Matrix4x3

The Matrix4x3 type provides a highly optimized and flexible container for 3D affine transformations. It supports efficient storage, manipulation, and composition of transformations such as translation, rotation, and scaling, and is designed for performance-critical applications in 3D graphics and simulation. Matrix4x3 uses row-major storage with 3 rows and 4 columns, omitting the final row of a full 4x4 matrix to reduce memory usage and improve performance when homogeneous coordinates are implicitly assumed.

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Matrix4x3 has a 16-byte alignment to ensure optimal performance and compatibility with SIMD operations.

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SIMD types can be used as template parameters for structure of array (SOA) calculations.

#include <math/TellusimMatrix.h>

Matrix4x3f

Represents a 3D affine transformation matrix of 32-bit floating-point numbers.

Matrix4x3d

Represents a 3D affine transformation matrix of 64-bit floating-point numbers.

Variables

Type	Name	Description
Type	m00, m01, m02, m03	Row 0 components.
Type	m10, m11, m12, m13	Row 1 components.
Type	m20, m21, m22, m23	Row 2 components.
Vector4	row_0	Row 0 vector.
Vector4	row_1	Row 1 vector.
Vector4	row_2	Row 2 vector.
Vector4	rows[3]	Vector access.
Type	m[4 * 3]	Array access.

Constants

Type	Name	Description
Matrix4x3	zero	Zero matrix.
Matrix4x3	identity	Identity matrix.

Constructors

Matrix4x3()
Matrix4x3(const Matrix4x3 &m)
Matrix4x3(const Vector4 &row_0, const Vector4 &row_1, const Vector4 &row_2)
Matrix4x3(const Vector3 &col_0, const Vector3 &col_1, const Vector3 &col_2, const Vector3 &col_3)
Matrix4x3(Type m00, Type m01, Type m02, Type m03, Type m10, Type m11, Type m12, Type m13, Type m20, Type m21, Type m22, Type m23)
explicit Matrix4x3(const Matrix4x4 &m)
explicit Matrix4x3(const Quaternion &q)
explicit Matrix4x3(const Type *m, uint32_t size = Size, bool row_major = true)
explicit Matrix4x3(const Matrix4x3<CType> &m)
explicit Matrix4x3(const Matrix4x4<CType> &m)
explicit Matrix4x3(Type v)

Methods

Update matrix data.

void set(const Vector4 &r0, const Vector4 &r1, const Vector4 &r2)
void set(const Vector3 &col_0, const Vector3 &col_1, const Vector3 &col_2, const Vector3 &col_3)
void set(const Type *m, uint32_t size = Size, bool row_major = true)
void get(Type *m, uint32_t size = Size, bool row_major = true) const

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Matrix to matrix operators.

Matrix4x3 &operator*=(const Matrix4x3 &m)
Matrix4x3 &operator+=(const Matrix4x3 &m)
Matrix4x3 &operator-=(const Matrix4x3 &m)

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Zero matrix.

void setZero()
bool isZero() const

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Identity matrix.

void setIdentity()
bool isIdentity() const

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Outer product matrix.

void setOuter(const Vector3 &v0, const Vector3 &v1)
static Matrix4x3 outer(const Vector3 &v0, const Vector3 &v1)

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Scaling matrix.

void setScale(const Vector3 &s)
void setScale(Type x, Type y, Type z)
Vector3 getScale() const
static Matrix4x3 scale(const Vector3 &s)
static Matrix4x3 scale(Type x, Type y, Type z)
static Matrix4x3 scale(Type s)

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Translation matrix.

void setTranslate(const Vector3 &t)
void setTranslate(Type x, Type y, Type z)
Vector3 getTranslate() const
static Matrix4x3 translate(const Vector3 &t)
static Matrix4x3 translate(Type x, Type y, Type z)

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Rotation matrix.

void setRotateX(Type angle)
void setRotateY(Type angle)
void setRotateZ(Type angle)
void setRotate(const Vector3 &axis, Type angle)
void setRotate(Type x, Type y, Type z, Type angle)
Matrix4x3 getRotate() const
static Matrix4x3 rotateX(Type angle)
static Matrix4x3 rotateY(Type angle)
static Matrix4x3 rotateZ(Type angle)
static Matrix4x3 rotate(const Vector3 &axis, Type angle)
static Matrix4x3 rotate(Type x, Type y, Type z, Type angle)

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Look at matrix.

void setLookAt(const Vector3 &from, const Vector3 &to, const Vector3 &up)
static Matrix4x3 lookAt(const Vector3 &from, const Vector3 &to, const Vector3 &up)

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Place to matrix.

void setPlaceTo(const Vector3 &to, const Vector3 &from, const Vector3 &up)
static Matrix4x3 placeTo(const Vector3 &to, const Vector3 &from, const Vector3 &up)

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Cube at matrix.

void setCubeAt(const Vector3 &from, uint32_t face)
static Matrix4x3 cubeAt(const Vector3 &from, uint32_t face)

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Right-handed orthonormal basis.

void setBasis(const Vector3 &normal, const Vector3 &t)
static Matrix4x3 basis(const Vector3 &normal)
static Matrix4x3 basis(const Vector3 &normal, const Vector3 &t)

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Matrix determinant.

Type getDeterminant() const

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Matrix composition.

void setComponents(const Vector3 &t, const Quaternion &r)
void setComponents(const Vector3 &t, const Quaternion &r, const Vector3 &s)
void getComponents(Vector3 &t, Quaternion &r) const
void getComponents(Vector3 &t, Quaternion &r, Vector3 &s) const
static Matrix4x3 compose(const Vector3 &t, const Quaternion &r)
static Matrix4x3 compose(const Vector3 &t, const Quaternion &r, const Vector3 &s)

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Matrix rows.

void setRow(uint32_t index, const Vector4 &r)
const Vector4 &getRow(uint32_t index) const
Vector4 &getRow(uint32_t index)

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Matrix columns.

void setColumn(uint32_t index, const Vector3 &c)
Vector3 getColumn(uint32_t index) const

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Matrix data.

const Vector4 &operator[](uint32_t index) const
Vector4 &operator[](uint32_t index)

Operators

Unary operators.

Matrix4x3 operator-(const Matrix4x3 &m)

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Matrix to scalar multiplication.

Matrix4x3 operator*(const Matrix4x3 &m, const Type &v)

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Matrix to vector multiplications.

Vector2 operator*(const Matrix4x3 &m, const Vector2 &v)
Vector3 operator*(const Matrix4x3 &m, const Vector3 &v)
Vector4 operator*(const Matrix4x3 &m, const Vector4 &v)
Vector2 mul2x2(const Matrix4x3 &m, const Vector2 &v)
Vector3 mul3x3(const Matrix4x3 &m, const Vector3 &v)

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Vector to matrix multiplications.

Vector2 operator*(const Vector2 &v, const Matrix4x3 &m)
Vector3 operator*(const Vector3 &v, const Matrix4x3 &m)
Vector4 operator*(const Vector4 &v, const Matrix4x3 &m)

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Matrix to matrix multiplications.

Matrix4x3 operator*(const Matrix4x3 &m0, const Matrix4x3 &m1)

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Matrix to matrix operators.

Matrix4x3 operator+(const Matrix4x3 &m0, const Matrix4x3 &m1)
Matrix4x3 operator-(const Matrix4x3 &m0, const Matrix4x3 &m1)

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Comparison operators.

bool operator==(const Matrix4x3 &m0, const Matrix4x3 &m1)
bool operator!=(const Matrix4x3 &m0, const Matrix4x3 &m1)
bool compare(const Matrix4x3 &m0, const Matrix4x3 &m1, const Type &a)
bool compare(const Matrix4x3 &m0, const Matrix4x3 &m1, const Type &a, const Type &r)

Functions

Matrix functions.

Matrix4x3 normalize(const Matrix4x3 &m)
Matrix4x3 transpose(const Matrix4x3 &m)
Matrix4x3 inverse(const Matrix4x3 &m)
Matrix4x3 inverse33(const Matrix4x3 &m)
Matrix4x3 lerp(const Matrix4x3 &m0, const Matrix4x3 &m1, float32_t k)
Matrix4x3 jacobi(const Matrix4x3 &m, Matrix4x3 &v, float32_t threshold = 1e-6f)