Class MathHelper

Namespace

Microsoft.Xna.Framework

Assembly

MonoGame.Framework.dll

Contains commonly used precalculated values and mathematical operations.

public static class MathHelper

Inheritance

object

MathHelper

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Fields

E

Represents the mathematical constant e(2.71828175).

public const float E = 2.7182817

Field Value

float

Log10E

Represents the log base ten of e(0.4342945).

public const float Log10E = 0.4342945

Field Value

float

Log2E

Represents the log base two of e(1.442695).

public const float Log2E = 1.442695

Field Value

float

Pi

Represents the value of pi(3.14159274).

public const float Pi = 3.1415927

Field Value

float

PiOver2

Represents the value of pi divided by two(1.57079637).

public const float PiOver2 = 1.5707964

Field Value

float

PiOver4

Represents the value of pi divided by four(0.7853982).

public const float PiOver4 = 0.7853982

Field Value

float

Tau

Represents the value of pi times two(6.28318548). This is an alias of TwoPi.

public const float Tau = 6.2831855

Field Value

float

TwoPi

Represents the value of pi times two(6.28318548).

public const float TwoPi = 6.2831855

Field Value

float

Methods

Barycentric(float, float, float, float, float)

Returns the Cartesian coordinate for one axis of a point that is defined by a given triangle and two normalized barycentric (areal) coordinates.

public static float Barycentric(float value1, float value2, float value3, float amount1, float amount2)

Parameters

value1 float

The coordinate on one axis of vertex 1 of the defining triangle.

value2 float

The coordinate on the same axis of vertex 2 of the defining triangle.

value3 float

The coordinate on the same axis of vertex 3 of the defining triangle.

amount1 float

The normalized barycentric (areal) coordinate b2, equal to the weighting factor for vertex 2, the coordinate of which is specified in value2.

amount2 float

The normalized barycentric (areal) coordinate b3, equal to the weighting factor for vertex 3, the coordinate of which is specified in value3.

Returns

float

Cartesian coordinate of the specified point with respect to the axis being used.

CatmullRom(float, float, float, float, float)

Performs a Catmull-Rom interpolation using the specified positions.

public static float CatmullRom(float value1, float value2, float value3, float value4, float amount)

Parameters

value1 float

The first position in the interpolation.

value2 float

The second position in the interpolation.

value3 float

The third position in the interpolation.

value4 float

The fourth position in the interpolation.

amount float

Weighting factor.

Returns

float

A position that is the result of the Catmull-Rom interpolation.

Clamp(int, int, int)

Restricts a value to be within a specified range.

public static int Clamp(int value, int min, int max)

Parameters

value int

The value to clamp.

min int

The minimum value. If value is less than min, min will be returned.

max int

The maximum value. If value is greater than max, max will be returned.

Returns

int

The clamped value.

Clamp(float, float, float)

Restricts a value to be within a specified range.

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

Parameters

value float

The value to clamp.

min float

The minimum value. If value is less than min, min will be returned.

max float

The maximum value. If value is greater than max, max will be returned.

Returns

float

The clamped value.

Distance(float, float)

Calculates the absolute value of the difference of two values.

public static float Distance(float value1, float value2)

Parameters

value1 float

Source value.

value2 float

Source value.

Returns

float

Distance between the two values.

Hermite(float, float, float, float, float)

Performs a Hermite spline interpolation.

public static float Hermite(float value1, float tangent1, float value2, float tangent2, float amount)

Parameters

value1 float

Source position.

tangent1 float

Source tangent.

value2 float

Source position.

tangent2 float

Source tangent.

amount float

Weighting factor.

Returns

float

The result of the Hermite spline interpolation.

IsPowerOfTwo(int)

Determines if value is powered by two.

public static bool IsPowerOfTwo(int value)

Parameters

value int

A value.

Returns

bool

true if value is powered by two; otherwise false.

Lerp(float, float, float)

Linearly interpolates between two values.

public static float Lerp(float value1, float value2, float amount)

Parameters

value1 float

Source value.

value2 float

Destination value.

amount float

Value between 0 and 1 indicating the weight of value2.

Returns

float

Interpolated value.

Remarks

This method performs the linear interpolation based on the following formula:

value1 + (value2 - value1) * amount

. Passing amount a value of 0 will cause value1 to be returned, a value of 1 will cause value2 to be returned. See LerpPrecise(float, float, float) for a less efficient version with more precision around edge cases.

LerpPrecise(float, float, float)

Linearly interpolates between two values. This method is a less efficient, more precise version of Lerp(float, float, float). See remarks for more info.

public static float LerpPrecise(float value1, float value2, float amount)

Parameters

value1 float

Source value.

value2 float

Destination value.

amount float

Value between 0 and 1 indicating the weight of value2.

Returns

float

Interpolated value.

Remarks

This method performs the linear interpolation based on the following formula:

((1 - amount) * value1) + (value2 * amount)

. Passing amount a value of 0 will cause value1 to be returned, a value of 1 will cause value2 to be returned. This method does not have the floating point precision issue that Lerp(float, float, float) has. i.e. If there is a big gap between value1 and value2 in magnitude (e.g. value1=10000000000000000, value2=1), right at the edge of the interpolation range (amount=1), Lerp(float, float, float) will return 0 (whereas it should return 1). This also holds for value1=10^17, value2=10; value1=10^18,value2=10^2... so on. For an in depth explanation of the issue, see below references: Relevant Wikipedia Article: https://en.wikipedia.org/wiki/Linear_interpolation#Programming_language_support Relevant StackOverflow Answer: http://stackoverflow.com/questions/4353525/floating-point-linear-interpolation#answer-23716956

Max(int, int)

Returns the greater of two values.

public static int Max(int value1, int value2)

Parameters

value1 int

Source value.

value2 int

Source value.

Returns

int

The greater value.

Max(float, float)

Returns the greater of two values.

public static float Max(float value1, float value2)

Parameters

value1 float

Source value.

value2 float

Source value.

Returns

float

The greater value.

Min(int, int)

Returns the lesser of two values.

public static int Min(int value1, int value2)

Parameters

value1 int

Source value.

value2 int

Source value.

Returns

int

The lesser value.

Min(float, float)

Returns the lesser of two values.

public static float Min(float value1, float value2)

Parameters

value1 float

Source value.

value2 float

Source value.

Returns

float

The lesser value.

SmoothStep(float, float, float)

Interpolates between two values using a cubic equation.

public static float SmoothStep(float value1, float value2, float amount)

Parameters

value1 float

Source value.

value2 float

Source value.

amount float

Weighting value.

Returns

float

Interpolated value.

ToDegrees(float)

Converts radians to degrees.

public static float ToDegrees(float radians)

Parameters

radians float

The angle in radians.

Returns

float

The angle in degrees.

Remarks

This method uses double precision internally, though it returns single float Factor = 180 / pi

ToRadians(float)

Converts degrees to radians.

public static float ToRadians(float degrees)

Parameters

degrees float

The angle in degrees.

Returns

float

The angle in radians.

Remarks

This method uses double precision internally, though it returns single float Factor = pi / 180

WrapAngle(float)

Reduces a given angle to a value between π and -π.

public static float WrapAngle(float angle)

Parameters

angle float

The angle to reduce, in radians.

Returns

float

The new angle, in radians.