SRL::Math::Types::Matrix33 Struct Reference

Detailed Description

High-performance 3x3 matrix implementation optimized for Saturn hardware.

The Matrix33 class provides a comprehensive set of matrix operations optimized for 3D transformations, rotations, and linear algebra calculations on Saturn hardware. It uses fixed-point arithmetic for all operations to ensure consistent behavior across platforms and maximize performance.

Key features:

• Memory-efficient representation (three row vectors)
• Comprehensive set of transformation operations
• Optimized for performance-critical graphics 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 |

Where:

• Row0 (XAxis): Right vector, defines the local X direction
• Row1 (YAxis): Up vector, defines the local Y direction
• Row2 (ZAxis): Forward vector, defines the local Z direction

Common applications:

• 3D rotations and orientations
• Local-to-world and world-to-local transformations
• Inertia tensors for rigid body physics
• Basis transformations
• Normal transformations for lighting calculations

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
• Consider using specialized functions for common operations:
  • CreateRotationX/Y/Z for single-axis rotations
  • CreateScale for uniform/non-uniform scaling
  • CreateFromAxisAngle for arbitrary axis rotations

Implementation notes:

• The rows form an orthonormal basis in a right-handed coordinate system
• Matrix operations are designed to minimize temporary object creation
• Critical operations have specialized implementations for Saturn hardware

See also

Matrix43 For 4x3 matrix with translation component

MatrixStack For hierarchical transformations

Vector3D For the underlying vector implementation

#include <mat33.hpp>

Inheritance diagram for SRL::Math::Types::Matrix33:

Public Member Functions
constexpr	Matrix33 ()
	Default constructor initializing to a zero matrix.
constexpr	Matrix33 (const Vector3D &row0In, const Vector3D &row1In, const Vector3D &row2In)
	Creates matrix from individual row vectors.
constexpr	Matrix33 (const Vector3D &up, const Vector3D &direction)
	Creates rotation matrix from up and direction vectors.
constexpr Fxp	Determinant () const
	Calculate the determinant of the matrix.
constexpr Matrix33	operator* (const Matrix33 &other) const
	Create a new matrix as the product of this and another matrix.
constexpr Vector3D	operator* (const Vector3D &v) const
	Transform a vector by this matrix.
constexpr Matrix33 &	operator*= (const Matrix33 &other)
	Multiply this matrix by another matrix in-place.
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 Matrix33 &	Scale (const Vector3D &scale)
	Scale the matrix in-place along each axis.
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
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 consteval Matrix33	Identity ()
	Create an identity matrix.

Public Attributes
Vector3D	Row0
Vector3D	Row1
Vector3D	Row2