/*global define*/
define([
'../ThirdParty/mersenne-twister',
'./defaultValue',
'./defined',
'./DeveloperError'
], function(
MersenneTwister,
defaultValue,
defined,
DeveloperError) {
'use strict';
/**
* Math functions.
*
* @exports CesiumMath
*/
var CesiumMath = {};
/**
* 0.1
* @type {Number}
* @constant
*/
CesiumMath.EPSILON1 = 0.1;
/**
* 0.01
* @type {Number}
* @constant
*/
CesiumMath.EPSILON2 = 0.01;
/**
* 0.001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON3 = 0.001;
/**
* 0.0001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON4 = 0.0001;
/**
* 0.00001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON5 = 0.00001;
/**
* 0.000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON6 = 0.000001;
/**
* 0.0000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON7 = 0.0000001;
/**
* 0.00000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON8 = 0.00000001;
/**
* 0.000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON9 = 0.000000001;
/**
* 0.0000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON10 = 0.0000000001;
/**
* 0.00000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON11 = 0.00000000001;
/**
* 0.000000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON12 = 0.000000000001;
/**
* 0.0000000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON13 = 0.0000000000001;
/**
* 0.00000000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON14 = 0.00000000000001;
/**
* 0.000000000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON15 = 0.000000000000001;
/**
* 0.0000000000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON16 = 0.0000000000000001;
/**
* 0.00000000000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON17 = 0.00000000000000001;
/**
* 0.000000000000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON18 = 0.000000000000000001;
/**
* 0.0000000000000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON19 = 0.0000000000000000001;
/**
* 0.00000000000000000001
* @type {Number}
* @constant
*/
CesiumMath.EPSILON20 = 0.00000000000000000001;
/**
* 3.986004418e14
* @type {Number}
* @constant
*/
CesiumMath.GRAVITATIONALPARAMETER = 3.986004418e14;
/**
* Radius of the sun in meters: 6.955e8
* @type {Number}
* @constant
*/
CesiumMath.SOLAR_RADIUS = 6.955e8;
/**
* The mean radius of the moon, according to the "Report of the IAU/IAG Working Group on
* Cartographic Coordinates and Rotational Elements of the Planets and satellites: 2000",
* Celestial Mechanics 82: 83-110, 2002.
* @type {Number}
* @constant
*/
CesiumMath.LUNAR_RADIUS = 1737400.0;
/**
* 64 * 1024
* @type {Number}
* @constant
*/
CesiumMath.SIXTY_FOUR_KILOBYTES = 64 * 1024;
/**
* Returns the sign of the value; 1 if the value is positive, -1 if the value is
* negative, or 0 if the value is 0.
*
* @param {Number} value The value to return the sign of.
* @returns {Number} The sign of value.
*/
CesiumMath.sign = function(value) {
if (value > 0) {
return 1;
}
if (value < 0) {
return -1;
}
return 0;
};
/**
* Returns 1.0 if the given value is positive or zero, and -1.0 if it is negative.
* This is similar to {@link CesiumMath#sign} except that returns 1.0 instead of
* 0.0 when the input value is 0.0.
* @param {Number} value The value to return the sign of.
* @returns {Number} The sign of value.
*/
CesiumMath.signNotZero = function(value) {
return value < 0.0 ? -1.0 : 1.0;
};
/**
* Converts a scalar value in the range [-1.0, 1.0] to a SNORM in the range [0, rangeMax]
* @param {Number} value The scalar value in the range [-1.0, 1.0]
* @param {Number} [rangeMax=255] The maximum value in the mapped range, 255 by default.
* @returns {Number} A SNORM value, where 0 maps to -1.0 and rangeMax maps to 1.0.
*
* @see CesiumMath.fromSNorm
*/
CesiumMath.toSNorm = function(value, rangeMax) {
rangeMax = defaultValue(rangeMax, 255);
return Math.round((CesiumMath.clamp(value, -1.0, 1.0) * 0.5 + 0.5) * rangeMax);
};
/**
* Converts a SNORM value in the range [0, rangeMax] to a scalar in the range [-1.0, 1.0].
* @param {Number} value SNORM value in the range [0, 255]
* @param {Number} [rangeMax=255] The maximum value in the SNORM range, 255 by default.
* @returns {Number} Scalar in the range [-1.0, 1.0].
*
* @see CesiumMath.toSNorm
*/
CesiumMath.fromSNorm = function(value, rangeMax) {
rangeMax = defaultValue(rangeMax, 255);
return CesiumMath.clamp(value, 0.0, rangeMax) / rangeMax * 2.0 - 1.0;
};
/**
* Returns the hyperbolic sine of a number.
* The hyperbolic sine of <em>value</em> is defined to be
* (<em>e<sup>x</sup> - e<sup>-x</sup></em>)/2.0
* where <i>e</i> is Euler's number, approximately 2.71828183.
*
* <p>Special cases:
* <ul>
* <li>If the argument is NaN, then the result is NaN.</li>
*
* <li>If the argument is infinite, then the result is an infinity
* with the same sign as the argument.</li>
*
* <li>If the argument is zero, then the result is a zero with the
* same sign as the argument.</li>
* </ul>
*</p>
*
* @param {Number} value The number whose hyperbolic sine is to be returned.
* @returns {Number} The hyperbolic sine of <code>value</code>.
*/
CesiumMath.sinh = function(value) {
var part1 = Math.pow(Math.E, value);
var part2 = Math.pow(Math.E, -1.0 * value);
return (part1 - part2) * 0.5;
};
/**
* Returns the hyperbolic cosine of a number.
* The hyperbolic cosine of <strong>value</strong> is defined to be
* (<em>e<sup>x</sup> + e<sup>-x</sup></em>)/2.0
* where <i>e</i> is Euler's number, approximately 2.71828183.
*
* <p>Special cases:
* <ul>
* <li>If the argument is NaN, then the result is NaN.</li>
*
* <li>If the argument is infinite, then the result is positive infinity.</li>
*
* <li>If the argument is zero, then the result is 1.0.</li>
* </ul>
*</p>
*
* @param {Number} value The number whose hyperbolic cosine is to be returned.
* @returns {Number} The hyperbolic cosine of <code>value</code>.
*/
CesiumMath.cosh = function(value) {
var part1 = Math.pow(Math.E, value);
var part2 = Math.pow(Math.E, -1.0 * value);
return (part1 + part2) * 0.5;
};
/**
* Computes the linear interpolation of two values.
*
* @param {Number} p The start value to interpolate.
* @param {Number} q The end value to interpolate.
* @param {Number} time The time of interpolation generally in the range <code>[0.0, 1.0]</code>.
* @returns {Number} The linearly interpolated value.
*
* @example
* var n = Cesium.Math.lerp(0.0, 2.0, 0.5); // returns 1.0
*/
CesiumMath.lerp = function(p, q, time) {
return ((1.0 - time) * p) + (time * q);
};
/**
* pi
*
* @type {Number}
* @constant
*/
CesiumMath.PI = Math.PI;
/**
* 1/pi
*
* @type {Number}
* @constant
*/
CesiumMath.ONE_OVER_PI = 1.0 / Math.PI;
/**
* pi/2
*
* @type {Number}
* @constant
*/
CesiumMath.PI_OVER_TWO = Math.PI * 0.5;
/**
* pi/3
*
* @type {Number}
* @constant
*/
CesiumMath.PI_OVER_THREE = Math.PI / 3.0;
/**
* pi/4
*
* @type {Number}
* @constant
*/
CesiumMath.PI_OVER_FOUR = Math.PI / 4.0;
/**
* pi/6
*
* @type {Number}
* @constant
*/
CesiumMath.PI_OVER_SIX = Math.PI / 6.0;
/**
* 3pi/2
*
* @type {Number}
* @constant
*/
CesiumMath.THREE_PI_OVER_TWO = (3.0 * Math.PI) * 0.5;
/**
* 2pi
*
* @type {Number}
* @constant
*/
CesiumMath.TWO_PI = 2.0 * Math.PI;
/**
* 1/2pi
*
* @type {Number}
* @constant
*/
CesiumMath.ONE_OVER_TWO_PI = 1.0 / (2.0 * Math.PI);
/**
* The number of radians in a degree.
*
* @type {Number}
* @constant
* @default Math.PI / 180.0
*/
CesiumMath.RADIANS_PER_DEGREE = Math.PI / 180.0;
/**
* The number of degrees in a radian.
*
* @type {Number}
* @constant
* @default 180.0 / Math.PI
*/
CesiumMath.DEGREES_PER_RADIAN = 180.0 / Math.PI;
/**
* The number of radians in an arc second.
*
* @type {Number}
* @constant
* @default {@link CesiumMath.RADIANS_PER_DEGREE} / 3600.0
*/
CesiumMath.RADIANS_PER_ARCSECOND = CesiumMath.RADIANS_PER_DEGREE / 3600.0;
/**
* Converts degrees to radians.
* @param {Number} degrees The angle to convert in degrees.
* @returns {Number} The corresponding angle in radians.
*/
CesiumMath.toRadians = function(degrees) {
//>>includeStart('debug', pragmas.debug);
if (!defined(degrees)) {
throw new DeveloperError('degrees is required.');
}
//>>includeEnd('debug');
return degrees * CesiumMath.RADIANS_PER_DEGREE;
};
/**
* Converts radians to degrees.
* @param {Number} radians The angle to convert in radians.
* @returns {Number} The corresponding angle in degrees.
*/
CesiumMath.toDegrees = function(radians) {
//>>includeStart('debug', pragmas.debug);
if (!defined(radians)) {
throw new DeveloperError('radians is required.');
}
//>>includeEnd('debug');
return radians * CesiumMath.DEGREES_PER_RADIAN;
};
/**
* Converts a longitude value, in radians, to the range [<code>-Math.PI</code>, <code>Math.PI</code>).
*
* @param {Number} angle The longitude value, in radians, to convert to the range [<code>-Math.PI</code>, <code>Math.PI</code>).
* @returns {Number} The equivalent longitude value in the range [<code>-Math.PI</code>, <code>Math.PI</code>).
*
* @example
* // Convert 270 degrees to -90 degrees longitude
* var longitude = Cesium.Math.convertLongitudeRange(Cesium.Math.toRadians(270.0));
*/
CesiumMath.convertLongitudeRange = function(angle) {
//>>includeStart('debug', pragmas.debug);
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
//>>includeEnd('debug');
var twoPi = CesiumMath.TWO_PI;
var simplified = angle - Math.floor(angle / twoPi) * twoPi;
if (simplified < -Math.PI) {
return simplified + twoPi;
}
if (simplified >= Math.PI) {
return simplified - twoPi;
}
return simplified;
};
/**
* Convenience function that clamps a latitude value, in radians, to the range [<code>-Math.PI/2</code>, <code>Math.PI/2</code>).
* Useful for sanitizing data before use in objects requiring correct range.
*
* @param {Number} angle The latitude value, in radians, to clamp to the range [<code>-Math.PI/2</code>, <code>Math.PI/2</code>).
* @returns {Number} The latitude value clamped to the range [<code>-Math.PI/2</code>, <code>Math.PI/2</code>).
*
* @example
* // Clamp 108 degrees latitude to 90 degrees latitude
* var latitude = Cesium.Math.clampToLatitudeRange(Cesium.Math.toRadians(108.0));
*/
CesiumMath.clampToLatitudeRange = function(angle) {
//>>includeStart('debug', pragmas.debug);
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
//>>includeEnd('debug');
return CesiumMath.clamp(angle, -1*CesiumMath.PI_OVER_TWO, CesiumMath.PI_OVER_TWO);
};
/**
* Produces an angle in the range -Pi <= angle <= Pi which is equivalent to the provided angle.
*
* @param {Number} angle in radians
* @returns {Number} The angle in the range [<code>-CesiumMath.PI</code>, <code>CesiumMath.PI</code>].
*/
CesiumMath.negativePiToPi = function(x) {
//>>includeStart('debug', pragmas.debug);
if (!defined(x)) {
throw new DeveloperError('x is required.');
}
//>>includeEnd('debug');
return CesiumMath.zeroToTwoPi(x + CesiumMath.PI) - CesiumMath.PI;
};
/**
* Produces an angle in the range 0 <= angle <= 2Pi which is equivalent to the provided angle.
*
* @param {Number} angle in radians
* @returns {Number} The angle in the range [0, <code>CesiumMath.TWO_PI</code>].
*/
CesiumMath.zeroToTwoPi = function(x) {
//>>includeStart('debug', pragmas.debug);
if (!defined(x)) {
throw new DeveloperError('x is required.');
}
//>>includeEnd('debug');
var mod = CesiumMath.mod(x, CesiumMath.TWO_PI);
if (Math.abs(mod) < CesiumMath.EPSILON14 && Math.abs(x) > CesiumMath.EPSILON14) {
return CesiumMath.TWO_PI;
}
return mod;
};
/**
* The modulo operation that also works for negative dividends.
*
* @param {Number} m The dividend.
* @param {Number} n The divisor.
* @returns {Number} The remainder.
*/
CesiumMath.mod = function(m, n) {
//>>includeStart('debug', pragmas.debug);
if (!defined(m)) {
throw new DeveloperError('m is required.');
}
if (!defined(n)) {
throw new DeveloperError('n is required.');
}
//>>includeEnd('debug');
return ((m % n) + n) % n;
};
/**
* Determines if two values are equal using an absolute or relative tolerance test. This is useful
* to avoid problems due to roundoff error when comparing floating-point values directly. The values are
* first compared using an absolute tolerance test. If that fails, a relative tolerance test is performed.
* Use this test if you are unsure of the magnitudes of left and right.
*
* @param {Number} left The first value to compare.
* @param {Number} right The other value to compare.
* @param {Number} relativeEpsilon The maximum inclusive delta between <code>left</code> and <code>right</code> for the relative tolerance test.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The maximum inclusive delta between <code>left</code> and <code>right</code> for the absolute tolerance test.
* @returns {Boolean} <code>true</code> if the values are equal within the epsilon; otherwise, <code>false</code>.
*
* @example
* var a = Cesium.Math.equalsEpsilon(0.0, 0.01, Cesium.Math.EPSILON2); // true
* var b = Cesium.Math.equalsEpsilon(0.0, 0.1, Cesium.Math.EPSILON2); // false
* var c = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON7); // true
* var d = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON9); // false
*/
CesiumMath.equalsEpsilon = function(left, right, relativeEpsilon, absoluteEpsilon) {
//>>includeStart('debug', pragmas.debug);
if (!defined(left)) {
throw new DeveloperError('left is required.');
}
if (!defined(right)) {
throw new DeveloperError('right is required.');
}
if (!defined(relativeEpsilon)) {
throw new DeveloperError('relativeEpsilon is required.');
}
//>>includeEnd('debug');
absoluteEpsilon = defaultValue(absoluteEpsilon, relativeEpsilon);
var absDiff = Math.abs(left - right);
return absDiff <= absoluteEpsilon || absDiff <= relativeEpsilon * Math.max(Math.abs(left), Math.abs(right));
};
var factorials = [1];
/**
* Computes the factorial of the provided number.
*
* @param {Number} n The number whose factorial is to be computed.
* @returns {Number} The factorial of the provided number or undefined if the number is less than 0.
*
* @exception {DeveloperError} A number greater than or equal to 0 is required.
*
*
* @example
* //Compute 7!, which is equal to 5040
* var computedFactorial = Cesium.Math.factorial(7);
*
* @see {@link http://en.wikipedia.org/wiki/Factorial|Factorial on Wikipedia}
*/
CesiumMath.factorial = function(n) {
//>>includeStart('debug', pragmas.debug);
if (typeof n !== 'number' || n < 0) {
throw new DeveloperError('A number greater than or equal to 0 is required.');
}
//>>includeEnd('debug');
var length = factorials.length;
if (n >= length) {
var sum = factorials[length - 1];
for (var i = length; i <= n; i++) {
factorials.push(sum * i);
}
}
return factorials[n];
};
/**
* Increments a number with a wrapping to a minimum value if the number exceeds the maximum value.
*
* @param {Number} [n] The number to be incremented.
* @param {Number} [maximumValue] The maximum incremented value before rolling over to the minimum value.
* @param {Number} [minimumValue=0.0] The number reset to after the maximum value has been exceeded.
* @returns {Number} The incremented number.
*
* @exception {DeveloperError} Maximum value must be greater than minimum value.
*
* @example
* var n = Cesium.Math.incrementWrap(5, 10, 0); // returns 6
* var n = Cesium.Math.incrementWrap(10, 10, 0); // returns 0
*/
CesiumMath.incrementWrap = function(n, maximumValue, minimumValue) {
minimumValue = defaultValue(minimumValue, 0.0);
//>>includeStart('debug', pragmas.debug);
if (!defined(n)) {
throw new DeveloperError('n is required.');
}
if (maximumValue <= minimumValue) {
throw new DeveloperError('maximumValue must be greater than minimumValue.');
}
//>>includeEnd('debug');
++n;
if (n > maximumValue) {
n = minimumValue;
}
return n;
};
/**
* Determines if a positive integer is a power of two.
*
* @param {Number} n The positive integer to test.
* @returns {Boolean} <code>true</code> if the number if a power of two; otherwise, <code>false</code>.
*
* @exception {DeveloperError} A number greater than or equal to 0 is required.
*
* @example
* var t = Cesium.Math.isPowerOfTwo(16); // true
* var f = Cesium.Math.isPowerOfTwo(20); // false
*/
CesiumMath.isPowerOfTwo = function(n) {
//>>includeStart('debug', pragmas.debug);
if (typeof n !== 'number' || n < 0) {
throw new DeveloperError('A number greater than or equal to 0 is required.');
}
//>>includeEnd('debug');
return (n !== 0) && ((n & (n - 1)) === 0);
};
/**
* Computes the next power-of-two integer greater than or equal to the provided positive integer.
*
* @param {Number} n The positive integer to test.
* @returns {Number} The next power-of-two integer.
*
* @exception {DeveloperError} A number greater than or equal to 0 is required.
*
* @example
* var n = Cesium.Math.nextPowerOfTwo(29); // 32
* var m = Cesium.Math.nextPowerOfTwo(32); // 32
*/
CesiumMath.nextPowerOfTwo = function(n) {
//>>includeStart('debug', pragmas.debug);
if (typeof n !== 'number' || n < 0) {
throw new DeveloperError('A number greater than or equal to 0 is required.');
}
//>>includeEnd('debug');
// From http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2
--n;
n |= n >> 1;
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
++n;
return n;
};
/**
* Constraint a value to lie between two values.
*
* @param {Number} value The value to constrain.
* @param {Number} min The minimum value.
* @param {Number} max The maximum value.
* @returns {Number} The value clamped so that min <= value <= max.
*/
CesiumMath.clamp = function(value, min, max) {
//>>includeStart('debug', pragmas.debug);
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(min)) {
throw new DeveloperError('min is required.');
}
if (!defined(max)) {
throw new DeveloperError('max is required.');
}
//>>includeEnd('debug');
return value < min ? min : value > max ? max : value;
};
var randomNumberGenerator = new MersenneTwister();
/**
* Sets the seed used by the random number generator
* in {@link CesiumMath#nextRandomNumber}.
*
* @param {Number} seed An integer used as the seed.
*/
CesiumMath.setRandomNumberSeed = function(seed) {
//>>includeStart('debug', pragmas.debug);
if (!defined(seed)) {
throw new DeveloperError('seed is required.');
}
//>>includeEnd('debug');
randomNumberGenerator = new MersenneTwister(seed);
};
/**
* Generates a random number in the range of [0.0, 1.0)
* using a Mersenne twister.
*
* @returns {Number} A random number in the range of [0.0, 1.0).
*
* @see CesiumMath.setRandomNumberSeed
* @see {@link http://en.wikipedia.org/wiki/Mersenne_twister|Mersenne twister on Wikipedia}
*/
CesiumMath.nextRandomNumber = function() {
return randomNumberGenerator.random();
};
/**
* Computes <code>Math.acos(value)</acode>, but first clamps <code>value</code> to the range [-1.0, 1.0]
* so that the function will never return NaN.
*
* @param {Number} value The value for which to compute acos.
* @returns {Number} The acos of the value if the value is in the range [-1.0, 1.0], or the acos of -1.0 or 1.0,
* whichever is closer, if the value is outside the range.
*/
CesiumMath.acosClamped = function(value) {
//>>includeStart('debug', pragmas.debug);
if (!defined(value)) {
throw new DeveloperError('value is required.');
}
//>>includeEnd('debug');
return Math.acos(CesiumMath.clamp(value, -1.0, 1.0));
};
/**
* Computes <code>Math.asin(value)</acode>, but first clamps <code>value</code> to the range [-1.0, 1.0]
* so that the function will never return NaN.
*
* @param {Number} value The value for which to compute asin.
* @returns {Number} The asin of the value if the value is in the range [-1.0, 1.0], or the asin of -1.0 or 1.0,
* whichever is closer, if the value is outside the range.
*/
CesiumMath.asinClamped = function(value) {
//>>includeStart('debug', pragmas.debug);
if (!defined(value)) {
throw new DeveloperError('value is required.');
}
//>>includeEnd('debug');
return Math.asin(CesiumMath.clamp(value, -1.0, 1.0));
};
/**
* Finds the chord length between two points given the circle's radius and the angle between the points.
*
* @param {Number} angle The angle between the two points.
* @param {Number} radius The radius of the circle.
* @returns {Number} The chord length.
*/
CesiumMath.chordLength = function(angle, radius) {
//>>includeStart('debug', pragmas.debug);
if (!defined(angle)) {
throw new DeveloperError('angle is required.');
}
if (!defined(radius)) {
throw new DeveloperError('radius is required.');
}
//>>includeEnd('debug');
return 2.0 * radius * Math.sin(angle * 0.5);
};
/**
* Finds the logarithm of a number to a base.
*
* @param {Number} number The number.
* @param {Number} base The base.
* @returns {Number} The result.
*/
CesiumMath.logBase = function(number, base) {
//>>includeStart('debug', pragmas.debug);
if (!defined(number)) {
throw new DeveloperError('number is required.');
}
if (!defined(base)) {
throw new DeveloperError('base is required.');
}
//>>includeEnd('debug');
return Math.log(number) / Math.log(base);
};
/**
* @private
*/
CesiumMath.fog = function(distanceToCamera, density) {
var scalar = distanceToCamera * density;
return 1.0 - Math.exp(-(scalar * scalar));
};
return CesiumMath;
});