Class M

Provides standard mathematical functions and helpers for different types.

Inheritance

System.Object

M

Inherited Members

System.Object.Equals(System.Object)

System.Object.Equals(System.Object, System.Object)

System.Object.GetHashCode()

System.Object.GetType()

System.Object.MemberwiseClone()

System.Object.ReferenceEquals(System.Object, System.Object)

System.Object.ToString()

Namespace: Fusee.Math.Core

Assembly: Fusee.Math.Core.dll

Syntax

public static class M

Fields

E

Defines the value of E as a System.Single.

Declaration

public const float E = 2.71828175F

Field Value

Type	Description
System.Single

EpsilonDouble

Defines the value which represents the machine epsilon for System.Double in C#.

Declaration

public const double EpsilonDouble = 1.11022302462516E-16

Field Value

Type	Description
System.Double

EpsilonFloat

Defines the value which represents the machine epsilon for System.Single in C#.

Declaration

public const float EpsilonFloat = 1.192093E-07F

Field Value

Type	Description
System.Single

Log10E

Defines the base-10 logarithm of E.

Declaration

public const float Log10E = 0.4342945F

Field Value

Type	Description
System.Single

Log2E

Defines the base-2 logarithm of E.

Declaration

public const float Log2E = 1.442695F

Field Value

Type	Description
System.Single

Pi

Defines the value of Pi as a System.Single.

Declaration

public const float Pi = 3.14159274F

Field Value

Type	Description
System.Single

PiOver2

Defines the value of Pi divided by two as a System.Single.

Declaration

public const float PiOver2 = 1.57079637F

Field Value

Type	Description
System.Single

PiOver3

Defines the value of Pi divided by three as a System.Single.

Declaration

public const float PiOver3 = 1.04719758F

Field Value

Type	Description
System.Single

PiOver4

Defines the value of Pi divided by four as a System.Single.

Declaration

public const float PiOver4 = 0.7853982F

Field Value

Type	Description
System.Single

PiOver6

Defines the value of Pi divided by six as a System.Single.

Declaration

public const float PiOver6 = 0.5235988F

Field Value

Type	Description
System.Single

ThreePiOver2

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

Declaration

public const float ThreePiOver2 = 4.712389F

Field Value

Type	Description
System.Single

TwoPi

Defines the value of Pi multiplied by two as a System.Single.

Declaration

public const float TwoPi = 6.28318548F

Field Value

Type	Description
System.Single

Methods

BinomialCoefficient(Int32, Int32)

Calculates the binomial coefficient n above k.

Declaration

public static long BinomialCoefficient(int n, int k)

Parameters

Type	Name	Description
System.Int32	n	The n.
System.Int32	k	The k.

Returns

Type	Description
System.Int64	n! / (k! * (n - k)!)

CalculateCentroid(IEnumerable<double3>)

Calculates the centroid point (mean) from given vertices in double precision.

Declaration

public static double3 CalculateCentroid(IEnumerable<double3> vertices)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<double3>	vertices

Returns

Type	Description
double3

CalculateCentroid(IEnumerable<float3>)

Calculates the centroid point (mean) from given vertices in single precision.

Declaration

public static float3 CalculateCentroid(IEnumerable<float3> vertices)

Parameters

Type	Name	Description
System.Collections.Generic.IEnumerable<float3>	vertices

Returns

Type	Description
float3

Clamp(Double, Double, Double)

Clamp a value to the given minimum and maximum vectors.

Declaration

public static double Clamp(double val, double min, double max)

Parameters

Type	Name	Description
System.Double	val	Input value
System.Double	min	Minimum value
System.Double	max	Maximum value

Returns

Type	Description
System.Double	The clamped value.

Clamp(Single, Single, Single)

Clamp a value to the given minimum and maximum vectors.

Declaration

public static float Clamp(float val, float min, float max)

Parameters

Type	Name	Description
System.Single	val	Input value.
System.Single	min	Minimum value.
System.Single	max	Maximum value.

Returns

Type	Description
System.Single	The clamped value.

Cos(Single)

Returns the Cos of the given value as float.

Declaration

public static float Cos(float val)

Parameters

Type	Name	Description
System.Single	val	The value.

Returns

Type	Description
System.Single

CreateCovarianceMatrix(double3, IEnumerable<double3>)

Generates a covariance matrix from given centroid and vertices in double precision.

Declaration

public static double4x4 CreateCovarianceMatrix(double3 centroid, IEnumerable<double3> vertices)

Parameters

Type	Name	Description
double3	centroid	The centroid of the current mesh or point cloud.
System.Collections.Generic.IEnumerable<double3>	vertices	The vertex data.

Returns

Type	Description
double4x4

CreateCovarianceMatrix(float3, IEnumerable<float3>)

Generates a covariance matrix from given centroid and vertices in single precision.

Declaration

public static float4x4 CreateCovarianceMatrix(float3 centroid, IEnumerable<float3> vertices)

Parameters

Type	Name	Description
float3	centroid	The centroid of the current mesh or point cloud.
System.Collections.Generic.IEnumerable<float3>	vertices	The vertex data.

Returns

Type	Description
float4x4

DegreesToRadians(Single)

Convert degrees to radians

Declaration

public static float DegreesToRadians(float degrees)

Parameters

Type	Name	Description
System.Single	degrees	An angle in degrees

Returns

Type	Description
System.Single	The angle expressed in radians

DegreesToRadiansD(Double)

Convert degrees to radians

Declaration

public static double DegreesToRadiansD(double degrees)

Parameters

Type	Name	Description
System.Double	degrees	An angle in degrees

Returns

Type	Description
System.Double	The angle expressed in radians

Equals(Double, Double)

Compares two double values for equality.

Declaration

public static bool Equals(double a, double b)

Parameters

Type	Name	Description
System.Double	a	The first value.
System.Double	b	The second value.

Returns

Type	Description
System.Boolean	True if the numbers are equal.

Equals(Single, Single)

Compares two float values for equality.

Declaration

public static bool Equals(float a, float b)

Parameters

Type	Name	Description
System.Single	a	The first value.
System.Single	b	The second value.

Returns

Type	Description
System.Boolean	True if the numbers are equal.

Factorial(Int32)

Calculates the factorial of a given natural number.

Declaration

public static long Factorial(int n)

Parameters

Type	Name	Description
System.Int32	n	The number.

Returns

Type	Description
System.Int64	n!

Float4ToABGR(float4)

Converts a float4 to an ABGR value (Int64).

Declaration

public static uint Float4ToABGR(float4 value)

Parameters

Type	Name	Description
float4	value	The float4 to convert.

Returns

Type	Description
System.UInt32	The ABGR value.

InverseSqrtFast(Double)

Returns an approximation of the inverse square root of left number.

Declaration

public static double InverseSqrtFast(double x)

Parameters

Type	Name	Description
System.Double	x	A number.

Returns

Type	Description
System.Double	An approximation of the inverse square root of the specified number, with an upper error bound of 0.001

Remarks

This is an improved implementation of the the method known as Carmack's inverse square root which is found in the Quake III source code. This implementation comes from http://www.codemaestro.com/reviews/review00000105.html. For the history of this method, see http://www.beyond3d.com/content/articles/8/

InverseSqrtFast(Single)

Returns an approximation of the inverse square root of left number.

Declaration

public static float InverseSqrtFast(float x)

Parameters

Type	Name	Description
System.Single	x	A number.

Returns

Type	Description
System.Single	An approximation of the inverse square root of the specified number, with an upper error bound of 0.001

Remarks

This is an improved implementation of the the method known as Carmack's inverse square root which is found in the Quake III source code. This implementation comes from http://www.codemaestro.com/reviews/review00000105.html. For the history of this method, see http://www.beyond3d.com/content/articles/8/

IsPowerOfTwo(Int32)

Determines whether the specified value is a power of two.

Declaration

public static bool IsPowerOfTwo(int val)

Parameters

Type	Name	Description
System.Int32	val	The value.

Returns

Type	Description
System.Boolean

Lerp(Single, Single, Single)

Returns a new float value that is the linear blend of the 2 given floats

Declaration

public static float Lerp(float a, float b, float blend)

Parameters

Type	Name	Description
System.Single	a	First input float
System.Single	b	Second input float
System.Single	blend	The blend factor. a when blend=0, b when blend=1.

Returns

Type	Description
System.Single	a when blend=0, b when blend=1, and a linear combination otherwise

Max(Double, Double)

Calculates the maximum of a and b.

Declaration

public static double Max(double a, double b)

Parameters

Type	Name	Description
System.Double	a	a.
System.Double	b	b.

Returns

Type	Description
System.Double	The maximum of a and b.

Max(Int16, Int16)

Calculates the maximum of a and b.

Declaration

public static short Max(short a, short b)

Parameters

Type	Name	Description
System.Int16	a	a.
System.Int16	b	b.

Returns

Type	Description
System.Int16	The maximum of a and b.

Max(Int32, Int32)

Calculates the maximum of a and b.

Declaration

public static int Max(int a, int b)

Parameters

Type	Name	Description
System.Int32	a	a.
System.Int32	b	b.

Returns

Type	Description
System.Int32	The maximum of a and b.

Max(Single, Single)

Calculates the maximum of a and b.

Declaration

public static float Max(float a, float b)

Parameters

Type	Name	Description
System.Single	a	a.
System.Single	b	b.

Returns

Type	Description
System.Single	The maximum of a and b.

Max(UInt16, UInt16)

Calculates the maximum of a and b.

Declaration

public static ushort Max(ushort a, ushort b)

Parameters

Type	Name	Description
System.UInt16	a	a.
System.UInt16	b	b.

Returns

Type	Description
System.UInt16	The maximum of a and b.

Max(UInt32, UInt32)

Calculates the maximum of a and b.

Declaration

public static uint Max(uint a, uint b)

Parameters

Type	Name	Description
System.UInt32	a	a.
System.UInt32	b	b.

Returns

Type	Description
System.UInt32	The maximum of a and b.

Min(Double, Double)

Calculates the minimum of a and b.

Declaration

public static double Min(double a, double b)

Parameters

Type	Name	Description
System.Double	a	a.
System.Double	b	b.

Returns

Type	Description
System.Double	The minimum of a and b.

Min(Int16, Int16)

Calculates the minimum of a and b.

Declaration

public static short Min(short a, short b)

Parameters

Type	Name	Description
System.Int16	a	a.
System.Int16	b	b.

Returns

Type	Description
System.Int16	The minimum of a and b.

Min(Int32, Int32)

Calculates the minimum of a and b.

Declaration

public static int Min(int a, int b)

Parameters

Type	Name	Description
System.Int32	a	a.
System.Int32	b	b.

Returns

Type	Description
System.Int32	The minimum of a and b.

Min(Single, Single)

Calculates the minimum of a and b.

Declaration

public static float Min(float a, float b)

Parameters

Type	Name	Description
System.Single	a	a.
System.Single	b	b.

Returns

Type	Description
System.Single	The minimum of a and b.

Min(UInt16, UInt16)

Calculates the minimum of a and b.

Declaration

public static ushort Min(ushort a, ushort b)

Parameters

Type	Name	Description
System.UInt16	a	a.
System.UInt16	b	b.

Returns

Type	Description
System.UInt16	The minimum of a and b.

Min(UInt32, UInt32)

Calculates the minimum of a and b.

Declaration

public static uint Min(uint a, uint b)

Parameters

Type	Name	Description
System.UInt32	a	a.
System.UInt32	b	b.

Returns

Type	Description
System.UInt32	The minimum of a and b.

MinAngle(Double)

Wrap-around to keep angle in the interval of (-PI , +PI]

Declaration

public static double MinAngle(double angle)

Parameters

Type	Name	Description
System.Double	angle	The angle to minimize.

Returns

Type	Description
System.Double	The angle limited to a maximum magnitude of PI.

MinAngle(Single)

Wrap-around to keep angle in the interval of (-PI , +PI]

Declaration

public static float MinAngle(float angle)

Parameters

Type	Name	Description
System.Single	angle	The angle to minimize.

Returns

Type	Description
System.Single	The angle limited to a maximum magnitude of PI.

NextPowerOfTwo(Double)

Returns the next power of two that is larger than the specified number.

Declaration

public static double NextPowerOfTwo(double n)

Parameters

Type	Name	Description
System.Double	n	The specified number.

Returns

Type	Description
System.Double	The next power of two.

NextPowerOfTwo(Int32)

Returns the next power of two that is larger than the specified number.

Declaration

public static int NextPowerOfTwo(int n)

Parameters

Type	Name	Description
System.Int32	n	The specified number.

Returns

Type	Description
System.Int32	The next power of two.

NextPowerOfTwo(Int64)

Returns the next power of two that is larger than the specified number.

Declaration

public static long NextPowerOfTwo(long n)

Parameters

Type	Name	Description
System.Int64	n	The specified number.

Returns

Type	Description
System.Int64	The next power of two.

NextPowerOfTwo(Single)

Returns the next power of two that is larger than the specified number.

Declaration

public static float NextPowerOfTwo(float n)

Parameters

Type	Name	Description
System.Single	n	The specified number.

Returns

Type	Description
System.Single	The next power of two.

RadiansToDegrees(Single)

Convert radians to degrees

Declaration

public static float RadiansToDegrees(float radians)

Parameters

Type	Name	Description
System.Single	radians	An angle in radians

Returns

Type	Description
System.Single	The angle expressed in degrees

RadiansToDegreesD(Double)

Convert radians to degrees

Declaration

public static double RadiansToDegreesD(double radians)

Parameters

Type	Name	Description
System.Double	radians	An angle in radians

Returns

Type	Description
System.Double	The angle expressed in degrees

ScreenPointToWorld(float2, Single, float4x4, float4x4, float4x4, float4x4, Int32, Int32)

Calculates a world position from given screen point (e. g. mouse coordinates in window space coordinates) at any desired z coordinate specified by zPosition

Declaration

public static float3 ScreenPointToWorld(float2 windowCoordIn, float zPosition, float4x4 Projection, float4x4 View, float4x4 InvProjection, float4x4 InvView, int windowWidth, int windowHeight)

Parameters

Type	Name	Description
float2	windowCoordIn	Position in window space coordinates
System.Single	zPosition	Desired z coordinate in clip space
float4x4	Projection	Projection matrix
float4x4	View	View matrix
float4x4	InvProjection	Inverse Projection matrix
float4x4	InvView	Inverse View matrix
System.Int32	windowWidth	Width of window
System.Int32	windowHeight	Height of window

Returns

Type	Description
float3

Sin(Single)

Returns the Sin of the given value as float.

Declaration

public static float Sin(float val)

Parameters

Type	Name	Description
System.Single	val	The value.

Returns

Type	Description
System.Single

SineStep(Single)

Smoothes out the interpolation t when approaching 0.0 and 1.0, using the sinestep function.

Declaration

public static float SineStep(float t)

Parameters

Type	Name	Description
System.Single	t	t will be clamped between 0.0 and 1.0.

Returns

Type	Description
System.Single	Returns a value between 0.0 and 1.0, corresponding to t.

SmootherStep(Single)

Smoothes out the interpolation t when approaching 0.0 and 1.0, using the smootherstep function.

Declaration

public static float SmootherStep(float t)

Parameters

Type	Name	Description
System.Single	t	t will be clamped between 0.0 and 1.0.

Returns

Type	Description
System.Single	Returns a value between 0.0 and 1.0, corresponding to t.

SmoothStep(Single)

Smoothes out the interpolation t when approaching 0.0 and 1.0, using the smoothstep function.

Declaration

public static float SmoothStep(float t)

Parameters

Type	Name	Description
System.Single	t	t will be clamped between 0.0 and 1.0.

Returns

Type	Description
System.Single	Returns a value between 0.0 and 1.0, corresponding to t.

Step(Double, Double)

Generates a step function by comparing "val" to "edge". 0.0 is returned if "val" is smaller than "edge" and 1.0 is returned otherwise.

Declaration

public static double Step(double edge, double val)

Parameters

Type	Name	Description
System.Double	edge	Specifies the location of the edge of the step function.
System.Double	val	Specifies the value to be used to generate the step function.

Returns

Type	Description
System.Double

Step(Single, Single)

Generates a step function by comparing "val" to "edge". 0.0 is returned if "val" is smaller than "edge" and 1.0 is returned otherwise.

Declaration

public static float Step(float edge, float val)

Parameters

Type	Name	Description
System.Single	edge	Specifies the location of the edge of the step function.
System.Single	val	Specifies the value to be used to generate the step function.

Returns

Type	Description
System.Single

Swap(ref Double, ref Double)

Swaps two double values.

Declaration

public static void Swap(ref double a, ref double b)

Parameters

Type	Name	Description
System.Double	a	The first value.
System.Double	b	The second value.

Swap(ref Single, ref Single)

Swaps two float values.

Declaration

public static void Swap(ref float a, ref float b)

Parameters

Type	Name	Description
System.Single	a	The first value.
System.Single	b	The second value.