Class MathHelper

Contains common mathematical functions and constants.

Inheritance

object

MathHelper

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Namespace: OpenTK.Mathematics

Assembly: OpenTK.Mathematics.dll

Syntax

public static class MathHelper

Fields

E

Defines the value of E as a float.

Declaration

public const float E = 2.7182817

Field Value

Type	Description
float

Log10E

Defines the base-10 logarithm of E.

Declaration

public const float Log10E = 0.4342945

Field Value

Type	Description
float

Log2E

Defines the base-2 logarithm of E.

Declaration

public const float Log2E = 1.442695

Field Value

Type	Description
float

Pi

Defines the value of Pi as a float.

Declaration

public const float Pi = 3.1415927

Field Value

Type	Description
float

PiOver2

Defines the value of Pi divided by two as a float.

Declaration

public const float PiOver2 = 1.5707964

Field Value

Type	Description
float

PiOver3

Defines the value of Pi divided by three as a float.

Declaration

public const float PiOver3 = 1.0471976

Field Value

Type	Description
float

PiOver4

Defines the value of Pi divided by four as a float.

Declaration

public const float PiOver4 = 0.7853982

Field Value

Type	Description
float

PiOver6

Defines the value of Pi divided by six as a float.

Declaration

public const float PiOver6 = 0.5235988

Field Value

Type	Description
float

ThreePiOver2

Defines the value of Pi multiplied by 3 and divided by two as a float.

Declaration

public const float ThreePiOver2 = 4.712389

Field Value

Type	Description
float

TwoPi

Defines the value of Pi multiplied by two as a float.

Declaration

public const float TwoPi = 6.2831855

Field Value

Type	Description
float

Methods

ApproximatelyEqual(float, float, int)

Approximates floating point equality with a maximum number of different bits. This is typically used in place of an epsilon comparison. see: https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ see: https://stackoverflow.com/questions/3874627/floating-point-comparison-functions-for-c-sharp.

Declaration

[Pure]
public static bool ApproximatelyEqual(float a, float b, int maxDeltaBits)

Parameters

Type	Name	Description
float	a	the first value to compare.
float	b	the second value to compare.
int	maxDeltaBits	the number of floating point bits to check.

Returns

Type	Description
bool	true if the values are approximately equal; otherwise, false.

ApproximatelyEqualEpsilon(double, double, double)

Approximates double-precision floating point equality by an epsilon (maximum error) value. This method is designed as a "fits-all" solution and attempts to handle as many cases as possible.

Declaration

[Pure]
public static bool ApproximatelyEqualEpsilon(double a, double b, double epsilon)

Parameters

Type	Name	Description
double	a	The first float.
double	b	The second float.
double	epsilon	The maximum error between the two.

Returns

Type	Description
bool	true if the values are approximately equal within the error margin; otherwise, false.

ApproximatelyEqualEpsilon(float, float, float)

Approximates single-precision floating point equality by an epsilon (maximum error) value. This method is designed as a "fits-all" solution and attempts to handle as many cases as possible.

Declaration

[Pure]
public static bool ApproximatelyEqualEpsilon(float a, float b, float epsilon)

Parameters

Type	Name	Description
float	a	The first float.
float	b	The second float.
float	epsilon	The maximum error between the two.

Returns

Type	Description
bool	true if the values are approximately equal within the error margin; otherwise, false.

ApproximatelyEquivalent(double, double, double)

Approximates equivalence between two double-precision floating-point numbers on a direct human scale. It is important to note that this does not approximate equality - instead, it merely checks whether or not two numbers could be considered equivalent to each other within a certain tolerance. The tolerance is inclusive.

Declaration

[Pure]
public static bool ApproximatelyEquivalent(double a, double b, double tolerance)

Parameters

Type	Name	Description
double	a	The first value to compare.
double	b	The second value to compare.
double	tolerance	The tolerance within which the two values would be considered equivalent.

Returns

Type	Description
bool	Whether or not the values can be considered equivalent within the tolerance.

ApproximatelyEquivalent(float, float, float)

Approximates equivalence between two single-precision floating-point numbers on a direct human scale. It is important to note that this does not approximate equality - instead, it merely checks whether or not two numbers could be considered equivalent to each other within a certain tolerance. The tolerance is inclusive.

Declaration

[Pure]
public static bool ApproximatelyEquivalent(float a, float b, float tolerance)

Parameters

Type	Name	Description
float	a	The first value to compare.
float	b	The second value to compare.
float	tolerance	The tolerance within which the two values would be considered equivalent.

Returns

Type	Description
bool	Whether or not the values can be considered equivalent within the tolerance.

BinomialCoefficient(int, int)

Calculates the binomial coefficient n above k.

Declaration

[Pure]
public static long BinomialCoefficient(int n, int k)

Parameters

Type	Name	Description
int	n	The n.
int	k	The k.

Returns

Type	Description
long	n! / (k! * (n - k)!).

ClampAngle(double)

Clamps an angle to the range [0, 360).

Declaration

public static double ClampAngle(double angle)

Parameters

Type	Name	Description
double	angle	The angle to clamp in degrees.

Returns

Type	Description
double	The clamped angle in the range [0, 360).

ClampAngle(float)

Clamps an angle to the range [0, 360).

Declaration

public static float ClampAngle(float angle)

Parameters

Type	Name	Description
float	angle	The angle to clamp in degrees.

Returns

Type	Description
float	The clamped angle in the range [0, 360).

ClampRadians(double)

Clamps an angle to the range [0, 2π).

Declaration

public static double ClampRadians(double angle)

Parameters

Type	Name	Description
double	angle	The angle to clamp in radians.

Returns

Type	Description
double	The clamped angle in the range [0, 2π).

ClampRadians(float)

Clamps an angle to the range [0, 2π).

Declaration

public static float ClampRadians(float angle)

Parameters

Type	Name	Description
float	angle	The angle to clamp in radians.

Returns

Type	Description
float	The clamped angle in the range [0, 2π).

DegreesToRadians(double)

Convert degrees to radians.

Declaration

[Pure]
public static double DegreesToRadians(double degrees)

Parameters

Type	Name	Description
double	degrees	An angle in degrees.

Returns

Type	Description
double	The angle expressed in radians.

DegreesToRadians(float)

Convert degrees to radians.

Declaration

[Pure]
public static float DegreesToRadians(float degrees)

Parameters

Type	Name	Description
float	degrees	An angle in degrees.

Returns

Type	Description
float	The angle expressed in radians.

Elerp(double, double, double)

Exponentially interpolates between start and end by t. Equivalent to start * pow(end/start, t). Useful for scaling and zooms where constant change in t should result in a multiplicative change in output.

Declaration

public static double Elerp(double start, double end, double t)

Parameters

Type	Name	Description
double	start	Start value. Must be non-negative.
double	end	End value. Must be non-negative.
double	t	Value of the interpolation between start and end. Not clamped.

Returns

Type	Description
double	The interpolated result between the start and end values.

Elerp(float, float, float)

Exponentially interpolates between start and end by t. Equivalent to start * pow(end/start, t). Useful for scaling and zooms where constant change in t should result in a multiplicative change in output.

Declaration

public static float Elerp(float start, float end, float t)

Parameters

Type	Name	Description
float	start	Start value. Must be non-negative.
float	end	End value. Must be non-negative.
float	t	Value of the interpolation between start and end. Not clamped.

Returns

Type	Description
float	The interpolated result between the start and end values.

Factorial(int)

Calculates the factorial of a given natural number.

Declaration

[Pure]
public static long Factorial(int n)

Parameters

Type	Name	Description
int	n	The number.

Returns

Type	Description
long	The factorial of n.

Lerp(double, double, double)

Linearly interpolates between start and end by t.

Declaration

[Pure]
public static double Lerp(double start, double end, double t)

Parameters

Type	Name	Description
double	start	Start value.
double	end	End value.
double	t	Value of the interpolation between start and end. Not clamped.

Returns

Type	Description
double	The interpolated result between the start and end values.

Lerp(float, float, float)

Linearly interpolates between start and end by t.

Declaration

[Pure]
public static float Lerp(float start, float end, float t)

Parameters

Type	Name	Description
float	start	Start value.
float	end	End value.
float	t	Value of the interpolation between start and end. Not clamped.

Returns

Type	Description
float	The interpolated result between the start and end values.

MapRange(double, double, double, double, double)

Scales the specified number linearly between a minimum and a maximum.

Declaration

[Pure]
public static double MapRange(double value, double valueMin, double valueMax, double resultMin, double resultMax)

Parameters

Type	Name	Description
double	value	The number to scale.
double	valueMin	The minimum expected number (inclusive).
double	valueMax	The maximum expected number (inclusive).
double	resultMin	The minimum output number (inclusive).
double	resultMax	The maximum output number (inclusive).

Returns

Type	Description
double	The number, scaled linearly between min and max.

Remarks

If the value range is zero, this function will throw a divide by zero exception.

MapRange(int, int, int, int, int)

Scales the specified number linearly between a minimum and a maximum.

Declaration

[Pure]
public static int MapRange(int value, int valueMin, int valueMax, int resultMin, int resultMax)

Parameters

Type	Name	Description
int	value	The number to scale.
int	valueMin	The minimum expected number (inclusive).
int	valueMax	The maximum expected number (inclusive).
int	resultMin	The minimum output number (inclusive).
int	resultMax	The maximum output number (inclusive).

Returns

Type	Description
int	The number, scaled linearly between min and max.

Remarks

If the value range is zero, this function will throw a divide by zero exception.

MapRange(float, float, float, float, float)

Scales the specified number linearly between a minimum and a maximum.

Declaration

[Pure]
public static float MapRange(float value, float valueMin, float valueMax, float resultMin, float resultMax)

Parameters

Type	Name	Description
float	value	The number to scale.
float	valueMin	The minimum expected number (inclusive).
float	valueMax	The maximum expected number (inclusive).
float	resultMin	The minimum output number (inclusive).
float	resultMax	The maximum output number (inclusive).

Returns

Type	Description
float	The number, scaled linearly between min and max.

Remarks

If the value range is zero, this function will throw a divide by zero exception.

NextPowerOfTwo(double)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

[Pure]
public static double NextPowerOfTwo(double n)

Parameters

Type	Name	Description
double	n	The specified number.

Returns

Type	Description
double	The next power of two.

NextPowerOfTwo(int)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

[Pure]
public static int NextPowerOfTwo(int n)

Parameters

Type	Name	Description
int	n	The specified number.

Returns

Type	Description
int	The next power of two.

NextPowerOfTwo(long)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

[Pure]
public static long NextPowerOfTwo(long n)

Parameters

Type	Name	Description
long	n	The specified number.

Returns

Type	Description
long	The next power of two.

NextPowerOfTwo(float)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

[Pure]
public static float NextPowerOfTwo(float n)

Parameters

Type	Name	Description
float	n	The specified number.

Returns

Type	Description
float	The next power of two.

NormalizeAngle(double)

Normalizes an angle to the range (-180, 180].

Declaration

public static double NormalizeAngle(double angle)

Parameters

Type	Name	Description
double	angle	The angle in degrees to normalize.

Returns

Type	Description
double	The normalized angle in the range (-180, 180].

NormalizeAngle(float)

Normalizes an angle to the range (-180, 180].

Declaration

public static float NormalizeAngle(float angle)

Parameters

Type	Name	Description
float	angle	The angle in degrees to normalize.

Returns

Type	Description
float	The normalized angle in the range (-180, 180].

NormalizeRadians(double)

Normalizes an angle to the range (-π, π].

Declaration

public static double NormalizeRadians(double angle)

Parameters

Type	Name	Description
double	angle	The angle in radians to normalize.

Returns

Type	Description
double	The normalized angle in the range (-π, π].

NormalizeRadians(float)

Normalizes an angle to the range (-π, π].

Declaration

public static float NormalizeRadians(float angle)

Parameters

Type	Name	Description
float	angle	The angle in radians to normalize.

Returns

Type	Description
float	The normalized angle in the range (-π, π].

RadiansToDegrees(double)

Convert radians to degrees.

Declaration

[Pure]
public static double RadiansToDegrees(double radians)

Parameters

Type	Name	Description
double	radians	An angle in radians.

Returns

Type	Description
double	The angle expressed in degrees.

RadiansToDegrees(float)

Convert radians to degrees.

Declaration

[Pure]
public static float RadiansToDegrees(float radians)

Parameters

Type	Name	Description
float	radians	An angle in radians.

Returns

Type	Description
float	The angle expressed in degrees.

Swap<T>(ref T, ref T)

Swaps two values.

Declaration

public static void Swap<T>(ref T a, ref T b)

Parameters

Type	Name	Description
T	a	The first value.
T	b	The second value.

Type Parameters

Name	Description
T	The type of the values to swap.