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The classic API provides basic mathematical constants and functions to perform mathematical operations using its data types.

另请参阅 Primitive Data Types Manual (Classic) .

警告: For MAXON API maths functions see Mathematical Functions .

常量

These mathematical constants are defined as a Float64 values:

maxon::PI : The value of pi.
maxon::PI_INV : The value of 1.0 / pi.
maxon::PI2 : The value of 2.0 * pi.
maxon::PI2_INV : The value of 1.0 / (2.0 * pi).
maxon::PI05 : The value of 0.5 * pi.

// This example calculates the area of the given "Disc" object.

GeData data; disc->GetParameter( DescID ( PRIM_DISC_ORAD ), data, DESCFLAGS_GET::NONE );

const Float64 radius = data. GetFloat (); const Float64 area = maxon::PI * maxon::Pow (radius, 2.0);

Further constants are:

COLORTOINT_MULTIPLIER : Constant to convert from vectors color components to integers. See also Color Functions Manual .
::PERCENT: Constant to convert from 0.0 - 1.0 range to percentage.
THIRD : Constant to calculate the third of a value.
SIXTH : Constant to calculate the sixth of a value.
MAXRANGE : Maximum value for metric data.
MAXELEMENTS : Maximum number of points of a polygon or spline object.
MIN_EPSILON : Minimum epsilon value.

Generic Datatypes

These template functions can be applied to all data types that support the required operations. The list, not limited to, includes:

Abs(X f) : Calculates the absolute value of any data type.
Min(X a, X b) : Calculates the minimum of two values and returns it.
Max(X a, X b) : Calculates the maximum of two values and returns it.
Swap(X &a, X &b) : Swaps two values. If available, move semantics will be used.
ClampValue(X a, X b, X c) : Clips a value against a lower and an upper limit. The new value is returned.
Sqr(X a, X b) : Calculates square of a 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) : Calculates the sign of a value.
Mod(T a, U b) : Calculates a modulo b.

Exponent

These exponential functions are available for Float32 and Float64 values. The list, not limited to, includes:

Exp() : Calculates e raised to the power of the given value.
Pow() : Calculates v1 raised to the power of v2.
Ln() : Calculates the natural logarithm of the given value.
Log10() : Calculates the logarithm in base 10 of the given value.
Log2() : Calculates the logarithm in base 2 of the given value.
Sqrt() : Calculates the square root of the given value.
Sqr() : Calculates the square of the given value.

注意: If faulty input values are given to these functions, no exceptions will be generated.

// This example calculates the 2D distance between the given points in space. const 向量 posA { 1, 1, 0 }; const 向量 posB { 9, 16, 0 }; const 向量 vec = posB - posA; const Float distance = maxon::Sqrt ( maxon::Sqr (vec. x ) + maxon::Sqr (vec. y ));

Trigonometry

These trigonometric functions are available for Float32 and Float64 values. The list, not limited to, includes:

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

注意: If faulty input values are given to these functions, no exceptions will be generated.

// This example creates null objects along a circle.

for ( Int i = 0; i < count; ++i) { // calculate position on circle maxon::SinCos (angle, sin, cos);

// create null BaseObject * const nullObject = BaseObject::Alloc ( Onull ); if (nullObject == nullptr ) return maxon::OutOfMemoryError( MAXON_SOURCE_LOCATION );

// place null const 向量 pos { sin* 100.0, cos* 100.0, 0 }; nullObject-> SetAbsPos (pos); nullObject-> SetName ( FormatNumber (angle, FORMAT_DEGREE , 0)); doc-> InsertObject (nullObject, nullptr , nullptr );

// next step angle = angle + step; }

Limit

These functions are available for Float32 and Float64 values. The list, not limited to, includes:

Floor() : Calculates the greatest integer less than or equal to the given value.
Ceil() : Calculates the least integer greater than or equal to the given value.
Clamp01() : Clips the given float value against the lower limit 0.0 and the upper limit 1.0. The result will be returned.
StepEx() : Returns 1.0 if x is greater than or equal to a, else 0.0. Only for Float64 .
Boxstep() : Returns 0.0 if x is less than a and 1.0 if x is greater than b, else returns x mapped on the range [a,b].
Smoothstep() : Returns 0.0 if x is less than a and 1.0 if x is greater than b, else returns x mapped on the range [a,b].

// This example calculates the integer values next to the given float value. const Float value = 9.123; const Float previousInteger = Floor (value); const Float nextInteger = Ceil (value);

And for Int32 and Int64 values:

LCut() : Limits the given value to the given borders.
VCut() : Limits the given value to the given borders.

杂项

These functions are available for Float32 and Float64 values:

Bias() : Returns the bias as the defined in the book "Texturing and Modeling" by Ebert.
Truncate() : Returns the next integer value towards zero.
Abs() : Calculates the absolute value of a floating point number.
Inverse() : Calculates the reciprocal value (multiplicative inverse).
Round() : Rounds a floating point value.
Blend() : Blend between two float values by a certain amount. The new value is returned.