Matrix33

The Matrix33 class template represents a 3x3 matrix, with predefined typedefs for float and double.

There are also various utility functions that operate on matrices defined in ImathMatrixAlgo.h and described in Matrix Functions.

Individual components of a matrix M may be referenced as either M[j][i] or M.x[j][i]. While the latter is a little awkward, it has an advantage when used in loops that may be auto-vectorized or explicitly vectorized by #pragma omp simd or other such hints, because the function call and pointer casting of operator[] can confuse the compiler just enough to prevent vectorization of the loop, whereas directly addressing the real underlying array (M.x[j][i]) does not.

Example:

#include <Imath/ImathMatrix.h>
#include <Imath/ImathMatrixAlgo.h>
#include <cassert>

void
matrix33_example()
{
    Imath::M33f M (Imath::UNINITIALIZED); // uninitialized

    M.makeIdentity();
    assert (M[0][0] == 1.0f);
    assert (M[0][1] == 0.0f);

    Imath::M33f Minv = M.inverse();

    Imath::M33f R;
    assert (R == Imath::identity33f);

    R.rotate (M_PI/4);
    
    M = R * M;

    Imath::V3f v3 (1.0f, 0.0f, 0.0f);
    Imath::V3f r3 = v3 * M;

    assert (r3.equalWithAbsError (Imath::V3f (0.707107f, 0.7071070f, 0.0f), 1e-6f));
}
typedef Matrix33<float> Imath::M33f

3x3 matrix of float

typedef Matrix33<double> Imath::M33d

3x3 matrix of double

template<class T>
class Matrix33

3x3 transformation matrix

Direct access to elements

template<>
T x[3][3]

Matrix elements.

Constructors and Assignment

Matrix33(Uninitialized)

Uninitialized.

constexpr Matrix33()

Default constructor: initialize to identity 1 0 0 0 1 0 0 0 1.

constexpr Matrix33(T a)

Initialize to scalar constant a a a a a a a a a.

constexpr Matrix33(const T a[3][3])

Construct from 3x3 array a[0][0] a[0][1] a[0][2] a[1][0] a[1][1] a[1][2] a[2][0] a[2][1] a[2][2].

constexpr Matrix33(T a, T b, T c, T d, T e, T f, T g, T h, T i)

Construct from given scalar values a b c d e f g h i.

constexpr Matrix33(const Matrix33 &v)

Copy constructor.

template<class S>
constexpr Matrix33(const Matrix33<S> &v)

Construct from Matrix33 of another base type.

constexpr const Matrix33<T> &operator=(const Matrix33 &v)

Assignment operator.

constexpr const Matrix33<T> &operator=(T a)

Assignment from scalar.

~Matrix33()

Destructor.

Compatibility with Sb

T *getValue()

Return a raw pointer to the array of values.

const T *getValue() const

Return a raw pointer to the array of values.

template<class S>
void getValue(Matrix33<S> &v) const

Return the value in v

template<class S>
constexpr Matrix33 &setValue(const Matrix33<S> &v)

Set the value.

template<class S>
constexpr Matrix33 &setTheMatrix(const Matrix33<S> &v)

Set the value.

Arithmetic and Comparison

constexpr bool operator==(const Matrix33 &v) const

Equality.

constexpr bool operator!=(const Matrix33 &v) const

Inequality.

constexpr bool equalWithAbsError(const Matrix33<T> &v, T e) const

Compare two matrices and test if they are “approximately equal”:

Return
True if the coefficients of this and m are the same with an absolute error of no more than e, i.e., for all i, j:
abs (this[i][j] - m[i][j]) <= e

constexpr bool equalWithRelError(const Matrix33<T> &v, T e) const

Compare two matrices and test if they are “approximately equal”:

Return
True if the coefficients of this and m are the same with a relative error of no more than e, i.e., for all i, j:
abs (this[i] - v[i][j]) <= e * abs (this[i][j])

constexpr const Matrix33<T> &operator+=(const Matrix33 &v)

Component-wise addition.

constexpr const Matrix33<T> &operator+=(T a)

Component-wise addition.

constexpr Matrix33<T> operator+(const Matrix33 &v) const

Component-wise addition.

constexpr const Matrix33<T> &operator-=(const Matrix33 &v)

Component-wise subtraction.

constexpr const Matrix33<T> &operator-=(T a)

Component-wise subtraction.

constexpr Matrix33<T> operator-(const Matrix33 &v) const

Component-wise subtraction.

constexpr Matrix33<T> operator-() const

Component-wise multiplication by -1.

constexpr const Matrix33<T> &negate()

Component-wise multiplication by -1.

constexpr const Matrix33<T> &operator*=(T a)

Component-wise multiplication.

constexpr Matrix33<T> operator*(T a) const

Component-wise multiplication.

constexpr const Matrix33<T> &operator/=(T a)

Component-wise division.

constexpr Matrix33<T> operator/(T a) const

Component-wise division.

constexpr const Matrix33<T> &operator*=(const Matrix33 &v)

Matrix-matrix multiplication.

constexpr Matrix33<T> operator*(const Matrix33 &v) const

Matrix-matrix multiplication.

template<class S>
void multVecMatrix(const Vec2<S> &src, Vec2<S> &dst) const

Vector-matrix multiplication: a homogeneous transformation by computing Vec3 (src.x, src.y, 1) * m and dividing by the result’s third element.

Parameters
  • src: The input vector
  • dst: The output vector

template<class S>
void multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const

Vector-matrix multiplication: multiply src by the upper left 2x2 submatrix, ignoring the rest of matrix.

Parameters
  • src: The input vector
  • dst: The output vector

Maniplation

void makeIdentity()

Set to the identity matrix.

constexpr const Matrix33<T> &transpose()

Transpose.

constexpr Matrix33<T> transposed() const

Return the transpose.

constexpr const Matrix33<T> &invert(bool singExc)

Invert in place using the determinant.

Return
const reference to this
Parameters
  • singExc: If true, throw an exception if the matrix cannot be inverted.

constexpr const Matrix33<T> &invert()

Invert in place using the determinant.

Return
const reference to this

constexpr Matrix33<T> inverse(bool singExc) const

Return the inverse using the determinant, leaving this unmodified.

Parameters
  • singExc: If true, throw an exception if the matrix cannot be inverted.

constexpr Matrix33<T> inverse() const

Return the inverse using the determinant, leaving this unmodified.

const Matrix33<T> &gjInvert(bool singExc)

Invert in place using the Gauss-Jordan method.

Significantly slower but more accurate than invert().

Return
const reference to this
Parameters
  • singExc: If true, throw an exception if the matrix cannot be inverted.

const Matrix33<T> &gjInvert()

Invert in place using the Gauss-Jordan method.

Significantly slower but more accurate than invert().

Return
const reference to this

Matrix33<T> gjInverse(bool singExc) const

Return the inverse using the Gauss-Jordan method, leaving this unmodified.

Significantly slower but more accurate than inverse().

Matrix33<T> gjInverse() const

Return the inverse using the Gauss-Jordan method.

Significantly slower, leaving this unmodified. Slower but more accurate than inverse().

constexpr T minorOf(const int r, const int c) const

Calculate the matrix minor of the (r,c) element.

constexpr T fastMinor(const int r0, const int r1, const int c0, const int c1) const

Build a minor using the specified rows and columns.

constexpr T determinant() const

Determinant.

constexpr T trace() const

Trace.

template<class S>
const Matrix33 &setRotation(S r)

Set matrix to rotation by r (in radians)

Return
const referenced to this

template<class S>
constexpr const Matrix33 &rotate(S r)

Return
const referenced to this

constexpr const Matrix33<T> &setScale(T s)

Set matrix to scale by given uniform factor.

Return
const referenced to this

template<class S>
constexpr const Matrix33 &setScale(const Vec2<S> &s)

Set matrix to scale by given vector.

Return
const referenced to this

template<class S>
constexpr const Matrix33 &scale(const Vec2<S> &s)

Scale the matrix by s.

Return
const referenced to this

template<class S>
constexpr const Matrix33 &setTranslation(const Vec2<S> &t)

Set matrix to translation by given vector.

Return
const referenced to this

constexpr Vec2<T> translation() const

Return the translation component.

template<class S>
constexpr const Matrix33 &translate(const Vec2<S> &t)

Translate the matrix by t.

Return
const referenced to this

template<class S>
constexpr const Matrix33 &setShear(const S &h)

Set matrix to shear x for each y coord.

by given factor xy

Return
const referenced to this

template<class S>
constexpr const Matrix33 &setShear(const Vec2<S> &h)

Set matrix to shear x for each y coord.

by given factor h.x and to shear y for each x coord. by given factor h.y

Return
const referenced to this

template<class S>
constexpr const Matrix33 &shear(const S &xy)

Shear the matrix in x for each y coord.

by given factor xy

Return
const referenced to this

template<class S>
constexpr const Matrix33 &shear(const Vec2<S> &h)

Shear the matrix in x for each y coord.

by given factor xy and shear y for each x coord. by given factor yx

Return
const referenced to this

Numeric Limits

static constexpr T baseTypeLowest()

Largest possible negative value.

static constexpr T baseTypeMax()

Largest possible positive value.

static constexpr T baseTypeSmallest()

Smallest possible positive value.

static constexpr T baseTypeEpsilon()

Smallest possible e for which 1+e != 1.

Public Types

typedef T BaseType

The base type: In templates that accept a parameter V (could be a Color4), you can refer to T as V::BaseType

typedef Vec3<T> BaseVecType

The base vector type.

Public Functions

T *operator[](int i)

Row access.

const T *operator[](int i) const

Row access.

template<class S>
constexpr Matrix33<T> &setValue(const Matrix33<S> &v)
template<class S>
constexpr Matrix33<T> &setTheMatrix(const Matrix33<S> &v)
template<class S>
const Matrix33<T> &setRotation(S r)
template<class S>
constexpr const Matrix33<T> &rotate(S r)
template<class S>
constexpr const Matrix33<T> &setScale(const Vec2<S> &s)
template<class S>
constexpr const Matrix33<T> &scale(const Vec2<S> &s)
template<class S>
constexpr const Matrix33<T> &setTranslation(const Vec2<S> &t)
template<class S>
constexpr const Matrix33<T> &translate(const Vec2<S> &t)
template<class S>
constexpr const Matrix33<T> &setShear(const S &xy)
template<class S>
constexpr const Matrix33<T> &setShear(const Vec2<S> &h)
template<class S>
constexpr const Matrix33<T> &shear(const S &xy)
template<class S>
constexpr const Matrix33<T> &shear(const Vec2<S> &h)

Public Static Functions

static constexpr unsigned int dimensions()

Return the number of the row and column dimensions, i.e. 3.

Warning

doxygenfunction: Unable to resolve multiple matches for function “operator<<” with arguments (std::ostream& s, const Matrix33<T>& m) in doxygen xml output for project “Imath” from directory: /build/ilmbase-pisqTC/ilmbase-3.1.11/obj-x86_64-linux-gnu/website/doxygen/xml. Potential matches:

- std::ostream &operator<<(std::ostream&, Imath::half)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Color4<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Euler<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Interval<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Line3<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Matrix22<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Matrix33<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Matrix44<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Plane3<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Quat<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Shear6<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Vec2<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Vec3<T>&)
- template<class T>
  std::ostream &Imath::operator<<(std::ostream&, const Vec4<T>&)