Class MathUtility

Collection of optimized math utility functions for WheelController3D. Provides garbage-free matrix and quaternion operations to minimize allocations in the physics loop. All methods use aggressive inlining for maximum performance.

Inheritance

object

MathUtility

Namespace: NWH.WheelController3D

Assembly: NWH.WheelController.dll

Syntax

public static class MathUtility

Remarks

These utilities avoid creating new objects or structs, instead modifying existing values by reference. This is critical for performance when called every physics frame for multiple wheels. Methods are marked with AggressiveInlining to eliminate function call overhead.

Methods

Abs(float)

Branchless absolute value.

Declaration

public static float Abs(float value)

Parameters

Type	Name	Description
float	value	Input value.

Returns

Type	Description
float	Absolute value of value.

ApplyRotationToVector(ref Quaternion, ref Vector3)

Applies a quaternion rotation to a vector, modifying the vector in place. Equivalent to vector = rotation * vector but without creating a new Vector3.

Declaration

public static void ApplyRotationToVector(ref Quaternion rotation, ref Vector3 vector)

Parameters

Type	Name	Description
Quaternion	rotation	Rotation to apply
Vector3	vector	Vector to rotate (modified in place)

ApplyVelocity(Matrix4x4, Vector3, Vector3, float)

Integrates linear and angular velocity into a transformation matrix over a timestep. Used for predicting future positions/orientations based on current velocities.

Declaration

public static Matrix4x4 ApplyVelocity(Matrix4x4 matrix, Vector3 velocity, Vector3 angularVelocity, float deltaTime)

Parameters

Type	Name	Description
Matrix4x4	matrix	Starting transformation matrix
Vector3	velocity	Linear velocity in m/s
Vector3	angularVelocity	Angular velocity in rad/s
float	deltaTime	Time step in seconds

Returns

Type	Description
Matrix4x4	New transformation matrix after applying velocities

Clamp01(float)

Clamps a value to the [0, 1] range.

Declaration

public static float Clamp01(float value)

Parameters

Type	Name	Description
float	value	Input value.

Returns

Type	Description
float	value clamped to [0, 1].

CopyMatrix(ref Matrix4x4, ref Matrix4x4)

Copies all values from one matrix to another without creating new objects. Faster than destination = source when matrices are already allocated.

Declaration

public static void CopyMatrix(ref Matrix4x4 source, ref Matrix4x4 destination)

Parameters

Type	Name	Description
Matrix4x4	source	Source matrix to copy from
Matrix4x4	destination	Destination matrix to copy to

CreateAngleAxisRotationMatrix(float, ref Vector3, ref Matrix4x4)

Creates a rotation matrix from an angle and axis without allocating memory. Equivalent to Matrix4x4.Rotate(Quaternion.AngleAxis(...)) but with zero allocations.

Declaration

public static void CreateAngleAxisRotationMatrix(float angle, ref Vector3 axis, ref Matrix4x4 result)

Parameters

Type	Name	Description
float	angle	Rotation angle in degrees
Vector3	axis	Rotation axis (will be normalized internally)
Matrix4x4	result	Output matrix to populate with the rotation

Cross(float, float, float, float, float, float, out float, out float, out float)

Inline cross product with float components. Writes result to out parameter.

Declaration

public static void Cross(float ax, float ay, float az, float bx, float by, float bz, out float rx, out float ry, out float rz)

Parameters

Type	Name	Description
float	ax
float	ay
float	az
float	bx
float	by
float	bz
float	rx
float	ry
float	rz

Cross(ref Vector3, ref Vector3, out Vector3)

Inline cross product. Writes result to out parameter, avoiding Vector3 allocation.

Declaration

public static void Cross(ref Vector3 a, ref Vector3 b, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a
Vector3	b
Vector3	result

Dot(ref Vector3, ref Vector3)

Inline dot product.

Declaration

public static float Dot(ref Vector3 a, ref Vector3 b)

Parameters

Type	Name	Description
Vector3	a
Vector3	b

Returns

Type	Description
float

ExtractRotationFromMatrix(ref Matrix4x4, out Quaternion)

Extracts a Quaternion rotation from a transformation matrix without allocating memory. Equivalent to matrix.rotation but writes directly to an existing Quaternion reference.

Declaration

public static void ExtractRotationFromMatrix(ref Matrix4x4 matrix, out Quaternion rotation)

Parameters

Type	Name	Description
Matrix4x4	matrix	Source transformation matrix
Quaternion	rotation	Output quaternion to populate with the extracted rotation

FastPow(float, float)

Fast power function using exp(y * ln(x)). ~30% faster than Mathf.Pow for typical physics exponents (0.8-2.0).

Declaration

public static float FastPow(float x, float y)

Parameters

Type	Name	Description
float	x
float	y

Returns

Type	Description
float

InvertAffineNoScale(in Matrix4x4, ref Matrix4x4)

Computes the inverse of an affine TRS matrix with scale=1. Faster than general Matrix4x4.inverse since rotation block is orthonormal (inverse = transpose).

Declaration

public static void InvertAffineNoScale(in Matrix4x4 src, ref Matrix4x4 dst)

Parameters

Type	Name	Description
Matrix4x4	src	Source matrix (must be TRS with scale=1)
Matrix4x4	dst	Destination matrix for the inverse

MultiplyMatricesNoAlloc(ref Matrix4x4, ref Matrix4x4, ref Matrix4x4)

Multiplies two matrices and stores the result in a third matrix without allocating memory. Equivalent to result = lhs * rhs but modifies result in place.

Declaration

public static void MultiplyMatricesNoAlloc(ref Matrix4x4 lhs, ref Matrix4x4 rhs, ref Matrix4x4 result)

Parameters

Type	Name	Description
Matrix4x4	lhs	Left matrix
Matrix4x4	rhs	Right matrix
Matrix4x4	result	Output matrix to store lhs * rhs

MultiplyQuaternions(ref Quaternion, ref Quaternion)

Multiplies two quaternions and returns the result. Alternative to Quaternion operator * that may reduce overhead in performance-critical paths.

Declaration

public static Quaternion MultiplyQuaternions(ref Quaternion a, ref Quaternion b)

Parameters

Type	Name	Description
Quaternion	a	First quaternion (left side of multiplication)
Quaternion	b	Second quaternion (right side of multiplication)

Returns

Type	Description
Quaternion	Result of a * b

MultiplyQuaternionsNoAlloc(ref Quaternion, ref Quaternion, ref Quaternion)

Multiplies two quaternions and writes result to existing quaternion (avoids return value copy).

Declaration

public static void MultiplyQuaternionsNoAlloc(ref Quaternion a, ref Quaternion b, ref Quaternion result)

Parameters

Type	Name	Description
Quaternion	a
Quaternion	b
Quaternion	result

RotateVector(ref Quaternion, ref Vector3, out Vector3)

Rotate vector by quaternion inline. Equivalent to q * v.

Declaration

public static void RotateVector(ref Quaternion q, ref Vector3 v, out Vector3 result)

Parameters

Type	Name	Description
Quaternion	q
Vector3	v
Vector3	result

Scale(ref Vector3, ref Vector3, out Vector3)

Inline component-wise scale (Vector3.Scale equivalent).

Declaration

public static void Scale(ref Vector3 a, ref Vector3 b, out Vector3 result)

Parameters

Type	Name	Description
Vector3	a
Vector3	b
Vector3	result

Sign(float)

Sign of a value. Returns +1 for zero.

Declaration

public static float Sign(float value)

Parameters

Type	Name	Description
float	value	Input value.

Returns

Type	Description
float	+1 when value is zero or positive, -1 when negative.

UpdateAngleAxisQuaternion(float, ref Vector3, ref Quaternion)

Updates an existing quaternion with angle-axis values without allocating memory. Equivalent to result = Quaternion.AngleAxis(...) but modifies in place.

Declaration

public static void UpdateAngleAxisQuaternion(float angle, ref Vector3 axis, ref Quaternion result)

Parameters

Type	Name	Description
float	angle	Rotation angle in degrees
Vector3	axis	Rotation axis (should be normalized)
Quaternion	result	Quaternion to update with the angle-axis rotation

ValueNoise2D(float, float)

Deterministic 2D value noise in [0, 1]. Bilinear interpolation of hashed lattice values with smoothstep weights. Same input always yields the same output.

Declaration

public static float ValueNoise2D(float x, float y)

Parameters

Type	Name	Description
float	x
float	y

Returns

Type	Description
float