Class Math

Common math helper functions.

Inheritance

object

Math

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Namespace: Unity.Physics

Assembly: Unity.Physics.dll

Syntax

public static class Math

Methods

CalculatePerpendicularNormalized(float3, out float3, out float3)

Return two normals perpendicular to the input vector.

Declaration

public static void CalculatePerpendicularNormalized(float3 v, out float3 p, out float3 q)

Parameters

Type	Name	Description
float3	v	Input vector.
float3	p	[out] Normal 1.
float3	q	[out] Normal 2.

CalculateTwistAngle(quaternion, int)

Returns the twist angle of the swing-twist decomposition of q about i, j, or k corresponding to index = 0, 1, or 2 respectively. Full calculation for readability: float invLength = RSqrtSafe(dot * dot + w * w); float sinHalfAngle = dot * invLength; float cosHalfAngle = w * invLength; Observe: invLength cancels in the tan^-1(sin / cos) calc, so avoid unnecessary calculations.

Declaration

public static float CalculateTwistAngle(quaternion q, int twistAxisIndex)

Parameters

Type	Name	Description
quaternion	q	A quaternion to process.
int	twistAxisIndex	Zero-based index of the twist axis.

Returns

Type	Description
float	The calculated twist angle.

ClampToMaxLength(float, ref float3)

Clamps the vector to to maximum length.

Declaration

public static void ClampToMaxLength(float maxLength, ref float3 vector)

Parameters

Type	Name	Description
float	maxLength	The maximum length.
float3	vector	[in,out] The vector to be clamped.

DecomposeRigidBodyOrientation(in float4x4)

Physics internally represents all rigid bodies in world space. If a static body is in a hierarchy, its local-to-world matrix must be decomposed when building the physics world. This method returns a world-space orientation that would be decomposed for such a rigid body.

Declaration

public static quaternion DecomposeRigidBodyOrientation(in float4x4 localToWorld)

Parameters

Type	Name	Description
float4x4	localToWorld	The local to world.

Returns

Type	Description
quaternion	A world-space orientation as used by physics.

DecomposeRigidBodyTransform(in float4x4)

Physics internally represents all rigid bodies in world space. If a static body is in a hierarchy, its local-to-world matrix must be decomposed when building the physics world. This method returns a world-space RigidTransform that would be decomposed for such a rigid body.

Declaration

public static RigidTransform DecomposeRigidBodyTransform(in float4x4 localToWorld)

Parameters

Type	Name	Description
float4x4	localToWorld	The local to world.

Returns

Type	Description
RigidTransform	A world-space RigidTransform as used by physics.

DecomposeScale(AffineTransform)

Obtain 3-dimensional scale vector of the provided affine transformation, the components of which represent the lengths of the three orthonormal basis vectors forming the 3x3 rotational sub-matrix, respectively.

Declaration

public static float3 DecomposeScale(this AffineTransform matrix)

Parameters

Type	Name	Description
AffineTransform	matrix	The affine transformation matrix.

Returns

Type	Description
float3	The three scale components of the provided affine transformation.

DecomposeScale(float4x4)

Obtain 3-dimensional scale vector of the provided 4x4 transformation matrix, the components of which represent the lengths of the three orthonormal basis vectors forming the 3x3 rotational sub-matrix, respectively.

Declaration

public static float3 DecomposeScale(this float4x4 matrix)

Parameters

Type	Name	Description
float4x4	matrix	The 4x4 transformation matrix.

Returns

Type	Description
float3	The three scale components of the provided transformation matrix.

HasNonIdentityScale(float4x4, float)

Checks if the matrix has non-identity scale.

Declaration

public static bool HasNonIdentityScale(this float4x4 m, float eps = 1E-05)

Parameters

Type	Name	Description
float4x4	m	The matrix.
float	eps	Epsilon value used in the non-identity scale determination.

Returns

Type	Description
bool	True if the matrix has non-identity scale.

HasNonUniformScale(float4x4, float)

Checks if the matrix has non-uniform scale.

Declaration

public static bool HasNonUniformScale(this float4x4 m, float eps = 1E-05)

Parameters

Type	Name	Description
float4x4	m	The matrix.
float	eps	Epsilon value used in the non-uniform scale determination.

Returns

Type	Description
bool	True if the matrix has non-uniform scale.

HasShear(float4x4)

Checks if the matrix has shear.

Declaration

public static bool HasShear(this float4x4 m)

Parameters

Type	Name	Description
float4x4	m	The matrix.

Returns

Type	Description
bool	True if the matrix has shear.

Inverse(MTransform)

Inverses the given transform.

Declaration

public static Math.MTransform Inverse(Math.MTransform transform)

Parameters

Type	Name	Description
Math.MTransform	transform	A MTransform to process.

Returns

Type	Description
Math.MTransform	An inverse of the provided transform.

Inverse(ScaledMTransform)

Inverses the given transform.

Declaration

public static Math.ScaledMTransform Inverse(Math.ScaledMTransform transform)

Parameters

Type	Name	Description
Math.ScaledMTransform	transform	A ScaledMTransform to process.

Returns

Type	Description
Math.ScaledMTransform	A ScaledMTransform that is the inverse of the input.

IsNormalized(float3)

Check if 'v' is normalized.

Declaration

public static bool IsNormalized(float3 v)

Parameters

Type	Name	Description
float3	v	A float3 to check if normalized.

Returns

Type	Description
bool	True if normalized, false if not.

Mul(MTransform, float3)

Multiplies the point by the transform.

Declaration

public static float3 Mul(Math.MTransform a, float3 x)

Parameters

Type	Name	Description
Math.MTransform	a	A MTransform to multiply with.
float3	x	A point to process.

Returns

Type	Description
float3	A transformed point.

Mul(MTransform, MTransform)

Returns cFromA = cFromB * bFromA.

Declaration

public static Math.MTransform Mul(Math.MTransform cFromB, Math.MTransform bFromA)

Parameters

Type	Name	Description
Math.MTransform	cFromB	cFromB.
Math.MTransform	bFromA	bFromA.

Returns

Type	Description
Math.MTransform	A MTransform, cFromA.

Mul(ScaledMTransform, float3)

Multiplies the point by the transform.

Declaration

public static float3 Mul(Math.ScaledMTransform a, float3 x)

Parameters

Type	Name	Description
Math.ScaledMTransform	a	A ScaledMTransform to multiply with.
float3	x	A point to process.

Returns

Type	Description
float3	A transformed point.

Mul(ScaledMTransform, ScaledMTransform)

Returns cFromA = cFromB * bFromA.

Declaration

public static Math.ScaledMTransform Mul(Math.ScaledMTransform cFromB, Math.ScaledMTransform bFromA)

Parameters

Type	Name	Description
Math.ScaledMTransform	cFromB	cFromB.
Math.ScaledMTransform	bFromA	bFromA.

Returns

Type	Description
Math.ScaledMTransform	A ScaledMTransform, cFromA.

NormalizeWithLength(float3, out float3)

Normalize and return the lenght of a vector.

Declaration

public static float NormalizeWithLength(float3 v, out float3 n)

Parameters

Type	Name	Description
float3	v	A float3 to normalize.
float3	n	[out] A normalized float3.

Returns

Type	Description
float	Length of v.