.867, .575]);
*/
Cartesian3.fromRadiansArray = function (coordinates, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("coordinates", coordinates);
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
throw new Check.DeveloperError(
"the number of coordinates must be a multiple of 2 and at least 2"
);
}
//>>includeEnd('debug');
var length = coordinates.length;
if (!when.defined(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (var i = 0; i < length; i += 2) {
var longitude = coordinates[i];
var latitude = coordinates[i + 1];
var index = i / 2;
result[index] = Cartesian3.fromRadians(
longitude,
latitude,
0,
ellipsoid,
result[index]
);
}
return result;
};
/**
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in degrees.
*
* @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* var positions = Cesium.Cartesian3.fromDegreesArrayHeights([-115.0, 37.0, 100000.0, -107.0, 33.0, 150000.0]);
*/
Cartesian3.fromDegreesArrayHeights = function (coordinates, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("coordinates", coordinates);
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
throw new Check.DeveloperError(
"the number of coordinates must be a multiple of 3 and at least 3"
);
}
//>>includeEnd('debug');
var length = coordinates.length;
if (!when.defined(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (var i = 0; i < length; i += 3) {
var longitude = coordinates[i];
var latitude = coordinates[i + 1];
var height = coordinates[i + 2];
var index = i / 3;
result[index] = Cartesian3.fromDegrees(
longitude,
latitude,
height,
ellipsoid,
result[index]
);
}
return result;
};
/**
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in radians.
*
* @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* var positions = Cesium.Cartesian3.fromRadiansArrayHeights([-2.007, 0.645, 100000.0, -1.867, .575, 150000.0]);
*/
Cartesian3.fromRadiansArrayHeights = function (coordinates, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("coordinates", coordinates);
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
throw new Check.DeveloperError(
"the number of coordinates must be a multiple of 3 and at least 3"
);
}
//>>includeEnd('debug');
var length = coordinates.length;
if (!when.defined(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (var i = 0; i < length; i += 3) {
var longitude = coordinates[i];
var latitude = coordinates[i + 1];
var height = coordinates[i + 2];
var index = i / 3;
result[index] = Cartesian3.fromRadians(
longitude,
latitude,
height,
ellipsoid,
result[index]
);
}
return result;
};
/**
* An immutable Cartesian3 instance initialized to (0.0, 0.0, 0.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.ZERO = Object.freeze(new Cartesian3(0.0, 0.0, 0.0));
/**
* An immutable Cartesian3 instance initialized to (1.0, 0.0, 0.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.UNIT_X = Object.freeze(new Cartesian3(1.0, 0.0, 0.0));
/**
* An immutable Cartesian3 instance initialized to (0.0, 1.0, 0.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.UNIT_Y = Object.freeze(new Cartesian3(0.0, 1.0, 0.0));
/**
* An immutable Cartesian3 instance initialized to (0.0, 0.0, 1.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.UNIT_Z = Object.freeze(new Cartesian3(0.0, 0.0, 1.0));
/**
* Duplicates this Cartesian3 instance.
*
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.prototype.clone = function (result) {
return Cartesian3.clone(this, result);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Cartesian3} [right] The right hand side Cartesian.
* @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
*/
Cartesian3.prototype.equals = function (right) {
return Cartesian3.equals(this, right);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* <code>true</code> if they pass an absolute or relative tolerance test,
* <code>false</code> otherwise.
*
* @param {Cartesian3} [right] The right hand side Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
*/
Cartesian3.prototype.equalsEpsilon = function (
right,
relativeEpsilon,
absoluteEpsilon
) {
return Cartesian3.equalsEpsilon(
this,
right,
relativeEpsilon,
absoluteEpsilon
);
};
/**
* Creates a string representing this Cartesian in the format '(x, y, z)'.
*
* @returns {String} A string representing this Cartesian in the format '(x, y, z)'.
*/
Cartesian3.prototype.toString = function () {
return "(" + this.x + ", " + this.y + ", " + this.z + ")";
};
var scaleToGeodeticSurfaceIntersection = new Cartesian3();
var scaleToGeodeticSurfaceGradient = new Cartesian3();
/**
* Scales the provided Cartesian position along the geodetic surface normal
* so that it is on the surface of this ellipsoid. If the position is
* at the center of the ellipsoid, this function returns undefined.
*
* @param {Cartesian3} cartesian The Cartesian position to scale.
* @param {Cartesian3} oneOverRadii One over radii of the ellipsoid.
* @param {Cartesian3} oneOverRadiiSquared One over radii squared of the ellipsoid.
* @param {Number} centerToleranceSquared Tolerance for closeness to the center.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
*
* @function scaleToGeodeticSurface
*
* @private
*/
function scaleToGeodeticSurface(
cartesian,
oneOverRadii,
oneOverRadiiSquared,
centerToleranceSquared,
result
) {
//>>includeStart('debug', pragmas.debug);
if (!when.defined(cartesian)) {
throw new Check.DeveloperError("cartesian is required.");
}
if (!when.defined(oneOverRadii)) {
throw new Check.DeveloperError("oneOverRadii is required.");
}
if (!when.defined(oneOverRadiiSquared)) {
throw new Check.DeveloperError("oneOverRadiiSquared is required.");
}
if (!when.defined(centerToleranceSquared)) {
throw new Check.DeveloperError("centerToleranceSquared is required.");
}
//>>includeEnd('debug');
var positionX = cartesian.x;
var positionY = cartesian.y;
var positionZ = cartesian.z;
var oneOverRadiiX = oneOverRadii.x;
var oneOverRadiiY = oneOverRadii.y;
var oneOverRadiiZ = oneOverRadii.z;
var x2 = positionX * positionX * oneOverRadiiX * oneOverRadiiX;
var y2 = positionY * positionY * oneOverRadiiY * oneOverRadiiY;
var z2 = positionZ * positionZ * oneOverRadiiZ * oneOverRadiiZ;
// Compute the squared ellipsoid norm.
var squaredNorm = x2 + y2 + z2;
var ratio = Math.sqrt(1.0 / squaredNorm);
// As an initial approximation, assume that the radial intersection is the projection point.
var intersection = Cartesian3.multiplyByScalar(
cartesian,
ratio,
scaleToGeodeticSurfaceIntersection
);
// If the position is near the center, the iteration will not converge.
if (squaredNorm < centerToleranceSquared) {
return !isFinite(ratio)
? undefined
: Cartesian3.clone(intersection, result);
}
var oneOverRadiiSquaredX = oneOverRadiiSquared.x;
var oneOverRadiiSquaredY = oneOverRadiiSquared.y;
var oneOverRadiiSquaredZ = oneOverRadiiSquared.z;
// Use the gradient at the intersection point in place of the true unit normal.
// The difference in magnitude will be absorbed in the multiplier.
var gradient = scaleToGeodeticSurfaceGradient;
gradient.x = intersection.x * oneOverRadiiSquaredX * 2.0;
gradient.y = intersection.y * oneOverRadiiSquaredY * 2.0;
gradient.z = intersection.z * oneOverRadiiSquaredZ * 2.0;
// Compute the initial guess at the normal vector multiplier, lambda.
var lambda =
((1.0 - ratio) * Cartesian3.magnitude(cartesian)) /
(0.5 * Cartesian3.magnitude(gradient));
var correction = 0.0;
var func;
var denominator;
var xMultiplier;
var yMultiplier;
var zMultiplier;
var xMultiplier2;
var yMultiplier2;
var zMultiplier2;
var xMultiplier3;
var yMultiplier3;
var zMultiplier3;
do {
lambda -= correction;
xMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredX);
yMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredY);
zMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredZ);
xMultiplier2 = xMultiplier * xMultiplier;
yMultiplier2 = yMultiplier * yMultiplier;
zMultiplier2 = zMultiplier * zMultiplier;
xMultiplier3 = xMultiplier2 * xMultiplier;
yMultiplier3 = yMultiplier2 * yMultiplier;
zMultiplier3 = zMultiplier2 * zMultiplier;
func = x2 * xMultiplier2 + y2 * yMultiplier2 + z2 * zMultiplier2 - 1.0;
// "denominator" here refers to the use of this expression in the velocity and acceleration
// computations in the sections to follow.
denominator =
x2 * xMultiplier3 * oneOverRadiiSquaredX +
y2 * yMultiplier3 * oneOverRadiiSquaredY +
z2 * zMultiplier3 * oneOverRadiiSquaredZ;
var derivative = -2.0 * denominator;
correction = func / derivative;
} while (Math.abs(func) > _Math.CesiumMath.EPSILON12);
if (!when.defined(result)) {
return new Cartesian3(
positionX * xMultiplier,
positionY * yMultiplier,
positionZ * zMultiplier
);
}
result.x = positionX * xMultiplier;
result.y = positionY * yMultiplier;
result.z = positionZ * zMultiplier;
return result;
}
/**
* A position defined by longitude, latitude, and height.
* @alias Cartographic
* @constructor
*
* @param {Number} [longitude=0.0] The longitude, in radians.
* @param {Number} [latitude=0.0] The latitude, in radians.
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
*
* @see Ellipsoid
*/
function Cartographic(longitude, latitude, height) {
/**
* The longitude, in radians.
* @type {Number}
* @default 0.0
*/
this.longitude = when.defaultValue(longitude, 0.0);
/**
* The latitude, in radians.
* @type {Number}
* @default 0.0
*/
this.latitude = when.defaultValue(latitude, 0.0);
/**
* The height, in meters, above the ellipsoid.
* @type {Number}
* @default 0.0
*/
this.height = when.defaultValue(height, 0.0);
}
/**
* Creates a new Cartographic instance from longitude and latitude
* specified in radians.
*
* @param {Number} longitude The longitude, in radians.
* @param {Number} latitude The latitude, in radians.
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
*/
Cartographic.fromRadians = function (longitude, latitude, height, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.number("longitude", longitude);
Check.Check.typeOf.number("latitude", latitude);
//>>includeEnd('debug');
height = when.defaultValue(height, 0.0);
if (!when.defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
/**
* Creates a new Cartographic instance from longitude and latitude
* specified in degrees. The values in the resulting object will
* be in radians.
*
* @param {Number} longitude The longitude, in degrees.
* @param {Number} latitude The latitude, in degrees.
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
*/
Cartographic.fromDegrees = function (longitude, latitude, height, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.number("longitude", longitude);
Check.Check.typeOf.number("latitude", latitude);
//>>includeEnd('debug');
longitude = _Math.CesiumMath.toRadians(longitude);
latitude = _Math.CesiumMath.toRadians(latitude);
return Cartographic.fromRadians(longitude, latitude, height, result);
};
var cartesianToCartographicN$1 = new Cartesian3();
var cartesianToCartographicP$1 = new Cartesian3();
var cartesianToCartographicH$1 = new Cartesian3();
var wgs84OneOverRadii = new Cartesian3(
1.0 / 6378137.0,
1.0 / 6378137.0,
1.0 / 6356752.3142451793
);
var wgs84OneOverRadiiSquared = new Cartesian3(
1.0 / (6378137.0 * 6378137.0),
1.0 / (6378137.0 * 6378137.0),
1.0 / (6356752.3142451793 * 6356752.3142451793)
);
var wgs84CenterToleranceSquared = _Math.CesiumMath.EPSILON1;
/**
* Creates a new Cartographic instance from a Cartesian position. The values in the
* resulting object will be in radians.
*
* @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
*/
Cartographic.fromCartesian = function (cartesian, ellipsoid, result) {
var oneOverRadii = when.defined(ellipsoid)
? ellipsoid.oneOverRadii
: wgs84OneOverRadii;
var oneOverRadiiSquared = when.defined(ellipsoid)
? ellipsoid.oneOverRadiiSquared
: wgs84OneOverRadiiSquared;
var centerToleranceSquared = when.defined(ellipsoid)
? ellipsoid._centerToleranceSquared
: wgs84CenterToleranceSquared;
//`cartesian is required.` is thrown from scaleToGeodeticSurface
var p = scaleToGeodeticSurface(
cartesian,
oneOverRadii,
oneOverRadiiSquared,
centerToleranceSquared,
cartesianToCartographicP$1
);
if (!when.defined(p)) {
return undefined;
}
var n = Cartesian3.multiplyComponents(
p,
oneOverRadiiSquared,
cartesianToCartographicN$1
);
n = Cartesian3.normalize(n, n);
var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH$1);
var longitude = Math.atan2(n.y, n.x);
var latitude = Math.asin(n.z);
var height =
_Math.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
if (!when.defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
/**
* Creates a new Cartesian3 instance from a Cartographic input. The values in the inputted
* object should be in radians.
*
* @param {Cartographic} cartographic Input to be converted into a Cartesian3 output.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*/
Cartographic.toCartesian = function (cartographic, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("cartographic", cartographic);
//>>includeEnd('debug');
return Cartesian3.fromRadians(
cartographic.longitude,
cartographic.latitude,
cartographic.height,
ellipsoid,
result
);
};
/**
* Duplicates a Cartographic instance.
*
* @param {Cartographic} cartographic The cartographic to duplicate.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. (Returns undefined if cartographic is undefined)
*/
Cartographic.clone = function (cartographic, result) {
if (!when.defined(cartographic)) {
return undefined;
}
if (!when.defined(result)) {
return new Cartographic(
cartographic.longitude,
cartographic.latitude,
cartographic.height
);
}
result.longitude = cartographic.longitude;
result.latitude = cartographic.latitude;
result.height = cartographic.height;
return result;
};
/**
* Compares the provided cartographics componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Cartographic} [left] The first cartographic.
* @param {Cartographic} [right] The second cartographic.
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
*/
Cartographic.equals = function (left, right) {
return (
left === right ||
(when.defined(left) &&
when.defined(right) &&
left.longitude === right.longitude &&
left.latitude === right.latitude &&
left.height === right.height)
);
};
/**
* Compares the provided cartographics componentwise and returns
* <code>true</code> if they are within the provided epsilon,
* <code>false</code> otherwise.
*
* @param {Cartographic} [left] The first cartographic.
* @param {Cartographic} [right] The second cartographic.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
*/
Cartographic.equalsEpsilon = function (left, right, epsilon) {
epsilon = when.defaultValue(epsilon, 0);
return (
left === right ||
(when.defined(left) &&
when.defined(right) &&
Math.abs(left.longitude - right.longitude) <= epsilon &&
Math.abs(left.latitude - right.latitude) <= epsilon &&
Math.abs(left.height - right.height) <= epsilon)
);
};
/**
* An immutable Cartographic instance initialized to (0.0, 0.0, 0.0).
*
* @type {Cartographic}
* @constant
*/
Cartographic.ZERO = Object.freeze(new Cartographic(0.0, 0.0, 0.0));
/**
* Duplicates this instance.
*
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
*/
Cartographic.prototype.clone = function (result) {
return Cartographic.clone(this, result);
};
/**
* Compares the provided against this cartographic componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Cartographic} [right] The second cartographic.
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
*/
Cartographic.prototype.equals = function (right) {
return Cartographic.equals(this, right);
};
/**
* Compares the provided against this cartographic componentwise and returns
* <code>true</code> if they are within the provided epsilon,
* <code>false</code> otherwise.
*
* @param {Cartographic} [right] The second cartographic.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
*/
Cartographic.prototype.equalsEpsilon = function (right, epsilon) {
return Cartographic.equalsEpsilon(this, right, epsilon);
};
/**
* Creates a string representing this cartographic in the format '(longitude, latitude, height)'.
*
* @returns {String} A string representing the provided cartographic in the format '(longitude, latitude, height)'.
*/
Cartographic.prototype.toString = function () {
return "(" + this.longitude + ", " + this.latitude + ", " + this.height + ")";
};
function initialize(ellipsoid, x, y, z) {
x = when.defaultValue(x, 0.0);
y = when.defaultValue(y, 0.0);
z = when.defaultValue(z, 0.0);
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.number.greaterThanOrEquals("x", x, 0.0);
Check.Check.typeOf.number.greaterThanOrEquals("y", y, 0.0);
Check.Check.typeOf.number.greaterThanOrEquals("z", z, 0.0);
//>>includeEnd('debug');
ellipsoid._radii = new Cartesian3(x, y, z);
ellipsoid._radiiSquared = new Cartesian3(x * x, y * y, z * z);
ellipsoid._radiiToTheFourth = new Cartesian3(
x * x * x * x,
y * y * y * y,
z * z * z * z
);
ellipsoid._oneOverRadii = new Cartesian3(
x === 0.0 ? 0.0 : 1.0 / x,
y === 0.0 ? 0.0 : 1.0 / y,
z === 0.0 ? 0.0 : 1.0 / z
);
ellipsoid._oneOverRadiiSquared = new Cartesian3(
x === 0.0 ? 0.0 : 1.0 / (x * x),
y === 0.0 ? 0.0 : 1.0 / (y * y),
z === 0.0 ? 0.0 : 1.0 / (z * z)
);
ellipsoid._minimumRadius = Math.min(x, y, z);
ellipsoid._maximumRadius = Math.max(x, y, z);
ellipsoid._centerToleranceSquared = _Math.CesiumMath.EPSILON1;
if (ellipsoid._radiiSquared.z !== 0) {
ellipsoid._squaredXOverSquaredZ =
ellipsoid._radiiSquared.x / ellipsoid._radiiSquared.z;
}
}
/**
* A quadratic surface defined in Cartesian coordinates by the equation
* <code>(x / a)^2 + (y / b)^2 + (z / c)^2 = 1</code>. Primarily used
* by Cesium to represent the shape of planetary bodies.
*
* Rather than constructing this object directly, one of the provided
* constants is normally used.
* @alias Ellipsoid
* @constructor
*
* @param {Number} [x=0] The radius in the x direction.
* @param {Number} [y=0] The radius in the y direction.
* @param {Number} [z=0] The radius in the z direction.
*
* @exception {DeveloperError} All radii components must be greater than or equal to zero.
*
* @see Ellipsoid.fromCartesian3
* @see Ellipsoid.WGS84
* @see Ellipsoid.UNIT_SPHERE
*/
function Ellipsoid(x, y, z) {
this._radii = undefined;
this._radiiSquared = undefined;
this._radiiToTheFourth = undefined;
this._oneOverRadii = undefined;
this._oneOverRadiiSquared = undefined;
this._minimumRadius = undefined;
this._maximumRadius = undefined;
this._centerToleranceSquared = undefined;
this._squaredXOverSquaredZ = undefined;
initialize(this, x, y, z);
}
Object.defineProperties(Ellipsoid.prototype, {
/**
* Gets the radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
radii: {
get: function () {
return this._radii;
},
},
/**
* Gets the squared radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
radiiSquared: {
get: function () {
return this._radiiSquared;
},
},
/**
* Gets the radii of the ellipsoid raise to the fourth power.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
radiiToTheFourth: {
get: function () {
return this._radiiToTheFourth;
},
},
/**
* Gets one over the radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
oneOverRadii: {
get: function () {
return this._oneOverRadii;
},
},
/**
* Gets one over the squared radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
oneOverRadiiSquared: {
get: function () {
return this._oneOverRadiiSquared;
},
},
/**
* Gets the minimum radius of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Number}
* @readonly
*/
minimumRadius: {
get: function () {
return this._minimumRadius;
},
},
/**
* Gets the maximum radius of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Number}
* @readonly
*/
maximumRadius: {
get: function () {
return this._maximumRadius;
},
},
});
/**
* Duplicates an Ellipsoid instance.
*
* @param {Ellipsoid} ellipsoid The ellipsoid to duplicate.
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
* instance should be created.
* @returns {Ellipsoid} The cloned Ellipsoid. (Returns undefined if ellipsoid is undefined)
*/
Ellipsoid.clone = function (ellipsoid, result) {
if (!when.defined(ellipsoid)) {
return undefined;
}
var radii = ellipsoid._radii;
if (!when.defined(result)) {
return new Ellipsoid(radii.x, radii.y, radii.z);
}
Cartesian3.clone(radii, result._radii);
Cartesian3.clone(ellipsoid._radiiSquared, result._radiiSquared);
Cartesian3.clone(ellipsoid._radiiToTheFourth, result._radiiToTheFourth);
Cartesian3.clone(ellipsoid._oneOverRadii, result._oneOverRadii);
Cartesian3.clone(ellipsoid._oneOverRadiiSquared, result._oneOverRadiiSquared);
result._minimumRadius = ellipsoid._minimumRadius;
result._maximumRadius = ellipsoid._maximumRadius;
result._centerToleranceSquared = ellipsoid._centerToleranceSquared;
return result;
};
/**
* Computes an Ellipsoid from a Cartesian specifying the radii in x, y, and z directions.
*
* @param {Cartesian3} [cartesian=Cartesian3.ZERO] The ellipsoid's radius in the x, y, and z directions.
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
* instance should be created.
* @returns {Ellipsoid} A new Ellipsoid instance.
*
* @exception {DeveloperError} All radii components must be greater than or equal to zero.
*
* @see Ellipsoid.WGS84
* @see Ellipsoid.UNIT_SPHERE
*/
Ellipsoid.fromCartesian3 = function (cartesian, result) {
if (!when.defined(result)) {
result = new Ellipsoid();
}
if (!when.defined(cartesian)) {
return result;
}
initialize(result, cartesian.x, cartesian.y, cartesian.z);
return result;
};
/**
* An Ellipsoid instance initialized to the WGS84 standard.
*
* @type {Ellipsoid}
* @constant
*/
Ellipsoid.WGS84 = Object.freeze(
new Ellipsoid(6378137.0, 6378137.0, 6356752.3142451793)
);
/**
* An Ellipsoid instance initialized to radii of (1.0, 1.0, 1.0).
*
* @type {Ellipsoid}
* @constant
*/
Ellipsoid.UNIT_SPHERE = Object.freeze(new Ellipsoid(1.0, 1.0, 1.0));
/**
* An Ellipsoid instance initialized to a sphere with the lunar radius.
*
* @type {Ellipsoid}
* @constant
*/
Ellipsoid.MOON = Object.freeze(
new Ellipsoid(
_Math.CesiumMath.LUNAR_RADIUS,
_Math.CesiumMath.LUNAR_RADIUS,
_Math.CesiumMath.LUNAR_RADIUS
)
);
/**
* Duplicates an Ellipsoid instance.
*
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
* instance should be created.
* @returns {Ellipsoid} The cloned Ellipsoid.
*/
Ellipsoid.prototype.clone = function (result) {
return Ellipsoid.clone(this, result);
};
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Ellipsoid.packedLength = Cartesian3.packedLength;
/**
* Stores the provided instance into the provided array.
*
* @param {Ellipsoid} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Ellipsoid.pack = function (value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("value", value);
Check.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = when.defaultValue(startingIndex, 0);
Cartesian3.pack(value._radii, array, startingIndex);
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Ellipsoid} [result] The object into which to store the result.
* @returns {Ellipsoid} The modified result parameter or a new Ellipsoid instance if one was not provided.
*/
Ellipsoid.unpack = function (array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = when.defaultValue(startingIndex, 0);
var radii = Cartesian3.unpack(array, startingIndex);
return Ellipsoid.fromCartesian3(radii, result);
};
/**
* Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position.
* @function
*
* @param {Cartesian3} cartesian The Cartesian for which to to determine the geocentric normal.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.geocentricSurfaceNormal = Cartesian3.normalize;
/**
* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
*
* @param {Cartographic} cartographic The cartographic position for which to to determine the geodetic normal.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.geodeticSurfaceNormalCartographic = function (
cartographic,
result
) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartographic", cartographic);
//>>includeEnd('debug');
var longitude = cartographic.longitude;
var latitude = cartographic.latitude;
var cosLatitude = Math.cos(latitude);
var x = cosLatitude * Math.cos(longitude);
var y = cosLatitude * Math.sin(longitude);
var z = Math.sin(latitude);
if (!when.defined(result)) {
result = new Cartesian3();
}
result.x = x;
result.y = y;
result.z = z;
return Cartesian3.normalize(result, result);
};
/**
* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
*
* @param {Cartesian3} cartesian The Cartesian position for which to to determine the surface normal.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided, or undefined if a normal cannot be found.
*/
Ellipsoid.prototype.geodeticSurfaceNormal = function (cartesian, result) {
if (
Cartesian3.equalsEpsilon(cartesian, Cartesian3.ZERO, _Math.CesiumMath.EPSILON14)
) {
return undefined;
}
if (!when.defined(result)) {
result = new Cartesian3();
}
result = Cartesian3.multiplyComponents(
cartesian,
this._oneOverRadiiSquared,
result
);
return Cartesian3.normalize(result, result);
};
var cartographicToCartesianNormal = new Cartesian3();
var cartographicToCartesianK = new Cartesian3();
/**
* Converts the provided cartographic to Cartesian representation.
*
* @param {Cartographic} cartographic The cartographic position.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*
* @example
* //Create a Cartographic and determine it's Cartesian representation on a WGS84 ellipsoid.
* var position = new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 5000);
* var cartesianPosition = Cesium.Ellipsoid.WGS84.cartographicToCartesian(position);
*/
Ellipsoid.prototype.cartographicToCartesian = function (cartographic, result) {
//`cartographic is required` is thrown from geodeticSurfaceNormalCartographic.
var n = cartographicToCartesianNormal;
var k = cartographicToCartesianK;
this.geodeticSurfaceNormalCartographic(cartographic, n);
Cartesian3.multiplyComponents(this._radiiSquared, n, k);
var gamma = Math.sqrt(Cartesian3.dot(n, k));
Cartesian3.divideByScalar(k, gamma, k);
Cartesian3.multiplyByScalar(n, cartographic.height, n);
if (!when.defined(result)) {
result = new Cartesian3();
}
return Cartesian3.add(k, n, result);
};
/**
* Converts the provided array of cartographics to an array of Cartesians.
*
* @param {Cartographic[]} cartographics An array of cartographic positions.
* @param {Cartesian3[]} [result] The object onto which to store the result.
* @returns {Cartesian3[]} The modified result parameter or a new Array instance if none was provided.
*
* @example
* //Convert an array of Cartographics and determine their Cartesian representation on a WGS84 ellipsoid.
* var positions = [new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 0),
* new Cesium.Cartographic(Cesium.Math.toRadians(21.321), Cesium.Math.toRadians(78.123), 100),
* new Cesium.Cartographic(Cesium.Math.toRadians(21.645), Cesium.Math.toRadians(78.456), 250)];
* var cartesianPositions = Cesium.Ellipsoid.WGS84.cartographicArrayToCartesianArray(positions);
*/
Ellipsoid.prototype.cartographicArrayToCartesianArray = function (
cartographics,
result
) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("cartographics", cartographics);
//>>includeEnd('debug')
var length = cartographics.length;
if (!when.defined(result)) {
result = new Array(length);
} else {
result.length = length;
}
for (var i = 0; i < length; i++) {
result[i] = this.cartographicToCartesian(cartographics[i], result[i]);
}
return result;
};
var cartesianToCartographicN = new Cartesian3();
var cartesianToCartographicP = new Cartesian3();
var cartesianToCartographicH = new Cartesian3();
/**
* Converts the provided cartesian to cartographic representation.
* The cartesian is undefined at the center of the ellipsoid.
*
* @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
*
* @example
* //Create a Cartesian and determine it's Cartographic representation on a WGS84 ellipsoid.
* var position = new Cesium.Cartesian3(17832.12, 83234.52, 952313.73);
* var cartographicPosition = Cesium.Ellipsoid.WGS84.cartesianToCartographic(position);
*/
Ellipsoid.prototype.cartesianToCartographic = function (cartesian, result) {
//`cartesian is required.` is thrown from scaleToGeodeticSurface
var p = this.scaleToGeodeticSurface(cartesian, cartesianToCartographicP);
if (!when.defined(p)) {
return undefined;
}
var n = this.geodeticSurfaceNormal(p, cartesianToCartographicN);
var h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);
var longitude = Math.atan2(n.y, n.x);
var latitude = Math.asin(n.z);
var height =
_Math.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
if (!when.defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
/**
* Converts the provided array of cartesians to an array of cartographics.
*
* @param {Cartesian3[]} cartesians An array of Cartesian positions.
* @param {Cartographic[]} [result] The object onto which to store the result.
* @returns {Cartographic[]} The modified result parameter or a new Array instance if none was provided.
*
* @example
* //Create an array of Cartesians and determine their Cartographic representation on a WGS84 ellipsoid.
* var positions = [new Cesium.Cartesian3(17832.12, 83234.52, 952313.73),
* new Cesium.Cartesian3(17832.13, 83234.53, 952313.73),
* new Cesium.Cartesian3(17832.14, 83234.54, 952313.73)]
* var cartographicPositions = Cesium.Ellipsoid.WGS84.cartesianArrayToCartographicArray(positions);
*/
Ellipsoid.prototype.cartesianArrayToCartographicArray = function (
cartesians,
result
) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("cartesians", cartesians);
//>>includeEnd('debug');
var length = cartesians.length;
if (!when.defined(result)) {
result = new Array(length);
} else {
result.length = length;
}
for (var i = 0; i < length; ++i) {
result[i] = this.cartesianToCartographic(cartesians[i], result[i]);
}
return result;
};
/**
* Scales the provided Cartesian position along the geodetic surface normal
* so that it is on the surface of this ellipsoid. If the position is
* at the center of the ellipsoid, this function returns undefined.
*
* @param {Cartesian3} cartesian The Cartesian position to scale.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
*/
Ellipsoid.prototype.scaleToGeodeticSurface = function (cartesian, result) {
return scaleToGeodeticSurface(
cartesian,
this._oneOverRadii,
this._oneOverRadiiSquared,
this._centerToleranceSquared,
result
);
};
/**
* Scales the provided Cartesian position along the geocentric surface normal
* so that it is on the surface of this ellipsoid.
*
* @param {Cartesian3} cartesian The Cartesian position to scale.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.scaleToGeocentricSurface = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
if (!when.defined(result)) {
result = new Cartesian3();
}
var positionX = cartesian.x;
var positionY = cartesian.y;
var positionZ = cartesian.z;
var oneOverRadiiSquared = this._oneOverRadiiSquared;
var beta =
1.0 /
Math.sqrt(
positionX * positionX * oneOverRadiiSquared.x +
positionY * positionY * oneOverRadiiSquared.y +
positionZ * positionZ * oneOverRadiiSquared.z
);
return Cartesian3.multiplyByScalar(cartesian, beta, result);
};
/**
* Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying
* its components by the result of {@link Ellipsoid#oneOverRadii}.
*
* @param {Cartesian3} position The position to transform.
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
* return a new instance.
* @returns {Cartesian3} The position expressed in the scaled space. The returned instance is the
* one passed as the result parameter if it is not undefined, or a new instance of it is.
*/
Ellipsoid.prototype.transformPositionToScaledSpace = function (
position,
result
) {
if (!when.defined(result)) {
result = new Cartesian3();
}
return Cartesian3.multiplyComponents(position, this._oneOverRadii, result);
};
/**
* Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying
* its components by the result of {@link Ellipsoid#radii}.
*
* @param {Cartesian3} position The position to transform.
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
* return a new instance.
* @returns {Cartesian3} The position expressed in the unscaled space. The returned instance is the
* one passed as the result parameter if it is not undefined, or a new instance of it is.
*/
Ellipsoid.prototype.transformPositionFromScaledSpace = function (
position,
result
) {
if (!when.defined(result)) {
result = new Cartesian3();
}
return Cartesian3.multiplyComponents(position, this._radii, result);
};
/**
* Compares this Ellipsoid against the provided Ellipsoid componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Ellipsoid} [right] The other Ellipsoid.
* @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
*/
Ellipsoid.prototype.equals = function (right) {
return (
this === right ||
(when.defined(right) && Cartesian3.equals(this._radii, right._radii))
);
};
/**
* Creates a string representing this Ellipsoid in the format '(radii.x, radii.y, radii.z)'.
*
* @returns {String} A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'.
*/
Ellipsoid.prototype.toString = function () {
return this._radii.toString();
};
/**
* Computes a point which is the intersection of the surface normal with the z-axis.
*
* @param {Cartesian3} position the position. must be on the surface of the ellipsoid.
* @param {Number} [buffer = 0.0] A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid.
* In earth case, with common earth datums, there is no need for this buffer since the intersection point is always (relatively) very close to the center.
* In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis).
* Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2
* @param {Cartesian3} [result] The cartesian to which to copy the result, or undefined to create and
* return a new instance.
* @returns {Cartesian3 | undefined} the intersection point if it's inside the ellipsoid, undefined otherwise
*
* @exception {DeveloperError} position is required.
* @exception {DeveloperError} Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y).
* @exception {DeveloperError} Ellipsoid.radii.z must be greater than 0.
*/
Ellipsoid.prototype.getSurfaceNormalIntersectionWithZAxis = function (
position,
buffer,
result
) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("position", position);
if (
!_Math.CesiumMath.equalsEpsilon(
this._radii.x,
this._radii.y,
_Math.CesiumMath.EPSILON15
)
) {
throw new Check.DeveloperError(
"Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)"
);
}
Check.Check.typeOf.number.greaterThan("Ellipsoid.radii.z", this._radii.z, 0);
//>>includeEnd('debug');
buffer = when.defaultValue(buffer, 0.0);
var squaredXOverSquaredZ = this._squaredXOverSquaredZ;
if (!when.defined(result)) {
result = new Cartesian3();
}
result.x = 0.0;
result.y = 0.0;
result.z = position.z * (1 - squaredXOverSquaredZ);
if (Math.abs(result.z) >= this._radii.z - buffer) {
return undefined;
}
return result;
};
var abscissas = [
0.14887433898163,
0.43339539412925,
0.67940956829902,
0.86506336668898,
0.97390652851717,
0.0,
];
var weights = [
0.29552422471475,
0.26926671930999,
0.21908636251598,
0.14945134915058,
0.066671344308684,
0.0,
];
/**
* Compute the 10th order Gauss-Legendre Quadrature of the given definite integral.
*
* @param {Number} a The lower bound for the integration.
* @param {Number} b The upper bound for the integration.
* @param {Ellipsoid~RealValuedScalarFunction} func The function to integrate.
* @returns {Number} The value of the integral of the given function over the given domain.
*
* @private
*/
function gaussLegendreQuadrature(a, b, func) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.number("a", a);
Check.Check.typeOf.number("b", b);
Check.Check.typeOf.func("func", func);
//>>includeEnd('debug');
// The range is half of the normal range since the five weights add to one (ten weights add to two).
// The values of the abscissas are multiplied by two to account for this.
var xMean = 0.5 * (b + a);
var xRange = 0.5 * (b - a);
var sum = 0.0;
for (var i = 0; i < 5; i++) {
var dx = xRange * abscissas[i];
sum += weights[i] * (func(xMean + dx) + func(xMean - dx));
}
// Scale the sum to the range of x.
sum *= xRange;
return sum;
}
/**
* A real valued scalar function.
* @callback Ellipsoid~RealValuedScalarFunction
*
* @param {Number} x The value used to evaluate the function.
* @returns {Number} The value of the function at x.
*
* @private
*/
/**
* Computes an approximation of the surface area of a rectangle on the surface of an ellipsoid using
* Gauss-Legendre 10th order quadrature.
*
* @param {Rectangle} rectangle The rectangle used for computing the surface area.
* @returns {Number} The approximate area of the rectangle on the surface of this ellipsoid.
*/
Ellipsoid.prototype.surfaceArea = function (rectangle) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
var minLongitude = rectangle.west;
var maxLongitude = rectangle.east;
var minLatitude = rectangle.south;
var maxLatitude = rectangle.north;
while (maxLongitude < minLongitude) {
maxLongitude += _Math.CesiumMath.TWO_PI;
}
var radiiSquared = this._radiiSquared;
var a2 = radiiSquared.x;
var b2 = radiiSquared.y;
var c2 = radiiSquared.z;
var a2b2 = a2 * b2;
return gaussLegendreQuadrature(minLatitude, maxLatitude, function (lat) {
// phi represents the angle measured from the north pole
// sin(phi) = sin(pi / 2 - lat) = cos(lat), cos(phi) is similar
var sinPhi = Math.cos(lat);
var cosPhi = Math.sin(lat);
return (
Math.cos(lat) *
gaussLegendreQuadrature(minLongitude, maxLongitude, function (lon) {
var cosTheta = Math.cos(lon);
var sinTheta = Math.sin(lon);
return Math.sqrt(
a2b2 * cosPhi * cosPhi +
c2 *
(b2 * cosTheta * cosTheta + a2 * sinTheta * sinTheta) *
sinPhi *
sinPhi
);
})
);
});
};
/**
* A two dimensional region specified as longitude and latitude coordinates.
*
* @alias Rectangle
* @constructor
*
* @param {Number} [west=0.0] The westernmost longitude, in radians, in the range [-Pi, Pi].
* @param {Number} [south=0.0] The southernmost latitude, in radians, in the range [-Pi/2, Pi/2].
* @param {Number} [east=0.0] The easternmost longitude, in radians, in the range [-Pi, Pi].
* @param {Number} [north=0.0] The northernmost latitude, in radians, in the range [-Pi/2, Pi/2].
*
* @see Packable
*/
function Rectangle(west, south, east, north) {
/**
* The westernmost longitude in radians in the range [-Pi, Pi].
*
* @type {Number}
* @default 0.0
*/
this.west = when.defaultValue(west, 0.0);
/**
* The southernmost latitude in radians in the range [-Pi/2, Pi/2].
*
* @type {Number}
* @default 0.0
*/
this.south = when.defaultValue(south, 0.0);
/**
* The easternmost longitude in radians in the range [-Pi, Pi].
*
* @type {Number}
* @default 0.0
*/
this.east = when.defaultValue(east, 0.0);
/**
* The northernmost latitude in radians in the range [-Pi/2, Pi/2].
*
* @type {Number}
* @default 0.0
*/
this.north = when.defaultValue(north, 0.0);
}
Object.defineProperties(Rectangle.prototype, {
/**
* Gets the width of the rectangle in radians.
* @memberof Rectangle.prototype
* @type {Number}
* @readonly
*/
width: {
get: function () {
return Rectangle.computeWidth(this);
},
},
/**
* Gets the height of the rectangle in radians.
* @memberof Rectangle.prototype
* @type {Number}
* @readonly
*/
height: {
get: function () {
return Rectangle.computeHeight(this);
},
},
});
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Rectangle.packedLength = 4;
/**
* Stores the provided instance into the provided array.
*
* @param {Rectangle} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Rectangle.pack = function (value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("value", value);
Check.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = when.defaultValue(startingIndex, 0);
array[startingIndex++] = value.west;
array[startingIndex++] = value.south;
array[startingIndex++] = value.east;
array[startingIndex] = value.north;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Rectangle} [result] The object into which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
*/
Rectangle.unpack = function (array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = when.defaultValue(startingIndex, 0);
if (!when.defined(result)) {
result = new Rectangle();
}
result.west = array[startingIndex++];
result.south = array[startingIndex++];
result.east = array[startingIndex++];
result.north = array[startingIndex];
return result;
};
/**
* Computes the width of a rectangle in radians.
* @param {Rectangle} rectangle The rectangle to compute the width of.
* @returns {Number} The width.
*/
Rectangle.computeWidth = function (rectangle) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
var east = rectangle.east;
var west = rectangle.west;
if (east < west) {
east += _Math.CesiumMath.TWO_PI;
}
return east - west;
};
/**
* Computes the height of a rectangle in radians.
* @param {Rectangle} rectangle The rectangle to compute the height of.
* @returns {Number} The height.
*/
Rectangle.computeHeight = function (rectangle) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
return rectangle.north - rectangle.south;
};
/**
* Creates a rectangle given the boundary longitude and latitude in degrees.
*
* @param {Number} [west=0.0] The westernmost longitude in degrees in the range [-180.0, 180.0].
* @param {Number} [south=0.0] The southernmost latitude in degrees in the range [-90.0, 90.0].
* @param {Number} [east=0.0] The easternmost longitude in degrees in the range [-180.0, 180.0].
* @param {Number} [north=0.0] The northernmost latitude in degrees in the range [-90.0, 90.0].
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*
* @example
* var rectangle = Cesium.Rectangle.fromDegrees(0.0, 20.0, 10.0, 30.0);
*/
Rectangle.fromDegrees = function (west, south, east, north, result) {
west = _Math.CesiumMath.toRadians(when.defaultValue(west, 0.0));
south = _Math.CesiumMath.toRadians(when.defaultValue(south, 0.0));
east = _Math.CesiumMath.toRadians(when.defaultValue(east, 0.0));
north = _Math.CesiumMath.toRadians(when.defaultValue(north, 0.0));
if (!when.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Creates a rectangle given the boundary longitude and latitude in radians.
*
* @param {Number} [west=0.0] The westernmost longitude in radians in the range [-Math.PI, Math.PI].
* @param {Number} [south=0.0] The southernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].
* @param {Number} [east=0.0] The easternmost longitude in radians in the range [-Math.PI, Math.PI].
* @param {Number} [north=0.0] The northernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*
* @example
* var rectangle = Cesium.Rectangle.fromRadians(0.0, Math.PI/4, Math.PI/8, 3*Math.PI/4);
*/
Rectangle.fromRadians = function (west, south, east, north, result) {
if (!when.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = when.defaultValue(west, 0.0);
result.south = when.defaultValue(south, 0.0);
result.east = when.defaultValue(east, 0.0);
result.north = when.defaultValue(north, 0.0);
return result;
};
/**
* Creates the smallest possible Rectangle that encloses all positions in the provided array.
*
* @param {Cartographic[]} cartographics The list of Cartographic instances.
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.fromCartographicArray = function (cartographics, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("cartographics", cartographics);
//>>includeEnd('debug');
var west = Number.MAX_VALUE;
var east = -Number.MAX_VALUE;
var westOverIDL = Number.MAX_VALUE;
var eastOverIDL = -Number.MAX_VALUE;
var south = Number.MAX_VALUE;
var north = -Number.MAX_VALUE;
for (var i = 0, len = cartographics.length; i < len; i++) {
var position = cartographics[i];
west = Math.min(west, position.longitude);
east = Math.max(east, position.longitude);
south = Math.min(south, position.latitude);
north = Math.max(north, position.latitude);
var lonAdjusted =
position.longitude >= 0
? position.longitude
: position.longitude + _Math.CesiumMath.TWO_PI;
westOverIDL = Math.min(westOverIDL, lonAdjusted);
eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
}
if (east - west > eastOverIDL - westOverIDL) {
west = westOverIDL;
east = eastOverIDL;
if (east > _Math.CesiumMath.PI) {
east = east - _Math.CesiumMath.TWO_PI;
}
if (west > _Math.CesiumMath.PI) {
west = west - _Math.CesiumMath.TWO_PI;
}
}
if (!when.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Creates the smallest possible Rectangle that encloses all positions in the provided array.
*
* @param {Cartesian3[]} cartesians The list of Cartesian instances.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid the cartesians are on.
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.fromCartesianArray = function (cartesians, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("cartesians", cartesians);
//>>includeEnd('debug');
ellipsoid = when.defaultValue(ellipsoid, Ellipsoid.WGS84);
var west = Number.MAX_VALUE;
var east = -Number.MAX_VALUE;
var westOverIDL = Number.MAX_VALUE;
var eastOverIDL = -Number.MAX_VALUE;
var south = Number.MAX_VALUE;
var north = -Number.MAX_VALUE;
for (var i = 0, len = cartesians.length; i < len; i++) {
var position = ellipsoid.cartesianToCartographic(cartesians[i]);
west = Math.min(west, position.longitude);
east = Math.max(east, position.longitude);
south = Math.min(south, position.latitude);
north = Math.max(north, position.latitude);
var lonAdjusted =
position.longitude >= 0
? position.longitude
: position.longitude + _Math.CesiumMath.TWO_PI;
westOverIDL = Math.min(westOverIDL, lonAdjusted);
eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
}
if (east - west > eastOverIDL - westOverIDL) {
west = westOverIDL;
east = eastOverIDL;
if (east > _Math.CesiumMath.PI) {
east = east - _Math.CesiumMath.TWO_PI;
}
if (west > _Math.CesiumMath.PI) {
west = west - _Math.CesiumMath.TWO_PI;
}
}
if (!when.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Duplicates a Rectangle.
*
* @param {Rectangle} rectangle The rectangle to clone.
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. (Returns undefined if rectangle is undefined)
*/
Rectangle.clone = function (rectangle, result) {
if (!when.defined(rectangle)) {
return undefined;
}
if (!when.defined(result)) {
return new Rectangle(
rectangle.west,
rectangle.south,
rectangle.east,
rectangle.north
);
}
result.west = rectangle.west;
result.south = rectangle.south;
result.east = rectangle.east;
result.north = rectangle.north;
return result;
};
/**
* Compares the provided Rectangles componentwise and returns
* <code>true</code> if they pass an absolute or relative tolerance test,
* <code>false</code> otherwise.
*
* @param {Rectangle} [left] The first Rectangle.
* @param {Rectangle} [right] The second Rectangle.
* @param {Number} [absoluteEpsilon=0] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
*/
Rectangle.equalsEpsilon = function (left, right, absoluteEpsilon) {
absoluteEpsilon = when.defaultValue(absoluteEpsilon, 0);
return (
left === right ||
(when.defined(left) &&
when.defined(right) &&
Math.abs(left.west - right.west) <= absoluteEpsilon &&
Math.abs(left.south - right.south) <= absoluteEpsilon &&
Math.abs(left.east - right.east) <= absoluteEpsilon &&
Math.abs(left.north - right.north) <= absoluteEpsilon)
);
};
/**
* Duplicates this Rectangle.
*
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.prototype.clone = function (result) {
return Rectangle.clone(this, result);
};
/**
* Compares the provided Rectangle with this Rectangle componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Rectangle} [other] The Rectangle to compare.
* @returns {Boolean} <code>true</code> if the Rectangles are equal, <code>false</code> otherwise.
*/
Rectangle.prototype.equals = function (other) {
return Rectangle.equals(this, other);
};
/**
* Compares the provided rectangles and returns <code>true</code> if they are equal,
* <code>false</code> otherwise.
*
* @param {Rectangle} [left] The first Rectangle.
* @param {Rectangle} [right] The second Rectangle.
* @returns {Boolean} <code>true</code> if left and right are equal; otherwise <code>false</code>.
*/
Rectangle.equals = function (left, right) {
return (
left === right ||
(when.defined(left) &&
when.defined(right) &&
left.west === right.west &&
left.south === right.south &&
left.east === right.east &&
left.north === right.north)
);
};
/**
* Compares the provided Rectangle with this Rectangle componentwise and returns
* <code>true</code> if they are within the provided epsilon,
* <code>false</code> otherwise.
*
* @param {Rectangle} [other] The Rectangle to compare.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} <code>true</code> if the Rectangles are within the provided epsilon, <code>false</code> otherwise.
*/
Rectangle.prototype.equalsEpsilon = function (other, epsilon) {
return Rectangle.equalsEpsilon(this, other, epsilon);
};
/**
* Checks a Rectangle's properties and throws if they are not in valid ranges.
*
* @param {Rectangle} rectangle The rectangle to validate
*
* @exception {DeveloperError} <code>north</code> must be in the interval [<code>-Pi/2</code>, <code>Pi/2</code>].
* @exception {DeveloperError} <code>south</code> must be in the interval [<code>-Pi/2</code>, <code>Pi/2</code>].
* @exception {DeveloperError} <code>east</code> must be in the interval [<code>-Pi</code>, <code>Pi</code>].
* @exception {DeveloperError} <code>west</code> must be in the interval [<code>-Pi</code>, <code>Pi</code>].
*/
Rectangle.validate = function (rectangle) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
var north = rectangle.north;
Check.Check.typeOf.number.greaterThanOrEquals(
"north",
north,
-_Math.CesiumMath.PI_OVER_TWO
);
Check.Check.typeOf.number.lessThanOrEquals("north", north, _Math.CesiumMath.PI_OVER_TWO);
var south = rectangle.south;
Check.Check.typeOf.number.greaterThanOrEquals(
"south",
south,
-_Math.CesiumMath.PI_OVER_TWO
);
Check.Check.typeOf.number.lessThanOrEquals("south", south, _Math.CesiumMath.PI_OVER_TWO);
var west = rectangle.west;
Check.Check.typeOf.number.greaterThanOrEquals("west", west, -Math.PI);
Check.Check.typeOf.number.lessThanOrEquals("west", west, Math.PI);
var east = rectangle.east;
Check.Check.typeOf.number.greaterThanOrEquals("east", east, -Math.PI);
Check.Check.typeOf.number.lessThanOrEquals("east", east, Math.PI);
//>>includeEnd('debug');
};
/**
* Computes the southwest corner of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.southwest = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
if (!when.defined(result)) {
return new Cartographic(rectangle.west, rectangle.south);
}
result.longitude = rectangle.west;
result.latitude = rectangle.south;
result.height = 0.0;
return result;
};
/**
* Computes the northwest corner of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.northwest = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
if (!when.defined(result)) {
return new Cartographic(rectangle.west, rectangle.north);
}
result.longitude = rectangle.west;
result.latitude = rectangle.north;
result.height = 0.0;
return result;
};
/**
* Computes the northeast corner of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.northeast = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
if (!when.defined(result)) {
return new Cartographic(rectangle.east, rectangle.north);
}
result.longitude = rectangle.east;
result.latitude = rectangle.north;
result.height = 0.0;
return result;
};
/**
* Computes the southeast corner of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.southeast = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
if (!when.defined(result)) {
return new Cartographic(rectangle.east, rectangle.south);
}
result.longitude = rectangle.east;
result.latitude = rectangle.south;
result.height = 0.0;
return result;
};
/**
* Computes the center of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the center
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.center = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
var east = rectangle.east;
var west = rectangle.west;
if (east < west) {
east += _Math.CesiumMath.TWO_PI;
}
var longitude = _Math.CesiumMath.negativePiToPi((west + east) * 0.5);
var latitude = (rectangle.south + rectangle.north) * 0.5;
if (!when.defined(result)) {
return new Cartographic(longitude, latitude);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = 0.0;
return result;
};
/**
* Computes the intersection of two rectangles. This function assumes that the rectangle's coordinates are
* latitude and longitude in radians and produces a correct intersection, taking into account the fact that
* the same angle can be represented with multiple values as well as the wrapping of longitude at the
* anti-meridian. For a simple intersection that ignores these factors and can be used with projected
* coordinates, see {@link Rectangle.simpleIntersection}.
*
* @param {Rectangle} rectangle On rectangle to find an intersection
* @param {Rectangle} otherRectangle Another rectangle to find an intersection
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
*/
Rectangle.intersection = function (rectangle, otherRectangle, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
Check.Check.typeOf.object("otherRectangle", otherRectangle);
//>>includeEnd('debug');
var rectangleEast = rectangle.east;
var rectangleWest = rectangle.west;
var otherRectangleEast = otherRectangle.east;
var otherRectangleWest = otherRectangle.west;
if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {
rectangleEast += _Math.CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
otherRectangleEast += _Math.CesiumMath.TWO_PI;
}
if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
otherRectangleWest += _Math.CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
rectangleWest += _Math.CesiumMath.TWO_PI;
}
var west = _Math.CesiumMath.negativePiToPi(
Math.max(rectangleWest, otherRectangleWest)
);
var east = _Math.CesiumMath.negativePiToPi(
Math.min(rectangleEast, otherRectangleEast)
);
if (
(rectangle.west < rectangle.east ||
otherRectangle.west < otherRectangle.east) &&
east <= west
) {
return undefined;
}
var south = Math.max(rectangle.south, otherRectangle.south);
var north = Math.min(rectangle.north, otherRectangle.north);
if (south >= north) {
return undefined;
}
if (!when.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Computes a simple intersection of two rectangles. Unlike {@link Rectangle.intersection}, this function
* does not attempt to put the angular coordinates into a consistent range or to account for crossing the
* anti-meridian. As such, it can be used for rectangles where the coordinates are not simply latitude
* and longitude (i.e. projected coordinates).
*
* @param {Rectangle} rectangle On rectangle to find an intersection
* @param {Rectangle} otherRectangle Another rectangle to find an intersection
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
*/
Rectangle.simpleIntersection = function (rectangle, otherRectangle, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
Check.Check.typeOf.object("otherRectangle", otherRectangle);
//>>includeEnd('debug');
var west = Math.max(rectangle.west, otherRectangle.west);
var south = Math.max(rectangle.south, otherRectangle.south);
var east = Math.min(rectangle.east, otherRectangle.east);
var north = Math.min(rectangle.north, otherRectangle.north);
if (south >= north || west >= east) {
return undefined;
}
if (!when.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Computes a rectangle that is the union of two rectangles.
*
* @param {Rectangle} rectangle A rectangle to enclose in rectangle.
* @param {Rectangle} otherRectangle A rectangle to enclose in a rectangle.
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.union = function (rectangle, otherRectangle, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
Check.Check.typeOf.object("otherRectangle", otherRectangle);
//>>includeEnd('debug');
if (!when.defined(result)) {
result = new Rectangle();
}
var rectangleEast = rectangle.east;
var rectangleWest = rectangle.west;
var otherRectangleEast = otherRectangle.east;
var otherRectangleWest = otherRectangle.west;
if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {
rectangleEast += _Math.CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
otherRectangleEast += _Math.CesiumMath.TWO_PI;
}
if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
otherRectangleWest += _Math.CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
rectangleWest += _Math.CesiumMath.TWO_PI;
}
var west = _Math.CesiumMath.convertLongitudeRange(
Math.min(rectangleWest, otherRectangleWest)
);
var east = _Math.CesiumMath.convertLongitudeRange(
Math.max(rectangleEast, otherRectangleEast)
);
result.west = west;
result.south = Math.min(rectangle.south, otherRectangle.south);
result.east = east;
result.north = Math.max(rectangle.north, otherRectangle.north);
return result;
};
/**
* Computes a rectangle by enlarging the provided rectangle until it contains the provided cartographic.
*
* @param {Rectangle} rectangle A rectangle to expand.
* @param {Cartographic} cartographic A cartographic to enclose in a rectangle.
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
*/
Rectangle.expand = function (rectangle, cartographic, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
Check.Check.typeOf.object("cartographic", cartographic);
//>>includeEnd('debug');
if (!when.defined(result)) {
result = new Rectangle();
}
result.west = Math.min(rectangle.west, cartographic.longitude);
result.south = Math.min(rectangle.south, cartographic.latitude);
result.east = Math.max(rectangle.east, cartographic.longitude);
result.north = Math.max(rectangle.north, cartographic.latitude);
return result;
};
/**
* Returns true if the cartographic is on or inside the rectangle, false otherwise.
*
* @param {Rectangle} rectangle The rectangle
* @param {Cartographic} cartographic The cartographic to test.
* @returns {Boolean} true if the provided cartographic is inside the rectangle, false otherwise.
*/
Rectangle.contains = function (rectangle, cartographic) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
Check.Check.typeOf.object("cartographic", cartographic);
//>>includeEnd('debug');
var longitude = cartographic.longitude;
var latitude = cartographic.latitude;
var west = rectangle.west;
var east = rectangle.east;
if (east < west) {
east += _Math.CesiumMath.TWO_PI;
if (longitude < 0.0) {
longitude += _Math.CesiumMath.TWO_PI;
}
}
return (
(longitude > west ||
_Math.CesiumMath.equalsEpsilon(longitude, west, _Math.CesiumMath.EPSILON14)) &&
(longitude < east ||
_Math.CesiumMath.equalsEpsilon(longitude, east, _Math.CesiumMath.EPSILON14)) &&
latitude >= rectangle.south &&
latitude <= rectangle.north
);
};
var subsampleLlaScratch = new Cartographic();
/**
* Samples a rectangle so that it includes a list of Cartesian points suitable for passing to
* {@link BoundingSphere#fromPoints}. Sampling is necessary to account
* for rectangles that cover the poles or cross the equator.
*
* @param {Rectangle} rectangle The rectangle to subsample.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid to use.
* @param {Number} [surfaceHeight=0.0] The height of the rectangle above the ellipsoid.
* @param {Cartesian3[]} [result] The array of Cartesians onto which to store the result.
* @returns {Cartesian3[]} The modified result parameter or a new Array of Cartesians instances if none was provided.
*/
Rectangle.subsample = function (rectangle, ellipsoid, surfaceHeight, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
ellipsoid = when.defaultValue(ellipsoid, Ellipsoid.WGS84);
surfaceHeight = when.defaultValue(surfaceHeight, 0.0);
if (!when.defined(result)) {
result = [];
}
var length = 0;
var north = rectangle.north;
var south = rectangle.south;
var east = rectangle.east;
var west = rectangle.west;
var lla = subsampleLlaScratch;
lla.height = surfaceHeight;
lla.longitude = west;
lla.latitude = north;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.longitude = east;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.latitude = south;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.longitude = west;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
if (north < 0.0) {
lla.latitude = north;
} else if (south > 0.0) {
lla.latitude = south;
} else {
lla.latitude = 0.0;
}
for (var i = 1; i < 8; ++i) {
lla.longitude = -Math.PI + i * _Math.CesiumMath.PI_OVER_TWO;
if (Rectangle.contains(rectangle, lla)) {
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
}
}
if (lla.latitude === 0.0) {
lla.longitude = west;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.longitude = east;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
}
result.length = length;
return result;
};
/**
* The largest possible rectangle.
*
* @type {Rectangle}
* @constant
*/
Rectangle.MAX_VALUE = Object.freeze(
new Rectangle(
-Math.PI,
-_Math.CesiumMath.PI_OVER_TWO,
Math.PI,
_Math.CesiumMath.PI_OVER_TWO
)
);
/**
* A 2D Cartesian point.
* @alias Cartesian2
* @constructor
*
* @param {Number} [x=0.0] The X component.
* @param {Number} [y=0.0] The Y component.
*
* @see Cartesian3
* @see Cartesian4
* @see Packable
*/
function Cartesian2(x, y) {
/**
* The X component.
* @type {Number}
* @default 0.0
*/
this.x = when.defaultValue(x, 0.0);
/**
* The Y component.
* @type {Number}
* @default 0.0
*/
this.y = when.defaultValue(y, 0.0);
}
/**
* Creates a Cartesian2 instance from x and y coordinates.
*
* @param {Number} x The x coordinate.
* @param {Number} y The y coordinate.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.fromElements = function (x, y, result) {
if (!when.defined(result)) {
return new Cartesian2(x, y);
}
result.x = x;
result.y = y;
return result;
};
/**
* Duplicates a Cartesian2 instance.
*
* @param {Cartesian2} cartesian The Cartesian to duplicate.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. (Returns undefined if cartesian is undefined)
*/
Cartesian2.clone = function (cartesian, result) {
if (!when.defined(cartesian)) {
return undefined;
}
if (!when.defined(result)) {
return new Cartesian2(cartesian.x, cartesian.y);
}
result.x = cartesian.x;
result.y = cartesian.y;
return result;
};
/**
* Creates a Cartesian2 instance from an existing Cartesian3. This simply takes the
* x and y properties of the Cartesian3 and drops z.
* @function
*
* @param {Cartesian3} cartesian The Cartesian3 instance to create a Cartesian2 instance from.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.fromCartesian3 = Cartesian2.clone;
/**
* Creates a Cartesian2 instance from an existing Cartesian4. This simply takes the
* x and y properties of the Cartesian4 and drops z and w.
* @function
*
* @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian2 instance from.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.fromCartesian4 = Cartesian2.clone;
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Cartesian2.packedLength = 2;
/**
* Stores the provided instance into the provided array.
*
* @param {Cartesian2} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Cartesian2.pack = function (value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("value", value);
Check.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = when.defaultValue(startingIndex, 0);
array[startingIndex++] = value.x;
array[startingIndex] = value.y;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Cartesian2} [result] The object into which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.unpack = function (array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = when.defaultValue(startingIndex, 0);
if (!when.defined(result)) {
result = new Cartesian2();
}
result.x = array[startingIndex++];
result.y = array[startingIndex];
return result;
};
/**
* Flattens an array of Cartesian2s into and array of components.
*
* @param {Cartesian2[]} array The array of cartesians to pack.
* @param {Number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 2 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 2) elements.
* @returns {Number[]} The packed array.
*/
Cartesian2.packArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("array", array);
//>>includeEnd('debug');
var length = array.length;
var resultLength = length * 2;
if (!when.defined(result)) {
result = new Array(resultLength);
} else if (!Array.isArray(result) && result.length !== resultLength) {
throw new Check.DeveloperError(
"If result is a typed array, it must have exactly array.length * 2 elements"
);
} else if (result.length !== resultLength) {
result.length = resultLength;
}
for (var i = 0; i < length; ++i) {
Cartesian2.pack(array[i], result, i * 2);
}
return result;
};
/**
* Unpacks an array of cartesian components into and array of Cartesian2s.
*
* @param {Number[]} array The array of components to unpack.
* @param {Cartesian2[]} [result] The array onto which to store the result.
* @returns {Cartesian2[]} The unpacked array.
*/
Cartesian2.unpackArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.defined("array", array);
Check.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 2);
if (array.length % 2 !== 0) {
throw new Check.DeveloperError("array length must be a multiple of 2.");
}
//>>includeEnd('debug');
var length = array.length;
if (!when.defined(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (var i = 0; i < length; i += 2) {
var index = i / 2;
result[index] = Cartesian2.unpack(array, i, result[index]);
}
return result;
};
/**
* Creates a Cartesian2 from two consecutive elements in an array.
* @function
*
* @param {Number[]} array The array whose two consecutive elements correspond to the x and y components, respectively.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*
* @example
* // Create a Cartesian2 with (1.0, 2.0)
* var v = [1.0, 2.0];
* var p = Cesium.Cartesian2.fromArray(v);
*
* // Create a Cartesian2 with (1.0, 2.0) using an offset into an array
* var v2 = [0.0, 0.0, 1.0, 2.0];
* var p2 = Cesium.Cartesian2.fromArray(v2, 2);
*/
Cartesian2.fromArray = Cartesian2.unpack;
/**
* Computes the value of the maximum component for the supplied Cartesian.
*
* @param {Cartesian2} cartesian The cartesian to use.
* @returns {Number} The value of the maximum component.
*/
Cartesian2.maximumComponent = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return Math.max(cartesian.x, cartesian.y);
};
/**
* Computes the value of the minimum component for the supplied Cartesian.
*
* @param {Cartesian2} cartesian The cartesian to use.
* @returns {Number} The value of the minimum component.
*/
Cartesian2.minimumComponent = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return Math.min(cartesian.x, cartesian.y);
};
/**
* Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
*
* @param {Cartesian2} first A cartesian to compare.
* @param {Cartesian2} second A cartesian to compare.
* @param {Cartesian2} result The object into which to store the result.
* @returns {Cartesian2} A cartesian with the minimum components.
*/
Cartesian2.minimumByComponent = function (first, second, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("first", first);
Check.Check.typeOf.object("second", second);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.min(first.x, second.x);
result.y = Math.min(first.y, second.y);
return result;
};
/**
* Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
*
* @param {Cartesian2} first A cartesian to compare.
* @param {Cartesian2} second A cartesian to compare.
* @param {Cartesian2} result The object into which to store the result.
* @returns {Cartesian2} A cartesian with the maximum components.
*/
Cartesian2.maximumByComponent = function (first, second, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("first", first);
Check.Check.typeOf.object("second", second);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.max(first.x, second.x);
result.y = Math.max(first.y, second.y);
return result;
};
/**
* Computes the provided Cartesian's squared magnitude.
*
* @param {Cartesian2} cartesian The Cartesian instance whose squared magnitude is to be computed.
* @returns {Number} The squared magnitude.
*/
Cartesian2.magnitudeSquared = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return cartesian.x * cartesian.x + cartesian.y * cartesian.y;
};
/**
* Computes the Cartesian's magnitude (length).
*
* @param {Cartesian2} cartesian The Cartesian instance whose magnitude is to be computed.
* @returns {Number} The magnitude.
*/
Cartesian2.magnitude = function (cartesian) {
return Math.sqrt(Cartesian2.magnitudeSquared(cartesian));
};
var distanceScratch = new Cartesian2();
/**
* Computes the distance between two points.
*
* @param {Cartesian2} left The first point to compute the distance from.
* @param {Cartesian2} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 1.0
* var d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(2.0, 0.0));
*/
Cartesian2.distance = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian2.subtract(left, right, distanceScratch);
return Cartesian2.magnitude(distanceScratch);
};
/**
* Computes the squared distance between two points. Comparing squared distances
* using this function is more efficient than comparing distances using {@link Cartesian2#distance}.
*
* @param {Cartesian2} left The first point to compute the distance from.
* @param {Cartesian2} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 4.0, not 2.0
* var d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(3.0, 0.0));
*/
Cartesian2.distanceSquared = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian2.subtract(left, right, distanceScratch);
return Cartesian2.magnitudeSquared(distanceScratch);
};
/**
* Computes the normalized form of the supplied Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian to be normalized.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.normalize = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
var magnitude = Cartesian2.magnitude(cartesian);
result.x = cartesian.x / magnitude;
result.y = cartesian.y / magnitude;
//>>includeStart('debug', pragmas.debug);
if (isNaN(result.x) || isNaN(result.y)) {
throw new Check.DeveloperError("normalized result is not a number");
}
//>>includeEnd('debug');
return result;
};
/**
* Computes the dot (scalar) product of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @returns {Number} The dot product.
*/
Cartesian2.dot = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
//>>includeEnd('debug');
return left.x * right.x + left.y * right.y;
};
/**
* Computes the magnitude of the cross product that would result from implicitly setting the Z coordinate of the input vectors to 0
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @returns {Number} The cross product.
*/
Cartesian2.cross = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
//>>includeEnd('debug');
return left.x * right.y - left.y * right.x;
};
/**
* Computes the componentwise product of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.multiplyComponents = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x * right.x;
result.y = left.y * right.y;
return result;
};
/**
* Computes the componentwise quotient of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.divideComponents = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x / right.x;
result.y = left.y / right.y;
return result;
};
/**
* Computes the componentwise sum of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.add = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x + right.x;
result.y = left.y + right.y;
return result;
};
/**
* Computes the componentwise difference of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.subtract = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x - right.x;
result.y = left.y - right.y;
return result;
};
/**
* Multiplies the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian2} cartesian The Cartesian to be scaled.
* @param {Number} scalar The scalar to multiply with.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.multiplyByScalar = function (cartesian, scalar, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.number("scalar", scalar);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = cartesian.x * scalar;
result.y = cartesian.y * scalar;
return result;
};
/**
* Divides the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian2} cartesian The Cartesian to be divided.
* @param {Number} scalar The scalar to divide by.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.divideByScalar = function (cartesian, scalar, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.number("scalar", scalar);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = cartesian.x / scalar;
result.y = cartesian.y / scalar;
return result;
};
/**
* Negates the provided Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian to be negated.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.negate = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = -cartesian.x;
result.y = -cartesian.y;
return result;
};
/**
* Computes the absolute value of the provided Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian whose absolute value is to be computed.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.abs = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.abs(cartesian.x);
result.y = Math.abs(cartesian.y);
return result;
};
var lerpScratch = new Cartesian2();
/**
* Computes the linear interpolation or extrapolation at t using the provided cartesians.
*
* @param {Cartesian2} start The value corresponding to t at 0.0.
* @param {Cartesian2} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.lerp = function (start, end, t, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("start", start);
Check.Check.typeOf.object("end", end);
Check.Check.typeOf.number("t", t);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
Cartesian2.multiplyByScalar(end, t, lerpScratch);
result = Cartesian2.multiplyByScalar(start, 1.0 - t, result);
return Cartesian2.add(lerpScratch, result, result);
};
var angleBetweenScratch = new Cartesian2();
var angleBetweenScratch2 = new Cartesian2();
/**
* Returns the angle, in radians, between the provided Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @returns {Number} The angle between the Cartesians.
*/
Cartesian2.angleBetween = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("left", left);
Check.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian2.normalize(left, angleBetweenScratch);
Cartesian2.normalize(right, angleBetweenScratch2);
return _Math.CesiumMath.acosClamped(
Cartesian2.dot(angleBetweenScratch, angleBetweenScratch2)
);
};
var mostOrthogonalAxisScratch = new Cartesian2();
/**
* Returns the axis that is most orthogonal to the provided Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian on which to find the most orthogonal axis.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The most orthogonal axis.
*/
Cartesian2.mostOrthogonalAxis = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.Check.typeOf.object("cartesian", cartesian);
Check.Check.typeOf.object("result", result);
//>>includeEnd('debug');
var f = Cartesian2.normalize(cartesian, mostOrthogonalAxisScratch);
Cartesian2.abs(f, f);
if (f.x <= f.y) {
result = Cartesian2.clone(Cartesian2.UNIT_X, result);
} else {
result = Cartesian2.clone(Cartesian2.UNIT_Y, result);
}
return result;
};
/**
* Compares the provided Cartesians componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Cartesian2} [left] The first Cartesian.
* @param {Cartesian2} [right] The second Cartesian.
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
*/
Cartesian2.equals = function (left, right) {
return (
left === right ||
(when.defined(left) &&
when.defined(right) &&
left.x === right.x &&
left.y === right.y)
);
};
/**
* @private
*/
Cartesian2.equalsArray = function (cartesian, array, offset) {
return cartesian.x === array[offset] && cartesian.y === array[offset + 1];
};
/**
* Compares the provided Cartesians componentwise and returns
* <code>true</code> if they pass an absolute or relative tolerance test,
* <code>false</code> otherwise.
*
* @param {Cartesian2} [left] The first Cartesian.
* @param {Cartesian2} [right] The second Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
*/
Cartesian2.equalsEpsilon = function (
left,
right,
relativeEpsilon,
absoluteEpsilon
) {
return (
left === right ||
(when.defined(left) &&
when.defined(right) &&
_Math.CesiumMath.equalsEpsilon(
left.x,
right.x,
relativeEpsilon,
absoluteEpsilon
) &&
_Math.CesiumMath.equalsEpsilon(
left.y,
right.y,
relativeEpsilon,
absoluteEpsilon
))
);
};
/**
* An immutable Cartesian2 instance initialized to (0.0, 0.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.ZERO = Object.freeze(new Cartesian2(0.0, 0.0));
/**
* An immutable Cartesian2 instance initialized to (1.0, 0.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.UNIT_X = Object.freeze(new Cartesian2(1.0, 0.0));
/**
* An immutable Cartesian2 instance initialized to (0.0, 1.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.UNIT_Y = Object.freeze(new Cartesian2(0.0, 1.0));
/**
* Duplicates this Cartesian2 instance.
*
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.prototype.clone = function (result) {
return Cartesian2.clone(this, result);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Cartesian2} [right] The right hand side Cartesian.
* @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
*/
Cartesian2.prototype.equals = function (right) {
return Cartesian2.equals(this, right);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* <code>true</code> if they pass an absolute or relative tolerance test,
* <code>false</code> otherwise.
*
* @param {Cartesian2} [right] The right hand side Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
*/
Cartesian2.prototype.equalsEpsilon = function (
right,
relativeEpsilon,
absoluteEpsilon
) {
return Cartesian2.equalsEpsilon(
this,
right,
relativeEpsilon,
absoluteEpsilon
);
};
/**
* Creates a string representing this Cartesian in the format '(x, y)'.
*
* @returns {String} A string representing the provided Cartesian in the format '(x, y)'.
*/
Cartesian2.prototype.toString = function () {
return "(" + this.x + ", " + this.y + ")";
};
exports.Cartesian2 = Cartesian2;
exports.Cartesian3 = Cartesian3;
exports.Cartographic = Cartographic;
exports.Ellipsoid = Ellipsoid;
exports.Rectangle = Rectangle;
});
