Math

Math()
engine/Source/Core/Math.js 13

Math functions.

Members

static constant Cesium.Math.DEGREES_PER_RADIAN : number
engine/Source/Core/Math.js 423

The number of degrees in a radian.

static constant Cesium.Math.EPSILON1 : number
engine/Source/Core/Math.js 20

0.1

static constant Cesium.Math.EPSILON2 : number
engine/Source/Core/Math.js 27

0.01

static constant Cesium.Math.EPSILON3 : number
engine/Source/Core/Math.js 34

0.001

static constant Cesium.Math.EPSILON4 : number
engine/Source/Core/Math.js 41

0.0001

static constant Cesium.Math.EPSILON5 : number
engine/Source/Core/Math.js 48

0.00001

static constant Cesium.Math.EPSILON6 : number
engine/Source/Core/Math.js 55

0.000001

static constant Cesium.Math.EPSILON7 : number
engine/Source/Core/Math.js 62

0.0000001

static constant Cesium.Math.EPSILON8 : number
engine/Source/Core/Math.js 69

0.00000001

static constant Cesium.Math.EPSILON9 : number
engine/Source/Core/Math.js 76

0.000000001

static constant Cesium.Math.EPSILON10 : number
engine/Source/Core/Math.js 83

0.0000000001

static constant Cesium.Math.EPSILON11 : number
engine/Source/Core/Math.js 90

0.00000000001

static constant Cesium.Math.EPSILON12 : number
engine/Source/Core/Math.js 97

0.000000000001

static constant Cesium.Math.EPSILON13 : number
engine/Source/Core/Math.js 104

0.0000000000001

static constant Cesium.Math.EPSILON14 : number
engine/Source/Core/Math.js 111

0.00000000000001

static constant Cesium.Math.EPSILON15 : number
engine/Source/Core/Math.js 118

0.000000000000001

static constant Cesium.Math.EPSILON16 : number
engine/Source/Core/Math.js 125

0.0000000000000001

static constant Cesium.Math.EPSILON17 : number
engine/Source/Core/Math.js 132

0.00000000000000001

static constant Cesium.Math.EPSILON18 : number
engine/Source/Core/Math.js 139

0.000000000000000001

static constant Cesium.Math.EPSILON19 : number
engine/Source/Core/Math.js 146

0.0000000000000000001

static constant Cesium.Math.EPSILON20 : number
engine/Source/Core/Math.js 153

0.00000000000000000001

static constant Cesium.Math.EPSILON21 : number
engine/Source/Core/Math.js 160

0.000000000000000000001

static constant Cesium.Math.FOUR_GIGABYTES : number
engine/Source/Core/Math.js 198

4 * 1024 * 1024 * 1024

static constant Cesium.Math.GRAVITATIONALPARAMETER : number
engine/Source/Core/Math.js 168

The gravitational parameter of the Earth in meters cubed per second squared as defined by the WGS84 model: 3.986004418e14

static constant Cesium.Math.LUNAR_RADIUS : number
engine/Source/Core/Math.js 184

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.

static constant Cesium.Math.ONE_OVER_PI : number
engine/Source/Core/Math.js 351

1/pi

static constant Cesium.Math.ONE_OVER_TWO_PI : number
engine/Source/Core/Math.js 407

1/2pi

static constant Cesium.Math.PI : number
engine/Source/Core/Math.js 343

pi

static constant Cesium.Math.PI_OVER_FOUR : number
engine/Source/Core/Math.js 375

pi/4

static constant Cesium.Math.PI_OVER_SIX : number
engine/Source/Core/Math.js 383

pi/6

static constant Cesium.Math.PI_OVER_THREE : number
engine/Source/Core/Math.js 367

pi/3

static constant Cesium.Math.PI_OVER_TWO : number
engine/Source/Core/Math.js 359

pi/2

static constant Cesium.Math.RADIANS_PER_ARCSECOND : number
engine/Source/Core/Math.js 431

The number of radians in an arc second.

static constant Cesium.Math.RADIANS_PER_DEGREE : number
engine/Source/Core/Math.js 415

The number of radians in a degree.

static constant Cesium.Math.SIXTY_FOUR_KILOBYTES : number
engine/Source/Core/Math.js 191

64 * 1024

static constant Cesium.Math.SOLAR_RADIUS : number
engine/Source/Core/Math.js 175

Radius of the sun in meters: 6.955e8

static constant Cesium.Math.THREE_PI_OVER_TWO : number
engine/Source/Core/Math.js 391

3pi/2

static constant Cesium.Math.TWO_PI : number
engine/Source/Core/Math.js 399

2pi

Methods

static Cesium.Math.acosClamped(value) → number
engine/Source/Core/Math.js 962

Computes Math.acos(value), but first clamps value to the range [-1.0, 1.0] so that the function will never return NaN.
Name Type Description
value number The value for which to compute acos.
Returns:
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.

static Cesium.Math.asinClamped(value) → number
engine/Source/Core/Math.js 979

Computes Math.asin(value), but first clamps value to the range [-1.0, 1.0] so that the function will never return NaN.
Name Type Description
value number The value for which to compute asin.
Returns:
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.

static Cesium.Math.cbrt(number) → number
engine/Source/Core/Math.js 1034

Finds the cube root of a number. Returns NaN if number is not provided.
Name Type Description
number number optional The number.
Returns:
The result.

static Cesium.Math.chordLength(angle, radius) → number
engine/Source/Core/Math.js 995

Finds the chord length between two points given the circle's radius and the angle between the points.
Name Type Description
angle number The angle between the two points.
radius number The radius of the circle.
Returns:
The chord length.

static Cesium.Math.clamp(value, min, max) → number
engine/Source/Core/Math.js 902

Constraint a value to lie between two values.
Name Type Description
value number The value to clamp.
min number The minimum value.
max number The maximum value.
Returns:
The clamped value such that min <= result <= max.

static Cesium.Math.clampToLatitudeRange(angle) → number
engine/Source/Core/Math.js 502

Convenience function that clamps a latitude value, in radians, to the range [-Math.PI/2, Math.PI/2). Useful for sanitizing data before use in objects requiring correct range.
Name Type Description
angle number The latitude value, in radians, to clamp to the range [-Math.PI/2, Math.PI/2).
Returns:
The latitude value clamped to the range [-Math.PI/2, Math.PI/2).
Example:
// Clamp 108 degrees latitude to 90 degrees latitude
const latitude = Cesium.Math.clampToLatitudeRange(Cesium.Math.toRadians(108.0));

static Cesium.Math.convertLongitudeRange(angle) → number
engine/Source/Core/Math.js 471

Converts a longitude value, in radians, to the range [-Math.PI, Math.PI).
Name Type Description
angle number The longitude value, in radians, to convert to the range [-Math.PI, Math.PI).
Returns:
The equivalent longitude value in the range [-Math.PI, Math.PI).
Example:
// Convert 270 degrees to -90 degrees longitude
const longitude = Cesium.Math.convertLongitudeRange(Cesium.Math.toRadians(270.0));

static Cesium.Math.cosh(value) → number
engine/Source/Core/Math.js 318

Returns the hyperbolic cosine of a number. The hyperbolic cosine of value is defined to be (ex + e-x)/2.0 where e is Euler's number, approximately 2.71828183.

Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is infinite, then the result is positive infinity.
  • If the argument is zero, then the result is 1.0.

Name Type Description
value number The number whose hyperbolic cosine is to be returned.
Returns:
The hyperbolic cosine of value.

static Cesium.Math.equalsEpsilon(left, right, relativeEpsilon, absoluteEpsilon) → boolean
engine/Source/Core/Math.js 609

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.
Name Type Default Description
left number The first value to compare.
right number The other value to compare.
relativeEpsilon number 0 optional The maximum inclusive delta between left and right for the relative tolerance test.
absoluteEpsilon number relativeEpsilon optional The maximum inclusive delta between left and right for the absolute tolerance test.
Returns:
true if the values are equal within the epsilon; otherwise, false.
Example:
const a = Cesium.Math.equalsEpsilon(0.0, 0.01, Cesium.Math.EPSILON2); // true
const b = Cesium.Math.equalsEpsilon(0.0, 0.1, Cesium.Math.EPSILON2);  // false
const c = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON7); // true
const d = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON9); // false

static Cesium.Math.factorial(n) → number
engine/Source/Core/Math.js 752

Computes the factorial of the provided number.
Name Type Description
n number The number whose factorial is to be computed.
Returns:
The factorial of the provided number or undefined if the number is less than 0.
Throws:
Example:
//Compute 7!, which is equal to 5040
const computedFactorial = Cesium.Math.factorial(7);
See:

static Cesium.Math.fastApproximateAtan(x) → number
engine/Source/Core/Math.js 1071

Computes a fast approximation of Atan for input in the range [-1, 1]. Based on Michal Drobot's approximation from ShaderFastLibs, which in turn is based on "Efficient approximations for the arctangent function," Rajan, S. Sichun Wang Inkol, R. Joyal, A., May 2006. Adapted from ShaderFastLibs under MIT License.
Name Type Description
x number An input number in the range [-1, 1]
Returns:
An approximation of atan(x)

static Cesium.Math.fastApproximateAtan2(x, y) → number
engine/Source/Core/Math.js 1088

Computes a fast approximation of Atan2(x, y) for arbitrary input scalars. Range reduction math based on nvidia's cg reference implementation: http://developer.download.nvidia.com/cg/atan2.html
Name Type Description
x number An input number that isn't zero if y is zero.
y number An input number that isn't zero if x is zero.
Returns:
An approximation of atan2(x, y)

static Cesium.Math.fromSNorm(value, rangeMaximum) → number
engine/Source/Core/Math.js 251

Converts a SNORM value in the range [0, rangeMaximum] to a scalar in the range [-1.0, 1.0].
Name Type Default Description
value number SNORM value in the range [0, rangeMaximum]
rangeMaximum number 255 optional The maximum value in the SNORM range, 255 by default.
Returns:
Scalar in the range [-1.0, 1.0].
See:
  • CesiumMath.toSNorm

static Cesium.Math.greaterThan(left, right, absoluteEpsilon) → boolean
engine/Source/Core/Math.js 695

Determines if the left value is greater the right value. If the two values are within absoluteEpsilon of each other, they are considered equal and this function returns false.
Name Type Description
left number The first number to compare.
right number The second number to compare.
absoluteEpsilon number The absolute epsilon to use in comparison.
Returns:
true if left is greater than right by more than absoluteEpsilon. false if left is less or if the two values are nearly equal.

static Cesium.Math.greaterThanOrEquals(left, right, absoluteEpsilon) → boolean
engine/Source/Core/Math.js 720

Determines if the left value is greater than or equal to the right value. If the two values are within absoluteEpsilon of each other, they are considered equal and this function returns true.
Name Type Description
left number The first number to compare.
right number The second number to compare.
absoluteEpsilon number The absolute epsilon to use in comparison.
Returns:
true if left is greater than right or if the the values are nearly equal.

static Cesium.Math.incrementWrap(n, maximumValue, minimumValue) → number
engine/Source/Core/Math.js 787

Increments a number with a wrapping to a minimum value if the number exceeds the maximum value.
Name Type Default Description
n number optional The number to be incremented.
maximumValue number optional The maximum incremented value before rolling over to the minimum value.
minimumValue number 0.0 optional The number reset to after the maximum value has been exceeded.
Returns:
The incremented number.
Throws:
Example:
const n = Cesium.Math.incrementWrap(5, 10, 0); // returns 6
const m = Cesium.Math.incrementWrap(10, 10, 0); // returns 0

static Cesium.Math.isPowerOfTwo(n) → boolean
engine/Source/Core/Math.js 819

Determines if a non-negative integer is a power of two. The maximum allowed input is (2^32)-1 due to 32-bit bitwise operator limitation in Javascript.
Name Type Description
n number The integer to test in the range [0, (2^32)-1].
Returns:
true if the number if a power of two; otherwise, false.
Throws:
Example:
const t = Cesium.Math.isPowerOfTwo(16); // true
const f = Cesium.Math.isPowerOfTwo(20); // false

static Cesium.Math.lerp(p, q, time) → number
engine/Source/Core/Math.js 333

Computes the linear interpolation of two values.
Name Type Description
p number The start value to interpolate.
q number The end value to interpolate.
time number The time of interpolation generally in the range [0.0, 1.0].
Returns:
The linearly interpolated value.
Example:
const n = Cesium.Math.lerp(0.0, 2.0, 0.5); // returns 1.0

static Cesium.Math.lessThan(left, right, absoluteEpsilon) → boolean
engine/Source/Core/Math.js 644

Determines if the left value is less than the right value. If the two values are within absoluteEpsilon of each other, they are considered equal and this function returns false.
Name Type Description
left number The first number to compare.
right number The second number to compare.
absoluteEpsilon number The absolute epsilon to use in comparison.
Returns:
true if left is less than right by more than absoluteEpsilon. false if left is greater or if the two values are nearly equal.

static Cesium.Math.lessThanOrEquals(left, right, absoluteEpsilon) → boolean
engine/Source/Core/Math.js 669

Determines if the left value is less than or equal to the right value. If the two values are within absoluteEpsilon of each other, they are considered equal and this function returns true.
Name Type Description
left number The first number to compare.
right number The second number to compare.
absoluteEpsilon number The absolute epsilon to use in comparison.
Returns:
true if left is less than right or if the the values are nearly equal.

static Cesium.Math.log2(number) → number
engine/Source/Core/Math.js 1046

Finds the base 2 logarithm of a number.
Name Type Description
number number The number.
Returns:
The result.

static Cesium.Math.logBase(number, base) → number
engine/Source/Core/Math.js 1014

Finds the logarithm of a number to a base.
Name Type Description
number number The number.
base number The base.
Returns:
The result.

static Cesium.Math.mod(m, n) → number
engine/Source/Core/Math.js 570

The modulo operation that also works for negative dividends.
Name Type Description
m number The dividend.
n number The divisor.
Returns:
The remainder.

static Cesium.Math.negativePiToPi(angle) → number
engine/Source/Core/Math.js 522

Produces an angle in the range -Pi <= angle <= Pi which is equivalent to the provided angle.
Name Type Description
angle number in radians
Returns:
The angle in the range [-CesiumMath.PI, CesiumMath.PI].

static Cesium.Math.nextPowerOfTwo(n) → number
engine/Source/Core/Math.js 842

Computes the next power-of-two integer greater than or equal to the provided non-negative integer. The maximum allowed input is 2^31 due to 32-bit bitwise operator limitation in Javascript.
Name Type Description
n number The integer to test in the range [0, 2^31].
Returns:
The next power-of-two integer.
Throws:
Example:
const n = Cesium.Math.nextPowerOfTwo(29); // 32
const m = Cesium.Math.nextPowerOfTwo(32); // 32

static Cesium.Math.nextRandomNumber() → number
engine/Source/Core/Math.js 939

Generates a random floating point number in the range of [0.0, 1.0) using a Mersenne twister.
Returns:
A random number in the range of [0.0, 1.0).
See:

static Cesium.Math.normalize(value, rangeMinimum, rangeMaximum) → number
engine/Source/Core/Math.js 265

Converts a scalar value in the range [rangeMinimum, rangeMaximum] to a scalar in the range [0.0, 1.0]
Name Type Description
value number The scalar value in the range [rangeMinimum, rangeMaximum]
rangeMinimum number The minimum value in the mapped range.
rangeMaximum number The maximum value in the mapped range.
Returns:
A scalar value, where rangeMinimum maps to 0.0 and rangeMaximum maps to 1.0.

static Cesium.Math.previousPowerOfTwo(n) → number
engine/Source/Core/Math.js 874

Computes the previous power-of-two integer less than or equal to the provided non-negative integer. The maximum allowed input is (2^32)-1 due to 32-bit bitwise operator limitation in Javascript.
Name Type Description
n number The integer to test in the range [0, (2^32)-1].
Returns:
The previous power-of-two integer.
Throws:
Example:
const n = Cesium.Math.previousPowerOfTwo(29); // 16
const m = Cesium.Math.previousPowerOfTwo(32); // 32

static Cesium.Math.randomBetween(min, max) → number
engine/Source/Core/Math.js 950

Generates a random number between two numbers.
Name Type Description
min number The minimum value.
max number The maximum value.
Returns:
A random number between the min and max.

static Cesium.Math.setRandomNumberSeed(seed)
engine/Source/Core/Math.js 920

Sets the seed used by the random number generator in CesiumMath#nextRandomNumber.
Name Type Description
seed number An integer used as the seed.

static Cesium.Math.sign(value) → number
engine/Source/Core/Math.js 208

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.
Name Type Description
value number The value to return the sign of.
Returns:
The sign of value.

static Cesium.Math.signNotZero(value) → number
engine/Source/Core/Math.js 224

Returns 1.0 if the given value is positive or zero, and -1.0 if it is negative. This is similar to CesiumMath#sign except that returns 1.0 instead of 0.0 when the input value is 0.0.
Name Type Description
value number The value to return the sign of.
Returns:
The sign of value.

static Cesium.Math.sinh(value) → number
engine/Source/Core/Math.js 294

Returns the hyperbolic sine of a number. The hyperbolic sine of value is defined to be (ex - e-x)/2.0 where e is Euler's number, approximately 2.71828183.

Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is infinite, then the result is an infinity with the same sign as the argument.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

Name Type Description
value number The number whose hyperbolic sine is to be returned.
Returns:
The hyperbolic sine of value.

static Cesium.Math.toDegrees(radians) → number
engine/Source/Core/Math.js 452

Converts radians to degrees.
Name Type Description
radians number The angle to convert in radians.
Returns:
The corresponding angle in degrees.

static Cesium.Math.toRadians(degrees) → number
engine/Source/Core/Math.js 438

Converts degrees to radians.
Name Type Description
degrees number The angle to convert in degrees.
Returns:
The corresponding angle in radians.

static Cesium.Math.toSNorm(value, rangeMaximum) → number
engine/Source/Core/Math.js 236

Converts a scalar value in the range [-1.0, 1.0] to a SNORM in the range [0, rangeMaximum]
Name Type Default Description
value number The scalar value in the range [-1.0, 1.0]
rangeMaximum number 255 optional The maximum value in the mapped range, 255 by default.
Returns:
A SNORM value, where 0 maps to -1.0 and rangeMaximum maps to 1.0.
See:
  • CesiumMath.fromSNorm

static Cesium.Math.zeroToTwoPi(angle) → number
engine/Source/Core/Math.js 542

Produces an angle in the range 0 <= angle <= 2Pi which is equivalent to the provided angle.
Name Type Description
angle number in radians
Returns:
The angle in the range [0, CesiumMath.TWO_PI].
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