Class MathUtilities

Contains various math utility functions

Inheritance

Object

MathUtilities

Inherited Members

Object.ToString()

Object.Equals(Object)

Object.Equals(Object, Object)

Object.ReferenceEquals(Object, Object)

Object.GetHashCode()

Object.GetType()

Object.MemberwiseClone()

Namespace: Unity.CharacterController

Syntax

public static class MathUtilities

Methods

AngleRadians(float3, float3)

Calculates angles in radians between two normalized direction vectors

Declaration

public static float AngleRadians(float3 from, float3 to)

Parameters

Type	Name	Description
float3	from	The source direction
float3	to	The destination direction

Returns

Type	Description
Single	Angle in radians

AngleRadiansToDotRatio(Single)

Calculates the dot product between two normalized direction vectors that are at a specified angle (in radians) from each other

Declaration

public static float AngleRadiansToDotRatio(float angleRadians)

Parameters

Type	Name	Description
Single	angleRadians	The angle in radians separating the two fictional direction vectors

Returns

Type	Description
Single	The dot product result

CalculatePointDisplacement(float3, RigidTransform, RigidTransform)

Calculates the displacement vector of a worldspace point from one transform pose to the next

Declaration

public static float3 CalculatePointDisplacement(float3 pointWorldSpace, RigidTransform fromTransform, RigidTransform toTransform)

Parameters

Type	Name	Description
float3	pointWorldSpace	The worldspace point that gets moved (before movement)
RigidTransform	fromTransform	The original transform pose
RigidTransform	toTransform	The destination transform pose

Returns

Type	Description
float3

CalculatePointDisplacementFromVelocity(Single, RigidTransform, float3, float3, float3)

Calculates the displacement vector of a worldspace point relatively to a transform that moves with linear/angular velocity

Declaration

public static float3 CalculatePointDisplacementFromVelocity(float deltaTime, RigidTransform bodyRigidTransform, float3 linearVelocity, float3 angularVelocity, float3 pointWorldSpace)

Parameters

Type	Name	Description
Single	deltaTime	The time delta of the movement
RigidTransform	bodyRigidTransform	The transform pose of the moving body
float3	linearVelocity	The linear velocity of the moving body
float3	angularVelocity	The angular velocity of the moving body
float3	pointWorldSpace	The worldspace point to move

Returns

Type	Description
float3

ClampToMaxLength(float3, Single)

Clamps a vector to a maximum length

Declaration

public static float3 ClampToMaxLength(float3 vector, float maxLength)

Parameters

Type	Name	Description
float3	vector	The vector to clamp
Single	maxLength	The max length to clamp to

Returns

Type	Description
float3	The clamped vector

CreateRotationWithUpPriority(float3, float3)

Builds a rotation that prioritizes having its up direction aligned with the designated up direction. Then, it orients its forwards towards the designated forward direction as much as is can without breaking the primary up direction constraint

Declaration

public static quaternion CreateRotationWithUpPriority(float3 up, float3 forward)

Parameters

Type	Name	Description
float3	up	The target up direction
float3	forward	The target forward direction

Returns

Type	Description
quaternion	The resulting rotation

DotRatioToAngleRadians(Single)

Calculates the angles in radians that represent the angle difference between two normalized direction vectors that would have a specified dot product result

Declaration

public static float DotRatioToAngleRadians(float dotRatio)

Parameters

Type	Name	Description
Single	dotRatio	The dot product result between the two fictional normalized direction vectors

Returns

Type	Description
Single	The angle in radians

FromToRotation(quaternion, quaternion)

Calculates a rotation delta from a certain rotation to another

Declaration

public static quaternion FromToRotation(quaternion from, quaternion to)

Parameters

Type	Name	Description
quaternion	from	The source rotation
quaternion	to	The destination rotation

Returns

Type	Description
quaternion	The rotation delta

GetAxisSystemFromForward(float3, out float3, out float3)

Creates perpendicular right and up directions based on a given forward direction

Declaration

public static void GetAxisSystemFromForward(float3 fwd, out float3 right, out float3 up)

Parameters

Type	Name	Description
float3	fwd	The designated forward direction
float3	right	Outputted right direction
float3	up	Outputted up direction

GetForwardFromRotation(quaternion)

Gets the forward direction of a given quaternion

Declaration

public static float3 GetForwardFromRotation(quaternion rot)

Parameters

Type	Name	Description
quaternion	rot	The rotation in quaternion

Returns

Type	Description
float3	The forward direction

GetRightFromRotation(quaternion)

Gets the right direction of a given quaternion

Declaration

public static float3 GetRightFromRotation(quaternion rot)

Parameters

Type	Name	Description
quaternion	rot	The rotation in quaternion

Returns

Type	Description
float3	The right direction

GetSharpnessInterpolant(Single, Single)

Returns an interpolant parameter that represents interpolating with a given sharpness

Declaration

public static float GetSharpnessInterpolant(float sharpness, float dt)

Parameters

Type	Name	Description
Single	sharpness	The desired interpolation sharpness
Single	dt	The interpolation time delta

Returns

Type	Description
Single	The resulting interpolant

GetUpFromRotation(quaternion)

Gets the up direction of a given quaternion

Declaration

public static float3 GetUpFromRotation(quaternion rot)

Parameters

Type	Name	Description
quaternion	rot	The rotation in quaternion

Returns

Type	Description
float3	The up direction

ProjectOnPlane(float3, float3)

Projects a vector on a plane

Declaration

public static float3 ProjectOnPlane(float3 vector, float3 onPlaneNormal)

Parameters

Type	Name	Description
float3	vector	The vector to project
float3	onPlaneNormal	The plane normal to project on

Returns

Type	Description
float3	The projected vector

ReorientVectorOnPlaneAlongDirection(float3, float3, float3)

Reorients a vector on a plane while constraining its direction so that the resulting vector is between the original vector and the specified direction

Declaration

public static float3 ReorientVectorOnPlaneAlongDirection(float3 vector, float3 onPlaneNormal, float3 alongDirection)

Parameters

Type	Name	Description
float3	vector	The original vector to reorient
float3	onPlaneNormal	The plane on which the vector should be reoriented
float3	alongDirection	The target direction along which the vector should be reoriented

Returns

Type	Description
float3	The reoriented vector

ReverseProjectOnVector(float3, float3, Single)

Calculates a vectorA in the direction of "onNormalizedVector", such that if vectorA was projected on the "projectedVector"'s normalized direction, it would result in "projectedVector"

Declaration

public static float3 ReverseProjectOnVector(float3 projectedVector, float3 onNormalizedVector, float maxLength)

Parameters

Type	Name	Description
float3	projectedVector	The projected vector that we want to de-project
float3	onNormalizedVector	The desired normalized direction of the de-projected vector
Single	maxLength	The maximum length of the de-projected vector (de-projection can lead to very large or infinite values for near-perpendicular directions)

Returns

Type	Description
float3	The resulting de-projected vector

RotateAroundPoint(ref quaternion, ref float3, float3, quaternion)

Applies a rotation delta to a transform's rotation, but also modifies its position so that the end result is as if the transform has rotated around a given point in order to reach the specified rotation

Declaration

public static void RotateAroundPoint(ref quaternion rotation, ref float3 position, float3 aroundPoint, quaternion addedRotation)

Parameters

Type	Name	Description
quaternion	rotation	The modified rotation
float3	position	The modified position
float3	aroundPoint	The point to rotate around
quaternion	addedRotation	The desired rotation delta

SetRotationAroundPoint(ref quaternion, ref float3, float3, quaternion)

Sets a transform's rotation to a target rotation, but also modifies its position so that the end result is as if the transform has rotated around a given point in order to reach the specified rotation

Declaration

public static void SetRotationAroundPoint(ref quaternion rotation, ref float3 position, float3 aroundPoint, quaternion targetRotation)

Parameters

Type	Name	Description
quaternion	rotation	The modified rotation
float3	position	The modified position
float3	aroundPoint	The point to rotate around
quaternion	targetRotation	The desired rotation