A static utility class for mathematical operations commonly used throughout embedded or real-time applications. More...

#include <Mathematics.h>

Static Public Member Functions
static String	DoubleToCleanString (float value)
	Converts a floating-point value to a String, removing trailing decimals if not needed.

static bool	IsNaN (float value)
	Checks if a floating-point value is NaN (Not a Number).

static bool	IsInfinite (float value)
	Checks if a floating-point value is infinite.

static bool	IsFinite (float value)
	Checks if a floating-point value is finite.

static bool	IsClose (float v1, float v2, float epsilon)
	Checks if two values are close within a specified epsilon.

static int	Sign (float value)
	Determines the sign of a floating-point value.

static float	Pow (float value, float exponent)
	Raises a value to a given exponent.

static float	Sqrt (float value)
	Computes the square root of a value.

static float	Fract (float value)
	Returns the fractional part of a floating-point value.

static float	CosineInterpolation (float beg, float fin, float ratio)
	Applies a cosine-based interpolation between two values.

static float	CosineTransition (float beg, float fin, float ratio)
	A convenience alias for `CosineInterpolation`.

static float	BounceInterpolation (float beg, float fin, float ratio)
	A 'bounce'-like interpolation between two values.

static float	FFloor (float f)
	Floors a floating-point value (rounds down).

static float	FAbs (float f)
	Returns the absolute value of a floating-point number.

static float	FSqrt (float f)
	Computes the square root of a value (internal wrapper for `std::sqrt`).

static float	HermiteInterpolation (float t)
	Hermite interpolation function for smooth transitions.

static float	QuinticInterpolation (float t)
	Quintic interpolation function for smooth transitions.

static float	Lerp (float a, float b, float t)
	Linear interpolation between two values.

static float	CubicLerp (float a, float b, float c, float d, float t)
	Cubic interpolation across four points (a, b, c, d).

static float	BilinearInterpolation (float scaleX, float scaleY, float x1, float y1, float x2, float y2, float v11, float v12, float v21, float v22)
	Performs a bilinear interpolation on a 2D grid.

static float	PingPong (float t)
	Repeats a value between 0 and 1, then mirrors back and forth (like a ping-pong).

static int	RoundUpWindow (int value, int multiple)
	Rounds `value` up to the nearest multiple of `multiple`.

template<typename T >
static T	Constrain (T value, T minimum, T maximum)
	Constrains a value between minimum and maximum.

template<typename T >
static T	DegreesToRadians (T degrees)
	Converts degrees to radians.

template<typename T >
static T	RadiansToDegrees (T radians)
	Converts radians to degrees.

template<typename T >
static T	Map (T value, T inLow, T inMax, T outMin, T outMax)
	Maps a value from one range to another.

template<typename T >
static T	Max (T value1, T value2)
	Returns the maximum of two values.

template<typename T >
static T	Min (T value1, T value2)
	Returns the minimum of two values.

template<typename T >
static T	Min (T v1, T v2, T v3)
	Returns the minimum of three values.

template<typename T >
static T	Max (T v1, T v2, T v3)
	Returns the maximum of three values.

template<typename T >
static T	ConstrainMap (T value, T inLow, T inMax, T outMin, T outMax)
	Combines Constrain and Map in one step: first maps `value` from [inLow, inMax] to [outMin, outMax], then constrains it to stay within [outMin, outMax].

Static Public Attributes
static const float	EPSILON = 0.001f
	A small constant used for floating-point comparisons.

static const float	MPI = 3.14159265358979323846f
	Mathematical constant \(\pi\) (3.14159265358979323846...).

static const float	MPID180 = 0.01745329251994329576f
	The value of \(\pi \div 180.0\), useful for converting degrees to radians.

static const float	M180DPI = 57.29577951308232087684f
	The value of \(180.0 \div \pi\), useful for converting radians to degrees.

static const float	FLTMAX = __FLT_MAX__
	Maximum float value (shortcut to a large number).

static const float	FLTMIN = __FLT_MIN__
	Minimum float value (shortcut to a very small or near-zero number).

Detailed Description

A static utility class for mathematical operations commonly used throughout embedded or real-time applications.

This class provides:

Constants (e.g., EPSILON, MPI, FLTMAX).
Methods for numeric checks (NaN, Infinity, etc.).
Interpolation methods (Lerp, Cosine, Bounce, Cubic).
Mapping and constraint utilities for data normalization.
Basic arithmetic wrappers (Pow, Sqrt, etc.).

Definition at line 32 of file Mathematics.h.

Member Function Documentation

◆ BilinearInterpolation()

float BilinearInterpolation	(	float	scaleX,
		float	scaleY,
		float	x1,
		float	y1,
		float	x2,
		float	y2,
		float	v11,
		float	v12,
		float	v21,
		float	v22
	)

static

Performs a bilinear interpolation on a 2D grid.

This is often used for texture sampling or heightmap sampling.

Parameters

scaleX	Normalized X interpolation factor (0 to 1).
scaleY	Normalized Y interpolation factor (0 to 1).
x1	Left X coordinate.
y1	Bottom Y coordinate.
x2	Right X coordinate.
y2	Top Y coordinate.
v11	Value at (x1, y1).
v12	Value at (x1, y2).
v21	Value at (x2, y1).
v22	Value at (x2, y2).

Returns: The interpolated value.

Definition at line 100 of file Mathematics.cpp.

Referenced by VectorField2D::GetVectorAtPosition().

◆ BounceInterpolation()

float BounceInterpolation	(	float	beg,
		float	fin,
		float	ratio
	)

static

A 'bounce'-like interpolation between two values.

Parameters

beg	The start value.
fin	The end value.
ratio	A normalized ratio (0 to 1).

Returns: The interpolated value, with a "bounce" effect near the end.

Definition at line 59 of file Mathematics.cpp.

References Map().

◆ Constrain()

template<typename T >

static T Constrain	(	T	value,
		T	minimum,
		T	maximum
	)

static

Constrains a value between minimum and maximum.

Template Parameters

T	A numeric type (e.g., int, float).

Parameters

value	The value to constrain.
minimum	The lower bound.
maximum	The upper bound.

Returns: The constrained value within [minimum, maximum].

Referenced by RGBColor::Add(), VectorField2D::Advect(), HorizontalBlur::ApplyEffect(), PhaseOffsetR::ApplyEffect(), PhaseOffsetX::ApplyEffect(), PhaseOffsetY::ApplyEffect(), RadialBlur::ApplyEffect(), VerticalBlur::ApplyEffect(), BoundaryCube::CollideSphere(), Vector2D::Constrain(), Vector3D::Constrain(), Vector2D::Constrain(), Vector3D::Constrain(), VectorField2D::Diffuse(), DerivativeFilter::Filter(), FFTFilter::Filter(), MaterialMask::GetRGB(), VectorField2D::MovingSquareField(), VectorField2D::ObjectField(), RGBColor::Scale(), Effect::SetRatio(), VectorField2D::SineField(), VectorField2D::SpiralField(), VectorField2D::StepField(), MicrophoneSimple::Update(), Boot::Update(), Crash::Update(), ClockAnimation::Update(), MicrophoneSimple::Update(), and MyntAnimation::UpdateFFTVisemes().

◆ ConstrainMap()

template<typename T >

static T ConstrainMap	(	T	value,
		T	inLow,
		T	inMax,
		T	outMin,
		T	outMax
	)

static

Combines Constrain and Map in one step: first maps value from [inLow, inMax] to [outMin, outMax], then constrains it to stay within [outMin, outMax].

Template Parameters

T	A numeric type.

Parameters

value	The value to map/constrain.
inLow	The lower bound of the input range.
inMax	The upper bound of the input range.
outMin	The lower bound of the output range.
outMax	The upper bound of the output range.

Returns: The mapped value, constrained between outMin and outMax.

Referenced by HeadsUpDisplay::EnableBitFaceRender().

◆ CosineInterpolation()

float CosineInterpolation	(	float	beg,
		float	fin,
		float	ratio
	)

static

Applies a cosine-based interpolation between two values.

Parameters

beg	The start value.
fin	The end value.
ratio	A normalized ratio (0 to 1).

Returns: The interpolated value.

See also: CosineTransition

Definition at line 46 of file Mathematics.cpp.

References MPI.

Referenced by TriangleGroupDeformer::CosineInterpolationDeformer(), ObjectDeformer::CosineInterpolationDeformer(), CosineTransition(), Crash::FadeIn(), Crash::FadeOut(), AudioReactiveGradient::GetRGB(), Oscilloscope::GetRGB(), SpectrumAnalyzer::GetRGB(), and Boot::Update().

◆ CosineTransition()

float CosineTransition	(	float	beg,
		float	fin,
		float	ratio
	)

static

A convenience alias for CosineInterpolation.

Parameters

beg	The start value.
fin	The end value.
ratio	A normalized ratio (0 to 1).

Returns: The interpolated value.

See also: CosineInterpolation

Definition at line 52 of file Mathematics.cpp.

References CosineInterpolation().

◆ CubicLerp()

float CubicLerp	(	float	a,
		float	b,
		float	c,
		float	d,
		float	t
	)

static

Cubic interpolation across four points (a, b, c, d).

Parameters

a	First point.
b	Second point (start).
c	Third point (end).
d	Fourth point.
t	A normalized ratio (0 to 1).

Returns: The cubic interpolation result.

Definition at line 91 of file Mathematics.cpp.

◆ DegreesToRadians()

template<typename T >

static T DegreesToRadians ( T degrees )

static

Converts degrees to radians.

Template Parameters

T	A numeric type.

Parameters

degrees The angle in degrees.

Returns: The angle in radians.

Referenced by Rotation::AxisAngleToQuaternion(), Rotation::EulerAnglesToQuaternion(), RotationMatrix::RotateX(), RotationMatrix::RotateY(), and RotationMatrix::RotateZ().

◆ DoubleToCleanString()

String DoubleToCleanString ( float value )

static

Converts a floating-point value to a String, removing trailing decimals if not needed.

Parameters

value The float to convert.

Returns: A String without unnecessary trailing zeros.

Definition at line 10 of file Mathematics.cpp.

Referenced by AxisAngle::ToString(), DirectionAngle::ToString(), Quaternion::ToString(), Vector2D::ToString(), Vector3D::ToString(), and YawPitchRoll::ToString().

◆ FAbs()

float FAbs ( float f )

static

Returns the absolute value of a floating-point number.

Parameters

f	The float to evaluate.

Returns: f if f >= 0, otherwise -f.

Definition at line 71 of file Mathematics.cpp.

◆ FFloor()

float FFloor ( float f )

static

Floors a floating-point value (rounds down).

Parameters

f	The float to floor.

Returns: The greatest integer less than or equal to f.

Definition at line 67 of file Mathematics.cpp.

◆ Fract()

float Fract ( float value )

static

Returns the fractional part of a floating-point value.

For example, Fract(3.75) = 0.75.

Parameters

value The float to evaluate.

Returns: The fractional component of value.

Definition at line 42 of file Mathematics.cpp.

Referenced by SpiralMaterial::GetRGB().

◆ FSqrt()

float FSqrt ( float f )

static

Computes the square root of a value (internal wrapper for std::sqrt).

Parameters

f	The float to take the square root of.

Returns: The square root of f.

Definition at line 75 of file Mathematics.cpp.

◆ HermiteInterpolation()

float HermiteInterpolation ( float t )

static

Hermite interpolation function for smooth transitions.

Parameters

t	A normalized value (0 to 1).

Returns: The Hermite-interpolated value.

Definition at line 79 of file Mathematics.cpp.

◆ IsClose()

bool IsClose	(	float	v1,
		float	v2,
		float	epsilon
	)

static

Checks if two values are close within a specified epsilon.

Parameters

v1	The first value.
v2	The second value.
epsilon	The tolerance for comparison.

Returns: true if v1 and v2 differ by less than epsilon.

Definition at line 26 of file Mathematics.cpp.

Referenced by DampedSpring::Calculate(), Quaternion::Divide(), Vector2D::Divide(), RampFilter::Filter(), ObjectAlign::GetPlaneOrientation(), AudioReactiveGradient::GetRGB(), Oscilloscope::GetRGB(), SpectrumAnalyzer::GetRGB(), VectorField2D::GetVectorAtPosition(), Quaternion::MultiplicativeInverse(), Quaternion::Multiply(), Vector2D::Multiply(), Vector2D::Normal(), Vector3D::Normal(), Vector2D::UnitCircle(), and Vector3D::UnitSphere().

◆ IsFinite()

bool IsFinite ( float value )

static

Checks if a floating-point value is finite.

Parameters

value The float value to check.

Returns: true if finite, otherwise false.

Definition at line 22 of file Mathematics.cpp.

Referenced by Quaternion::IsInfinite().

◆ IsInfinite()

bool IsInfinite ( float value )

static

Checks if a floating-point value is infinite.

Parameters

value The float value to check.

Returns: true if value is infinite, otherwise false.

Definition at line 18 of file Mathematics.cpp.

Referenced by Quaternion::IsFinite().

◆ IsNaN()

bool IsNaN ( float value )

static

Checks if a floating-point value is NaN (Not a Number).

Parameters

value The float value to check.

Returns: true if value is NaN, otherwise false.

Definition at line 14 of file Mathematics.cpp.

Referenced by Quaternion::IsNaN().

◆ Lerp()

float Lerp	(	float	a,
		float	b,
		float	t
	)

static

Linear interpolation between two values.

Parameters

a	The start value.
b	The end value.
t	A normalized ratio (0 to 1).

Returns: (1 - t)*a + t*b

Definition at line 87 of file Mathematics.cpp.

◆ Map()

template<typename T >

static T Map	(	T	value,
		T	inLow,
		T	inMax,
		T	outMin,
		T	outMax
	)

static

Maps a value from one range to another.

Template Parameters

T	A numeric type.

Parameters

value	The value to map.
inLow	The lower bound of the input range.
inMax	The upper bound of the input range.
outMin	The lower bound of the output range.
outMax	The upper bound of the output range.

Returns: The mapped value within [outMin, outMax].

Referenced by GlitchX::ApplyEffect(), HorizontalBlur::ApplyEffect(), PhaseOffsetR::ApplyEffect(), PhaseOffsetX::ApplyEffect(), PhaseOffsetY::ApplyEffect(), RadialBlur::ApplyEffect(), ShiftR::ApplyEffect(), VerticalBlur::ApplyEffect(), BounceInterpolation(), AudioReactiveGradient::GetRGB(), Oscilloscope::GetRGB(), SpectrumAnalyzer::GetRGB(), DepthMaterial::GetRGB(), Image::GetRGB(), UVMap::GetRGB(), VectorField2D::GetVectorAtPosition(), DrGonzoProject::Loading(), FunctionGenerator::SawtoothWave(), FanController::SetSpeed(), FunctionGenerator::SineWave(), FunctionGenerator::SquareWave(), FunctionGenerator::TriangleWave(), Boot::Update(), TVStatic::Update(), GalaxyAnimation::Update(), ClockAnimation::Update(), AlphaAnimation::Update(), PhysicsSimulator::Update(), and Controller::UpdateBrightness().

◆ Max() [1/2]

template<typename T >

static T Max	(	T	v1,
		T	v2,
		T	v3
	)

static

Returns the maximum of three values.

Template Parameters

T	A numeric type.

Parameters

v1	The first value.
v2	The second value.
v3	The third value.

Returns: The largest of v1, v2, and v3.

◆ Max() [2/2]

template<typename T >

static T Max	(	T	value1,
		T	value2
	)

static

Returns the maximum of two values.

Template Parameters

T	A numeric type.

Parameters

value1	The first value.
value2	The second value.

Returns: value1 if value1 >= value2, otherwise value2.

Referenced by Vector3D::AverageHighestTwoComponents(), Triangle2D::DidIntersectSAT(), ObjectAlign::GetPlaneOrientation(), and Vector3D::Max().

◆ Min() [1/2]

template<typename T >

static T Min	(	T	v1,
		T	v2,
		T	v3
	)

static

Returns the minimum of three values.

Template Parameters

T	A numeric type.

Parameters

v1	The first value.
v2	The second value.
v3	The third value.

Returns: The smallest of v1, v2, and v3.

◆ Min() [2/2]

template<typename T >

static T Min	(	T	value1,
		T	value2
	)

static

Returns the minimum of two values.

Template Parameters

T	A numeric type.

Parameters

value1	The first value.
value2	The second value.

Returns: value1 if value1 <= value2, otherwise value2.

Referenced by ObjectAlign::AlignObjects(), Triangle2D::DidIntersectSAT(), ObjectAlign::GetObjectPlanarityRatio(), ObjectAlign::GetTransform(), and Vector3D::Min().

◆ PingPong()

float PingPong ( float t )

static

Repeats a value between 0 and 1, then mirrors back and forth (like a ping-pong).

For example, PingPong(t) toggles between [0..1..0..1...] as t increases.

Parameters

t	The time or input value.

Returns: A float between 0 and 1, repeating in a ping-pong pattern.

Definition at line 114 of file Mathematics.cpp.

◆ Pow()

float Pow	(	float	value,
		float	exponent
	)

static

Raises a value to a given exponent.

Parameters

value	The base value.
exponent	The exponent to raise by.

Returns: value raised to exponent.

Definition at line 34 of file Mathematics.cpp.

Referenced by Quaternion::Power(), and Quaternion::Power().

◆ QuinticInterpolation()

float QuinticInterpolation ( float t )

static

Quintic interpolation function for smooth transitions.

Parameters

t	A normalized value (0 to 1).

Returns: The quintic-interpolated value.

Definition at line 83 of file Mathematics.cpp.

◆ RadiansToDegrees()

template<typename T >

static T RadiansToDegrees ( T radians )

static

Converts radians to degrees.

Template Parameters

T	A numeric type.

Parameters

radians The angle in radians.

Returns: The angle in degrees.

Referenced by Rotation::GetAxisAngle(), Rotation::GetDirectionAngle(), Rotation::GetEulerAngles(), and Rotation::GetYawPitchRoll().

◆ RoundUpWindow()

int RoundUpWindow	(	int	value,
		int	multiple
	)

static

Rounds value up to the nearest multiple of multiple.

Parameters

value	The integer to round up.
multiple	The multiple to round to.

Returns: value rounded up to the nearest multiple of multiple.

Definition at line 119 of file Mathematics.cpp.

Referenced by TriangleGroupDeformer::CosineInterpolationDeformer(), and ObjectDeformer::CosineInterpolationDeformer().

◆ Sign()

int Sign ( float value )

static

Determines the sign of a floating-point value.

Parameters

value The float to check.

Returns: +1 if value > 0, -1 if value < 0, and 0 if value == 0.

Definition at line 30 of file Mathematics.cpp.

◆ Sqrt()

float Sqrt ( float value )

static

Computes the square root of a value.

Parameters

value The float to take the square root of.

Returns: The square root of value.

Definition at line 38 of file Mathematics.cpp.

Referenced by Quaternion::Magnitude(), Vector2D::Magnitude(), Vector3D::Magnitude(), and Quaternion::Normal().

Member Data Documentation

◆ EPSILON

const float EPSILON = 0.001f

static

A small constant used for floating-point comparisons.

Definition at line 37 of file Mathematics.h.

Referenced by Quaternion::DeltaRotation(), Quaternion::Divide(), Vector2D::Divide(), Quaternion::Divide(), Vector2D::LineSegmentsIntersect(), Quaternion::MultiplicativeInverse(), Quaternion::Multiply(), Vector2D::Multiply(), Quaternion::Multiply(), Vector2D::Normal(), Vector3D::Normal(), Quaternion::RotateVector(), Quaternion::RotateVector(), Quaternion::RotateVectorUnit(), Quaternion::SphericalInterpolation(), Vector2D::UnitCircle(), Vector3D::UnitSphere(), Quaternion::UnrotateVector(), and Quaternion::UnrotateVector().

◆ FLTMAX

const float FLTMAX = __FLT_MAX__

static

Maximum float value (shortcut to a large number).

Definition at line 57 of file Mathematics.h.

◆ FLTMIN

const float FLTMIN = __FLT_MIN__

static

Minimum float value (shortcut to a very small or near-zero number).

Definition at line 62 of file Mathematics.h.

◆ M180DPI

const float M180DPI = 57.29577951308232087684f

static

The value of \(180.0 \div \pi\), useful for converting radians to degrees.

Definition at line 52 of file Mathematics.h.

Referenced by Vector2D::RadiansToDegrees(), and Vector3D::RadiansToDegrees().

◆ MPI

const float MPI = 3.14159265358979323846f

static

Mathematical constant \(\pi\) (3.14159265358979323846...).

Definition at line 42 of file Mathematics.h.

Referenced by PhaseOffsetR::ApplyEffect(), PhaseOffsetX::ApplyEffect(), PhaseOffsetY::ApplyEffect(), CosineInterpolation(), AudioReactiveGradient::GetRGB(), SpiralMaterial::GetRGB(), RGBColor::HueShift(), RGBColor::HueShift(), VectorField2D::MovingSquareField(), Rotation::QuaternionFromDirectionVectors(), VectorField2D::StepField(), and Menu::Update().

◆ MPID180

const float MPID180 = 0.01745329251994329576f

static

The value of \(\pi \div 180.0\), useful for converting degrees to radians.

Definition at line 47 of file Mathematics.h.

Referenced by Vector2D::DegreesToRadians(), Vector3D::DegreesToRadians(), Ellipse::IsInShape(), Rectangle::IsInShape(), and Vector2D::Rotate().

The documentation for this class was generated from the following files:

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ BilinearInterpolation()

◆ BounceInterpolation()

◆ Constrain()

◆ ConstrainMap()

◆ CosineInterpolation()

◆ CosineTransition()

◆ CubicLerp()

◆ DegreesToRadians()

◆ DoubleToCleanString()

◆ FAbs()

◆ FFloor()

◆ Fract()

◆ FSqrt()

◆ HermiteInterpolation()

◆ IsClose()

◆ IsFinite()

◆ IsInfinite()

◆ IsNaN()

◆ Lerp()

◆ Map()

◆ Max() [1/2]

◆ Max() [2/2]

◆ Min() [1/2]

◆ Min() [2/2]

◆ PingPong()

◆ Pow()

◆ QuinticInterpolation()

◆ RadiansToDegrees()

◆ RoundUpWindow()

◆ Sign()

◆ Sqrt()

Member Data Documentation

◆ EPSILON

◆ FLTMAX

◆ FLTMIN

◆ M180DPI

◆ MPI

◆ MPID180