Variable MathUtil`Const`

MathUtil: Readonly<{
    computeEigenValuesAndVectors: ((A: MutableMatrix33, Q: MutableMatrix33, w: MutableVector3) => -1 | 0);
    computeGaussianDistributionRatioWhoseSumIsOne: ((params: {
        effectiveDigit?: number;
        kernelSize: number;
        mean?: number;
        variance: number;
    }) => number[]);
    convertToStringAsGLSLFloat: ((value: number) => string);
    degreeToRadian: ((deg: number) => number);
    financial: ((val: string | number) => string);
    gaussianCdf: ((x: number, mu: number, sigma: number) => number);
    invGaussianCdf: ((U: number, mu: number, sigma: number) => number);
    isPowerOfTwo: ((x: number) => boolean);
    isPowerOfTwoTexture: ((width: number, height: number) => boolean);
    lerp: ((a: number, b: number, t: number) => number);
    nearZeroToZero: ((value: number) => number);
    packNormalizedVec4ToVec2: ((x: number, y: number, z: number, w: number, criteria: number) => number[]);
    radianToDegree: ((rad: number) => number);
    roundAsFloat: ((value: number) => number);
    toHalfFloat: (() => ((val: number) => number));
}> = ...

A utility class containing various mathematical functions and operations. This class provides static methods for common mathematical computations including:

Angle conversions (radians/degrees)
Floating point operations and conversions
Power-of-two checks
Vector packing utilities
Statistical functions (Gaussian distributions, error functions)
Matrix eigenvalue computations
Interpolation and formatting utilities

Type declaration

computeEigenValuesAndVectors: ((A: MutableMatrix33, Q: MutableMatrix33, w: MutableVector3) => -1 | 0)
- - (A, Q, w): -1 | 0
  - Computes eigenvalues and eigenvectors of a 3x3 symmetric matrix using the Jacobi method.
    Parameters
    - A: MutableMatrix33
      The input 3x3 symmetric matrix (will be modified during computation)
    - Q: MutableMatrix33
      The output matrix that will contain the eigenvectors
    - w: MutableVector3
      The output vector that will contain the eigenvalues
    Returns -1 | 0
    0 on success, -1 if maximum iterations exceeded
computeGaussianDistributionRatioWhoseSumIsOne: ((params: {
    effectiveDigit?: number;
    kernelSize: number;
    mean?: number;
    variance: number;
}) => number[])
- - (params): number[]
  - Computes a normalized discrete Gaussian distribution where the sum of all ratios equals 1. The sampling points are positioned at integer intervals around the mean.
    Parameters
    - params: {
          effectiveDigit?: number;
          kernelSize: number;
          mean?: number;
          variance: number;
      }
      Configuration object for the Gaussian distribution
      
      OptionaleffectiveDigit?: number
      Number of decimal places for precision (default: 4)
      
      kernelSize: number
      Number of sampling points in the distribution
      
      Optionalmean?: number
      Mean of the Gaussian distribution (default: 0)
      
      variance: number
      Variance of the Gaussian distribution
    Returns number[]
    An array of normalized ratios that sum to 1
    Example
```
// For kernelSize = 2 (mean=0): sampling points are at -0.5 and 0.5
// For kernelSize = 3 (mean=1): sampling points are at 0.0, 1.0, and 2.0
```
convertToStringAsGLSLFloat: ((value: number) => string)
- - (value): string
  - Converts a numeric value to a string formatted for GLSL float literals. Ensures that integer values are suffixed with ".0" for proper GLSL syntax.
    Parameters
    - value: number
      The numeric value to convert
    Returns string
    A string representation suitable for GLSL float literals
degreeToRadian: ((deg: number) => number)
- - (deg): number
  - Converts degrees to radians.
    Parameters
    - deg: number
      The angle in degrees
    Returns number
    The angle in radians
financial: ((val: string | number) => string)
- - (val): string
  - Formats a numeric value as a fixed-width financial string with 7 decimal places. Positive values are prefixed with a space for alignment.
    Parameters
    - val: string | number
      The numeric value to format
    Returns string
    A formatted string with consistent width for financial display
gaussianCdf: ((x: number, mu: number, sigma: number) => number)
- - (x, mu, sigma): number
  - Calculates the cumulative distribution function (CDF) for a Gaussian distribution.
    Parameters
    - x: number
      The value at which to evaluate the CDF
    - mu: number
      The mean of the Gaussian distribution
    - sigma: number
      The standard deviation of the Gaussian distribution
    Returns number
    The cumulative probability up to x
invGaussianCdf: ((U: number, mu: number, sigma: number) => number)
- - (U, mu, sigma): number
  - Calculates the inverse cumulative distribution function (inverse CDF) for a Gaussian distribution.
    Parameters
    - U: number
      The cumulative probability (should be in range [0, 1])
    - mu: number
      The mean of the Gaussian distribution
    - sigma: number
      The standard deviation of the Gaussian distribution
    Returns number
    The value x such that CDF(x) = U
isPowerOfTwo: ((x: number) => boolean)
- - (x): boolean
  - Checks whether a number is a power of two.
    Parameters
    - x: number
      The number to check
    Returns boolean
    True if the number is a power of two, false otherwise
isPowerOfTwoTexture: ((width: number, height: number) => boolean)
- - (width, height): boolean
  - Checks whether the given texture dimensions are both powers of two.
    Parameters
    - width: number
      The width of the texture
    - height: number
      The height of the texture
    Returns boolean
    True if both dimensions are powers of two, false otherwise
lerp: ((a: number, b: number, t: number) => number)
- - (a, b, t): number
  - Performs linear interpolation between two values.
    Parameters
    - a: number
      The starting value
    - b: number
      The ending value
    - t: number
      The interpolation parameter (0 returns a, 1 returns b)
    Returns number
    The interpolated value
nearZeroToZero: ((value: number) => number)
- - (value): number
  - Rounds very small values to zero and values very close to ±1 to exactly ±1. This helps reduce floating-point precision errors in calculations.
    Parameters
    - value: number
      The value to normalize
    Returns number
    The normalized value with small errors corrected
packNormalizedVec4ToVec2: ((x: number, y: number, z: number, w: number, criteria: number) => number[])
- - (x, y, z, w, criteria): number[]
  - Packs a normalized 4D vector into a 2D vector using a specific encoding scheme. All input values must be in the range [-1, 1].
    Parameters
    - x: number
      The x component of the vector (range: [-1, 1])
    - y: number
      The y component of the vector (range: [-1, 1])
    - z: number
      The z component of the vector (range: [-1, 1])
    - w: number
      The w component of the vector (range: [-1, 1])
    - criteria: number
      The encoding criteria/resolution
    Returns number[]
    A 2-element array containing the packed values
radianToDegree: ((rad: number) => number)
- - (rad): number
  - Converts radians to degrees.
    Parameters
    - rad: number
      The angle in radians
    Returns number
    The angle in degrees
roundAsFloat: ((value: number) => number)
- - (value): number
  - Rounds a floating-point number to 7 decimal places to reduce precision errors.
    Parameters
    - value: number
      The value to round
    Returns number
    The rounded value
toHalfFloat: (() => ((val: number) => number))
- - (): ((val: number) => number)
  - Converts a 32-bit floating point number to a 16-bit half-precision float. This implementation is based on the OpenEXR half-precision format with additional rounding. Implementation reference: https://gamedev.stackexchange.com/questions/17326/conversion-of-a-number-from-single-precision-floating-point-representation-to-a/17410#17410
    
    Returns ((val: number) => number)
    A function that converts a number to half-precision float representation
    - - (val): number
      - Parameters
        val: number
        Returns number

Variable MathUtilConst

Type declaration

computeEigenValuesAndVectors: ((A: MutableMatrix33, Q: MutableMatrix33, w: MutableVector3) => -1 | 0)

Parameters

Returns -1 | 0

computeGaussianDistributionRatioWhoseSumIsOne: ((params: { effectiveDigit?: number; kernelSize: number; mean?: number; variance: number; }) => number[])

Parameters

OptionaleffectiveDigit?: number

kernelSize: number

Optionalmean?: number

variance: number

Returns number[]

Example

convertToStringAsGLSLFloat: ((value: number) => string)

Parameters

Returns string

degreeToRadian: ((deg: number) => number)

Parameters

Returns number

financial: ((val: string | number) => string)

Parameters

Returns string

gaussianCdf: ((x: number, mu: number, sigma: number) => number)

Parameters

Returns number

invGaussianCdf: ((U: number, mu: number, sigma: number) => number)

Parameters

Returns number

isPowerOfTwo: ((x: number) => boolean)

Parameters

Returns boolean

isPowerOfTwoTexture: ((width: number, height: number) => boolean)

Parameters

Returns boolean

lerp: ((a: number, b: number, t: number) => number)

Parameters

Returns number

nearZeroToZero: ((value: number) => number)

Parameters

Returns number

packNormalizedVec4ToVec2: ((x: number, y: number, z: number, w: number, criteria: number) => number[])

Parameters

Returns number[]

radianToDegree: ((rad: number) => number)

Parameters

Returns number

roundAsFloat: ((value: number) => number)

Parameters

Returns number

toHalfFloat: (() => ((val: number) => number))

Returns ((val: number) => number)

Parameters

Returns number

Settings

Variable MathUtil`Const`

computeGaussianDistributionRatioWhoseSumIsOne: ((params: {
effectiveDigit?: number;
kernelSize: number;
mean?: number;
variance: number;
}) => number[])

`Optional`effectiveDigit?: number

`Optional`mean?: number