Class MathUtility

Provides static helpers methods for mathematical functions not found in the .NET class.

Inheritance

System.Object

MathUtility

Namespace: X10D.Math

Assembly: X10D.dll

Syntax

public static class MathUtility : object

Methods

Bias(Double, Double)

Applies a simple bias function to value.

Declaration

public static double Bias(double value, double bias)

Parameters

Type	Name	Description
System.Double	value	The value to which the bias function will be applied.
System.Double	bias	The bias value. Valid values range from 0-1.

Returns

Type	Description
System.Double	The biased result.

Remarks

If bias is less than 0.5, value will be shifted downward; otherwise, upward.

Bias(Single, Single)

Applies a simple bias function to value.

Declaration

public static float Bias(float value, float bias)

Parameters

Type	Name	Description
System.Single	value	The value to which the bias function will be applied.
System.Single	bias	The bias value. Valid values range from 0-1.

Returns

Type	Description
System.Single	The biased result.

Remarks

If bias is less than 0.5, value will be shifted downward; otherwise, upward.

ExponentialDecay(Double, Double, Double)

Calculates exponential decay for a value.

Declaration

public static double ExponentialDecay(double value, double alpha, double decay)

Parameters

Type	Name	Description
System.Double	value	The value to decay.
System.Double	alpha	A factor by which to scale the decay.
System.Double	decay	The decay amount.

Returns

Type	Description
System.Double	The exponentially decayed value.

ExponentialDecay(Single, Single, Single)

Calculates exponential decay for a value.

Declaration

public static float ExponentialDecay(float value, float alpha, float decay)

Parameters

Type	Name	Description
System.Single	value	The value to decay.
System.Single	alpha	A factor by which to scale the decay.
System.Single	decay	The decay amount.

Returns

Type	Description
System.Single	The exponentially decayed value.

GammaToLinear(Double)

Converts a gamma-encoded value to a linear value using a gamma value of 2.2.

Declaration

public static double GammaToLinear(double value)

Parameters

Type	Name	Description
System.Double	value	The gamma-encoded value to convert. Expected range is [0, 1].

Returns

Type	Description
System.Double	The linear value.

GammaToLinear(Double, Double)

Converts a gamma-encoded value to a linear value using the specified gamma value.

Declaration

public static double GammaToLinear(double value, double gamma)

Parameters

Type	Name	Description
System.Double	value	The gamma-encoded value to convert. Expected range is [0, 1].
System.Double	gamma	The gamma value to use for decoding.

Returns

Type	Description
System.Double	The linear value.

GammaToLinear(Single)

Converts a gamma-encoded value to a linear value using a gamma value of 2.2.

Declaration

public static float GammaToLinear(float value)

Parameters

Type	Name	Description
System.Single	value	The gamma-encoded value to convert. Expected range is [0, 1].

Returns

Type	Description
System.Single	The linear value.

GammaToLinear(Single, Single)

Converts a gamma-encoded value to a linear value using the specified gamma value.

Declaration

public static float GammaToLinear(float value, float gamma)

Parameters

Type	Name	Description
System.Single	value	The gamma-encoded value to convert. Expected range is [0, 1].
System.Single	gamma	The gamma value to use for decoding.

Returns

Type	Description
System.Single	The linear value.

InverseLerp(Double, Double, Double)

Returns the linear interpolation inverse of a value, such that it determines where a value lies between two other values.

Declaration

public static double InverseLerp(double alpha, double start, double end)

Parameters

Type	Name	Description
System.Double	alpha	The value whose lerp inverse is to be found.
System.Double	start	The start of the range.
System.Double	end	The end of the range.

Returns

Type	Description
System.Double	A value determined by (alpha - start) / (end - start).

InverseLerp(Single, Single, Single)

Returns the linear interpolation inverse of a value, such that it determines where a value lies between two other values.

Declaration

public static float InverseLerp(float alpha, float start, float end)

Parameters

Type	Name	Description
System.Single	alpha	The value whose lerp inverse is to be found.
System.Single	start	The start of the range.
System.Single	end	The end of the range.

Returns

Type	Description
System.Single	A value determined by (alpha - start) / (end - start).

Lerp(Double, Double, Double)

Linearly interpolates from one value to a target using a specified alpha.

Declaration

public static double Lerp(double value, double target, double alpha)

Parameters

Type	Name	Description
System.Double	value	The interpolation source.
System.Double	target	The interpolation target.
System.Double	alpha	The interpolation alpha.

Returns

Type	Description
System.Double	The interpolation result as determined by (1 - alpha) * value + alpha * target.

Lerp(Single, Single, Single)

Linearly interpolates from one value to a target using a specified alpha.

Declaration

public static float Lerp(float value, float target, float alpha)

Parameters

Type	Name	Description
System.Single	value	The interpolation source.
System.Single	target	The interpolation target.
System.Single	alpha	The interpolation alpha.

Returns

Type	Description
System.Single	The interpolation result as determined by (1 - alpha) * value + alpha * target.

LinearToGamma(Double)

Converts a linear value to a gamma-encoded value using a gamma value of 2.2.

Declaration

public static double LinearToGamma(double value)

Parameters

Type	Name	Description
System.Double	value	The linear value to convert. Expected range is [0, 1].

Returns

Type	Description
System.Double	The gamma-encoded value.

LinearToGamma(Double, Double)

Converts a linear value to a gamma-encoded value using the specified gamma value.

Declaration

public static double LinearToGamma(double value, double gamma)

Parameters

Type	Name	Description
System.Double	value	The linear value to convert. Expected range is [0, 1].
System.Double	gamma	The gamma value to use for encoding.

Returns

Type	Description
System.Double	The gamma-encoded value.

LinearToGamma(Single)

Converts a linear value to a gamma-encoded value using a gamma value of 2.2.

Declaration

public static float LinearToGamma(float value)

Parameters

Type	Name	Description
System.Single	value	The linear value to convert. Expected range is [0, 1].

Returns

Type	Description
System.Single	The gamma-encoded value.

LinearToGamma(Single, Single)

Converts a linear value to a gamma-encoded value using the specified gamma value.

Declaration

public static float LinearToGamma(float value, float gamma)

Parameters

Type	Name	Description
System.Single	value	The linear value to convert. Expected range is [0, 1].
System.Single	gamma	The gamma value to use for encoding.

Returns

Type	Description
System.Single	The gamma-encoded value.

Pulse(Double, Double, Double)

Returns the pulse wave for a given value.

Declaration

public static double Pulse(double value, double lowerBound, double upperBound)

Parameters

Type	Name	Description
System.Double	value	The value to calculate.
System.Double	lowerBound	The inclusive lower bound of the pulse.
System.Double	upperBound	The inclusive upper bound of the pulse.

Returns

Type	Description
System.Double	1 if value lies between lowerBound and upperBound; otherwise, 0.

Pulse(Single, Single, Single)

Returns the pulse wave for a given value.

Declaration

public static float Pulse(float value, float lowerBound, float upperBound)

Parameters

Type	Name	Description
System.Single	value	The value to calculate.
System.Single	lowerBound	The inclusive lower bound of the pulse.
System.Single	upperBound	The inclusive upper bound of the pulse.

Returns

Type	Description
System.Single	1 if value lies between lowerBound and upperBound; otherwise, 0.

Sawtooth(Double)

Returns the incremental sawtooth wave of a given value.

Declaration

public static double Sawtooth(double value)

Parameters

Type	Name	Description
System.Double	value	The value to calculate.

Returns

Type	Description
System.Double	The sawtooth wave of the given value.

Sawtooth(Single)

Returns the incremental sawtooth wave of a given value.

Declaration

public static float Sawtooth(float value)

Parameters

Type	Name	Description
System.Single	value	The value to calculate.

Returns

Type	Description
System.Single	The sawtooth wave of the given value.

ScaleRange(Double, Double, Double, Double, Double)

Converts a value from being a percentage of one range, to being the same percentage in a new range.

Declaration

public static double ScaleRange(double value, double oldMin, double oldMax, double newMin, double newMax)

Parameters

Type	Name	Description
System.Double	value	The value to convert.
System.Double	oldMin	The old minimum value.
System.Double	oldMax	The old maximum value.
System.Double	newMin	The new minimum value.
System.Double	newMax	The new maximum value.

Returns

Type	Description
System.Double	The scaled value.

ScaleRange(Single, Single, Single, Single, Single)

Converts a value from being a percentage of one range, to being the same percentage in a new range.

Declaration

public static float ScaleRange(float value, float oldMin, float oldMax, float newMin, float newMax)

Parameters

Type	Name	Description
System.Single	value	The value to convert.
System.Single	oldMin	The old minimum value.
System.Single	oldMax	The old maximum value.
System.Single	newMin	The new minimum value.
System.Single	newMax	The new maximum value.

Returns

Type	Description
System.Single	The scaled value.

Sigmoid(Double)

Calculates the sigmoid function for the given input value.

Declaration

public static double Sigmoid(double value)

Parameters

Type	Name	Description
System.Double	value	The input value for which to calculate the sigmoid function.

Returns

Type	Description
System.Double	The result of applying the sigmoid function to the input value.

Remarks

The sigmoid function is a commonly used activation function in artificial neural networks and logistic regression. It maps any real-valued number to a value between 0 and 1.

Sigmoid(Single)

Calculates the sigmoid function for the given input value.

Declaration

public static float Sigmoid(float value)

Parameters

Type	Name	Description
System.Single	value	The input value for which to calculate the sigmoid function.

Returns

Type	Description
System.Single	The result of applying the sigmoid function to the input value.

Remarks

The sigmoid function is a commonly used activation function in artificial neural networks and logistic regression. It maps any real-valued number to a value between 0 and 1.

SmoothStep(Double, Double, Double)

Performs smooth Hermite interpolation from one value to a target using a specified alpha.

Declaration

public static double SmoothStep(double value, double target, double alpha)

Parameters

Type	Name	Description
System.Double	value	The interpolation source.
System.Double	target	The interpolation target.
System.Double	alpha	The interpolation alpha.

Returns

Type	Description
System.Double	The interpolation result.

SmoothStep(Single, Single, Single)

Performs smooth Hermite interpolation from one value to a target using a specified alpha.

Declaration

public static float SmoothStep(float value, float target, float alpha)

Parameters

Type	Name	Description
System.Single	value	The interpolation source.
System.Single	target	The interpolation target.
System.Single	alpha	The interpolation alpha.

Returns

Type	Description
System.Single	The interpolation result.