Group math¶

Represent a triangle geometry.

A triangle is a collection of three vertices oriented in a Clock-Wise (CW) manner.

Generates a random number between ditherMin andditherMax .

inline AmReal32 AmDitherReal32 (
    const AmReal32 ditherMin,
    const AmReal32 ditherMax
) 

Parameters:

• ditherMin The minimum value for the random number.
• ditherMax The maximum value for the random number.

Returns:

A random number between ditherMin and ditherMax.

Converts a 32-bit floating-point audio sample to a fixed-point representation.

inline AmInt32 AmFloatToFixedPoint (
    const AmReal32 x
) 

Parameters:

• x The 32-bit floating-point audio sample to convert.

Returns:

The fixed-point representation of the input 32-bit floating-point audio sample.

Converts a 16-bit signed integer audio sample to a 32-bit floating-point representation.

inline AmReal32 AmInt16ToReal32 (
    const AmInt16 x
) 

Parameters:

• x The 16-bit signed integer audio sample to convert.

Returns:

The 32-bit floating-point representation of the input 16-bit signed integer audio sample.

Note:

For more accurate conversion, the SDK should be compiled with the AM_ACCURATE_CONVERSION macro defined.

Converts a 32-bit signed integer audio sample to a 32-bit floating-point representation.

inline AmReal32 AmInt32ToReal32 (
    const AmInt32 x
) 

Parameters:

• x The 32-bit signed integer audio sample to convert.

Returns:

The 32-bit floating-point representation of the input 32-bit signed integer audio sample.

Note:

For more accurate conversion, the SDK should be compiled with the AM_ACCURATE_CONVERSION macro defined.

Converts a 32-bit floating-point audio sample to a 16-bit signed integer representation.

inline AmInt16 AmReal32ToInt16 (
    const AmReal32 x,
    bool dithering=false
) 

Parameters:

• x The 32-bit floating-point audio sample to convert.
• dithering If true, adds a dithering noise to the output.

Returns:

The 16-bit signed integer representation of the input 32-bit floating-point audio sample.

Note:

For more accurate conversion, the SDK should be compiled with the AM_ACCURATE_CONVERSION macro defined.

Finds the closest rational approximation of numerator /denominator whose terms are both lower than or equal tomaxTerm .

inline AmRational ApproximateRational (
    AmUInt64 numerator,
    AmUInt64 denominator,
    AmUInt64 maxTerm
) 

The reduced input is returned unchanged when it already fits, with exact set to true. Otherwise the best continued-fraction convergent or semiconvergent within the bound is returned, with exact set to false.

The computation uses integer arithmetic only, performs no allocation, and runs in a bounded number of steps, so it is safe to call from the audio thread and produces identical results on every platform.

The comparison arithmetic assumes terms small enough that the cross-products a * q and b * p fit in 64 bits: 32-bit inputs with a maxTerm in the low thousands are safely within that domain.

Parameters:

• numerator The numerator of the ratio to approximate. Must be greater than zero.
• denominator The denominator of the ratio to approximate. Must be greater than zero.
• maxTerm The maximum value allowed for both terms of the result. Must be greater than zero.

Returns:

The approximated ratio. Both terms are lower than or equal to maxTerm, and the denominator is never zero.

Computes the Catmull-Rom interpolation value at a given time t between four points.

inline AmReal32 CatmullRom (
    const AmReal32 t,
    const AmReal32 p0,
    const AmReal32 p1,
    const AmReal32 p2,
    const AmReal32 p3
) 

Parameters:

• t The time value between 0 and 1.
• p0 The first point.
• p1 The second point.
• p2 The third point.
• p3 The fourth point.

Returns:

The Catmull-Rom interpolation value at the given time t.

Finds the greatest common divisor (GCD) of two integers.

inline AmInt64 FindGCD (
    AmInt64 a,
    AmInt64 b
) 

Parameters:

• a First integer.
• b Second integer.

Returns:

The greatest common divisor of a and b.

Computes the value base^exp using the squared exponentiation method.

template<typename T>
inline T IntegerPow (
    T base,
    AmInt32 exp
) 

Template parameters:

• T An integer type, a floating-point type, or any other type where operator *= is defined.

Parameters:

• base Input of the power function.
• exp The exponent of the power function. Must be non-negative.

Returns:

The result of raising the base to the power of the exponent.

Calculates the inverse square root of a number using Quake III's implementation.

inline AmReal32 InverseSquareRoot (
    AmReal32 x
) 

Parameters:

• x The number to calculate the inverse square root of.

Returns:

The inverse square root of the input number.

Calculates the linear interpolation value at a given time t between two points.

inline AmReal32 Lerp (
    const AmReal32 t,
    const AmReal32 p0,
    const AmReal32 p1
) 

Parameters:

• t The time value between 0 and 1.
• p0 The first point.
• p1 The second point.

Returns:

The linear interpolation value at the given time t.

Returns the next power of 2 of a given number.

template<typename T>
inline T NextPowerOf2 (
    const T & val
) 

Template parameters:

• T An integer type, a floating-point type, or any other type where operator *= is defined.

Parameters:

• val The number.

Returns:

The next power of 2.