Mathematical Functions

内容表

关于
常量
Template Functions
Exponent
Trigonometry
Limit
Iterables
杂项
延伸阅读

关于

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 .

常量

Generic constants are:

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

注意: 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.

见 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);

杂项

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.

延伸阅读

static constexpr Float64 PI2

floating point constant: 2.0 * PI

定义： apibasemath.h:145

maxon::GetAverage

MAXON_ATTRIBUTE_FORCE_INLINE std::remove_reference< ITERABLETYPE >::type::ValueType GetAverage(ITERABLETYPE &&array)

Returns the average of all elements.

定义： lib_math.h:300

maxon::ClampValue

MAXON_ATTRIBUTE_FORCE_INLINE X ClampValue(X value, X lowerLimit, X upperLimit)

Clips a value against a lower and upper limit. The new value is returned.

定义： apibasemath.h:358

MAXON_ATTRIBUTE_FORCE_INLINE X Blend(const X &value1, const X &value2, Y blendValue)

Blends two values. If blendValue is 0.0 value1 is returned, if blendValue is 1.0 value2 is returned....

定义： apibasemath.h:365

定义： string.h:1197

MAXON_ATTRIBUTE_FORCE_INLINE void SinCos(Float32 val, Float32 &sn, Float32 &cs)

Calculates both sine and cosine of a value.

定义： apibasemath.h:481

#define iferr_return

定义： resultbase.h:1434

Float64 Float

定义： apibase.h:193

maxon::BaseArray

定义： basearray.h:366

DiagnosticOutput

#define DiagnosticOutput(formatString,...)

定义： debugdiagnostics.h:166

static constexpr Float64 PI

floating point constant: PI

定义： apibasemath.h:139

MAXON_ATTRIBUTE_FORCE_INLINE std::remove_reference< ITERABLETYPE >::type::ValueType GetSum(ITERABLETYPE &&array)

Returns the sum of all elements.

定义： lib_math.h:287

maxon::BaseArray::Append

MAXON_ATTRIBUTE_FORCE_INLINE ResultRef< T > Append()

定义： basearray.h:569

Int64 Int

signed 32/64 bit int, size depends on the platform

定义： apibase.h:184

MAXON_ATTRIBUTE_FORCE_INLINE Float32 Ceil(Float32 val)

Rounds to the smallest following integer number.

定义： apibasemath.h:278

#define FormatString(...)

定义： string.h:2031

MAXON_ATTRIBUTE_FORCE_INLINE Float32 Floor(Float32 val)

Rounds to the largest previous integer number.

定义： apibasemath.h:272

MAXON_ATTRIBUTE_FORCE_INLINE X Sqr(X a, X b)

Calculates square difference of two values.

定义： apibasemath.h:368

maxon::RadToDeg

MAXON_ATTRIBUTE_FORCE_INLINE Float32 RadToDeg(Float32 r)

Converts float value from radians to degrees.

定义： apibasemath.h:475