Detailed Description

High-performance 4x3 transformation matrix optimized for Saturn hardware.

The Matrix43 class extends Matrix33 to provide a complete set of affine transformation operations (rotation, scaling, translation) optimized for 3D graphics and physics on Saturn hardware. It uses a memory-efficient 4x3 layout where the last row [0,0,0,1] is implicit.

Key features:

Memory-efficient representation (three rotation rows + translation vector)
Complete set of affine transformation operations
Optimized for performance-critical rendering and physics calculations
Fixed-point arithmetic for consistent precision and hardware acceleration
Support for various precision levels in calculations

Matrix layout:

| Row0.x Row0.y Row0.z |
| Row1.x Row1.y Row1.z |
| Row2.x Row2.y Row2.z |
| Row3.x Row3.y Row3.z |

Where:

Row0, Row1, Row2: Rotation and scale components (from Matrix33)
Row3: Translation vector (position)
The implicit 4th column [0,0,0,1] is not stored for memory efficiency

This represents the transformation matrix:

| Row0.x Row0.y Row0.z 0 |
| Row1.x Row1.y Row1.z 0 |
| Row2.x Row2.y Row2.z 0 |
| Row3.x Row3.y Row3.z 1 |

Common applications:

Object transformations (position, rotation, scale)
Camera view matrices
Hierarchical transformations (parent-child relationships)
Skeletal animation
Coordinate system conversions

Performance considerations:

Matrix multiplication is an O(n³) operation and can be expensive
Inverse calculation is even more costly and should be cached when possible
For hierarchical transformations, consider using MatrixStack
When applying multiple transformations, combine them into a single matrix when possible to reduce the number of matrix multiplications

Implementation notes:

Inherits rotation/scale components from Matrix33
Adds translation component as Row3
The implicit last row [0,0,0,1] enables affine transformations
Critical operations have specialized implementations for Saturn hardware

See also: Matrix33 For rotation-only transformations; MatrixStack For hierarchical transformations; Vector3D For the underlying vector implementation

#include <mat43.hpp>

Inheritance diagram for SRL::Math::Types::Matrix43:

Public Member Functions
constexpr	Matrix43 ()
	Default constructor initializing to a zero matrix.

constexpr	Matrix43 (const Matrix33 &rotation, const Vector3D &translation)
	Combines rotation matrix with translation.

constexpr	Matrix43 (const Vector3D &row0, const Vector3D &row1, const Vector3D &row2, const Vector3D &row3)
	Creates matrix from individual row vectors.

constexpr	Matrix43 (const Vector3D &up, const Vector3D &direction, const Vector3D &position)
	Creates transformation from orientation and position.

template<Precision P = Precision::Default>
constexpr void	Decompose (Vector3D &scale, Vector3D &rotation, Vector3D &translation) const
	Extracts scale, rotation, and translation components.

constexpr Fxp	Determinant () const
	Calculate the determinant of the matrix.

constexpr Matrix43	Invert () const
	Inverts the matrix.

constexpr Vector3D	operator* (const Vector3D &v) const
	Transform a vector by this matrix.

constexpr Matrix43	operator* (const Matrix33 &other) const
	Creates new matrix as product of this and another 3x3 matrix.

Matrix43	operator* (const Matrix43 &other) const
	Creates new matrix as product of this and other.

constexpr Matrix43 &	operator*= (const Matrix33 &other)
	Multiplies this matrix by another 3x3 matrix.

constexpr Matrix43 &	operator*= (const Matrix43 &other)
	Multiplies this matrix by another, combining transformations.

constexpr Matrix33 &	RotateX (const Angle &angleX)
	Apply X-axis rotation to the current matrix.

constexpr Matrix33 &	RotateY (const Angle &angleY)
	Apply Y-axis rotation to the current matrix.

constexpr Matrix33 &	RotateZ (const Angle &angleZ)
	Apply Z-axis rotation to the current matrix.

constexpr Vector3D	TransformPoint (const Vector3D &point) const
	Transforms a point by this matrix.

constexpr Vector3D	TransformVector (const Vector3D &vector) const
	Transforms a vector by this matrix.

constexpr Matrix43 &	Translate (const Vector3D &translation)
	Modifies current matrix by adding translation.

constexpr Matrix33 &	Transpose ()
	Transpose the matrix in-place.

bool constexpr	TryInverse (Matrix33 &out) const
	Attempt to compute the inverse of the matrix.

Static Public Member Functions
template<Precision P = Precision::Default>
static constexpr Matrix43	CreateBillboard (const Vector3D &position, const Vector3D &cameraPosition, const Vector3D &up=Vector3D::UnitY())
	Create a billboard matrix that always faces the camera.

template<Precision P = Precision::Default>
static constexpr Matrix43	CreateLookAt (const Vector3D &eye, const Vector3D &target, const Vector3D &up=Vector3D::UnitY())
	Creates a look-at matrix for positioning a camera in 3D space.

static constexpr Matrix33	CreateRotation (const Angle &angleX, const Angle &angleY, const Angle &angleZ)
	Create a rotation matrix from Euler angles.

static constexpr Matrix33	CreateRotationX (const Angle &angle)
	Create a new X-axis rotation matrix.

static constexpr Matrix33	CreateRotationY (const Angle &angle)
	Create a new Y-axis rotation matrix.

static constexpr Matrix33	CreateRotationZ (const Angle &angle)
	Create a new Z-axis rotation matrix.

static constexpr Matrix33	CreateScale (const Vector3D &scale)
	Create a scale matrix.

static constexpr Matrix43	CreateTransform (const Vector3D &translation, const EulerAngles &rotation, const Vector3D &scale=Vector3D(1, 1, 1))
	Creates transformation matrix.

static constexpr Matrix43	CreateTranslation (const Vector3D &translation)
	Creates translation matrix.

static consteval Matrix43	Identity ()
	Creates identity matrix.

static constexpr Matrix43	Scale (const Fxp &scale)
	Creates a uniform scale matrix.

static constexpr Matrix43	Scale (const Fxp &x, const Fxp &y, const Fxp &z)
	Creates a non-uniform scale matrix.

static constexpr Matrix43	Scale (const Vector3D &scale)
	Creates a uniform scale matrix from a Vector3D.

static constexpr Matrix43	Translation (const Fxp &x, const Fxp &y, const Fxp &z)
	Creates a translation matrix.

Public Attributes
Vector3D	Row0

Vector3D	Row1

Vector3D	Row2

Vector3D	Row3

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes