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

Warning: For MAXON API maths functions see Mathematical Functions.

Constants

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(ConstDescID(DescLevel(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.

Note: 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 Vector posA { 1, 1, 0 };
    const Vector posB { 9, 16, 0 };
 
    const Vector 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.

Note: 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 Vector 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.

Miscellaneous

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.

Minimum and maximum checks for Float32, Float64, Int32 and Int64:

FMin(): Gets the minimum of two float values.
FMax(): Gets the maximum of two float values.
LMin(): Gets the minimum of two integer values (single precision version).
VMin(): Gets the minimum of two integer values (double precision version).
LMax(): Gets the maximum of two integer values (single precision version).
VMax(): Gets the maximum of two integer values (double precision version).

Modulo operations for Float32, Float64, Int32 and Int64:

Modulo(): Returns a modulo b.
FMod(): Calculates floating point modulo.
Modf(): Breaks a value into an integral and a fractional part.
LModulo(): Returns a modulo b (integer modulo).

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