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The MAXON API contains mathematical constants and functions that can be used with the basic data types. These constants and functions are defined in the general_math.h and lib_math.h header files. See also Basic Data Types.

Constants

Generic constants are:

maxon::NOTOK: Generic error value of -1.
maxon::InvalidArrayIndex: Invalid array index.

Note: If an error occurs in a function, this function should return a proper error object. See Error Handling.

Mathematical floating point constants are:

maxon::PI: The value of pi.
maxon::PI_INV: The value of 1.0 / pi.
maxon::PI2: The value of 2 * pi.
maxon::PI2_INV: The value of 1.0 / (2 * pi).
maxon::PI05: The value of 0.5 * pi.
maxon::SQRT2: The value of the square root of 2.
maxon::SQRT_PI2: The value of the square root of 2.0 * pi.
maxon::SQRT2_INV: The inverse value of the square root of 2.
maxon::SQRT3: The value of the square root of 3.
maxon::LOG2: The value of Log(2.0).

For values and limits of data types see Basic Data Types.

    // This example calculates the area of a circle of the given radius.
 
    const maxon::Float radius = 123.0;
    const maxon::Float area = maxon::PI * maxon::Sqr(radius);

Template Functions

These template functions can be used with any data type that supports the required operations:

maxon::Abs(X f): Returns the absolute value.
maxon::Min(X a, X b): Returns the minimum of the given values.
maxon::Max(X a, X b): Returns the maximum of the given values.
maxon::Swap(X &a, X &b): Switches the values of the given elements.
maxon::ClampValue(X value, X lowerLimit, X upperLimit): Returns the value clamped to the given limits.
maxon::Blend(const X &value1, const X &value2, Y blendValue): Returns the interpolated value.
maxon::Sqr(X a, X b): Returns the square difference of two values.
maxon::Sqr(X a): Returns the square value.
SetMax(T &a, const T &b): Assigns the maximum of two values to the first value.
SetMin(T &a, const T &b): Assigns the minimum of two values to the first value.
Sign(X f): Returns the sign of a value.
maxon::Mod(T a, T b): Calculates the modulo value for integer values.

// This example template function clamps the given values and returned a mixed result.
// It uses template sub-functions.
 
template <typename T> static T ClampAndBlend(T a, T b, T min, T max, T blend)
{
  a = maxon::ClampValue(a, min, max);
  b = maxon::ClampValue(b, min, max);
 
  return maxon::Blend(a, b, blend);
}

Exponent

These exponential functions are available for maxon::Float32 and maxon::Float64 values:

maxon::Pow(): Calculates a^b.
maxon::Exp(): Calculates e^value.
maxon::Ln(): Calculates the logarithm of the given value.
maxon::Log10(): Calculates the logarithm with base 10 of the given value.
maxon::Log2(): Calculates the logarithm with base 2 of the given value.
maxon::Sqrt(): Calculates the square root of the given value.

Trigonometry

These trigonometric functions are available for maxon::Float32 and maxon::Float64 values:

maxon::Sin(): Calculates the sine of the given value.
maxon::Cos(): Calculates the cosine of the given value.
maxon::SinCos(): Calculates the sine and cosine of the given value in one operation.
maxon::Tan(): Calculates the tangent of the given value.
maxon::ATan(): Calculates the arctangent of the given value.
maxon::ATan2(): Calculates the arctangent of the given value.
maxon::Sinh(): Calculates the hyperbolic sine of the given value.
maxon::Cosh(): Calculates the hyperbolic cosine of the given value.
maxon::Tanh(): Calculates the hyperbolic tangent of the given value.
maxon::ASin(): Calculates the arcsine of the given value.
maxon::ACos(): Calculates the arccosine of the given value.
maxon::DegToRad(): Converts the given value from degrees to radians.
maxon::RadToDeg(): Converts the given value from radians to degrees.

    // This example calculates coordinates along a circle.
 
    const maxon::Int   count  = 100;
    const maxon::Float countF = maxon::Float(count);
 
    const maxon::Float step  = maxon::PI2 / countF;
    maxon::Float       angle = 0.0;
 
    for (maxon::Int i = 0; i < count; ++i)
    {
      maxon::Float sin;
      maxon::Float cos;
      maxon::SinCos(angle, sin, cos);
 
      const maxon::Float degree = maxon::RadToDeg(angle);
 
      // output
      const maxon::String result = FormatString("Pos X: @, Y: @, at @ degree.", sin, cos, degree);
      DiagnosticOutput(result);
 
      // next angle
      angle += step;
    }

Advanced functions are:

maxon::Si(): Calculates si (the unnormalized sinc function).
maxon::Sinc(): Calculates sinc.

Limit

These functions are available for maxon::Float32 and maxon::Float64 values:

maxon::Clamp01(): Clips a the given value against the lower limit 0 and the upper limit 1.
maxon::Floor(): Calculates the largest previous integer number.
maxon::Ceil(): Calculates the smallest following integer number.
maxon::SmoothStep(): Returns 0.0 if the given value is less than a and 1.0 if the value is greater than b, else returns the value mapped by a smooth curve on the range [a,b].
maxon::BoxStep(): Returns 0.0 if the given value is less than a and 1.0 if the value is greater than b, else returns the value mapped on the range [a,b].

    // This example calculates the previous and following integer numbers for the given float value.
 
    const maxon::Float value = 1.23;
 
    const maxon::Float previousInt = maxon::Floor(value);
    const maxon::Float nextInt = maxon::Ceil(value);

Iterables

These template functions work with all values stored in the given iterable e.g. a maxon::BaseArray:

maxon::GetSum(): Calculates the sum of all stored values.
maxon::GetAverage(): Calculates the average of all stored values.

See BaseArray Manual and Arrays Manual.

    // This example gets the sum and average value of all elements stored in the BaseArray.
 
    maxon::BaseArray<maxon::Float> baseArray;
    baseArray.Append(1.0) iferr_return;
    baseArray.Append(2.0) iferr_return;
    baseArray.Append(3.0) iferr_return;
 
    const maxon::Float sum = maxon::GetSum(baseArray);
    const maxon::Float average = maxon::GetAverage(baseArray);

Miscellaneous

These mathematical utility functions are available for maxon::Float32 and maxon::Float64 values:

maxon::Abs(): Calculates the absolute value of a floating point number.
maxon::Inverse(): Calculates the reciprocal value (multiplicative inverse).
maxon::Bias(): Returns the bias as the defined in the book "Texturing and Modeling" by Ebert.
maxon::Truncate(): Returns the next integer value towards zero.

Special maxon::UInt functions are:

maxon::LessThan(): Returns true if the product of the first two arguments is less than the product of the second two arguments.
maxon::IsPowerOfTwo(): Returns true if the given value is a power of 2.

This modulo operation is defined for maxon::Int32, maxon::Int64, maxon::Float32 and maxon::Float64.

maxon::Modulo(): Calculates the modulo of the two given values. For maxon::Float32 and maxon::Float64 there is also:
maxon::FMod(): Calculates floating point modulo.

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