Matrix22

The Matrix22 class template represents a 2x2 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.

Example:

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

void
matrix22_example()
{
    Imath::M22f M (Imath::UNINITIALIZED); // uninitialized

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

    Imath::M22f Minv = M.inverse();

    Imath::M22f R;
    assert (R == Imath::identity22f);

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

    Imath::V2f v2 (1.0f, 0.0f);
    Imath::V2f r2 = v2 * M;

    assert (r2.equalWithAbsError (Imath::V2f (0.707107f, 0.707107f), 1e-6f));
}
typedef Matrix22<float> Imath::M22f

2x2 matrix of float

typedef Matrix22<double> Imath::M22d

2x2 matrix of double

template <class T>
class Matrix22

2x2 transformation matrix

Direct access to elements

template<>
T x[2][2]

Matrix elements.

Constructors and Assignment

Matrix22(Uninitialized)

Uninitialized.

constexpr Matrix22()

Default constructor: initialize to identity.

1 0 0 1

constexpr Matrix22(T a)

Initialize to scalar constant:

a a a a

constexpr Matrix22(const T a[2][2])

Construct from 2x2 array:

a[0][0] a[0][1] a[1][0] a[1][1]

constexpr Matrix22(T a, T b, T c, T d)

Construct from given scalar values:

a b c d

constexpr Matrix22(const Matrix22 &v)

Copy constructor.

template <class S>
constexpr Matrix22(const Matrix22<S> &v)

Construct from Matrix22 of another base type.

constexpr const Matrix22<T> &operator=(const Matrix22 &v)

Assignment.

constexpr const Matrix22<T> &operator=(T a)

Assignment from scalar.

~Matrix22()

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(Matrix22<S> &v) const

Return the value in v

template <class S>
constexpr Matrix22 &setValue(const Matrix22<S> &v)

Set the value.

template <class S>
constexpr Matrix22 &setTheMatrix(const Matrix22<S> &v)

Set the value.

Arithmetic and Comparison

constexpr bool operator==(const Matrix22 &v) const

Equality.

constexpr bool operator!=(const Matrix22 &v) const

Inequality.

constexpr bool equalWithAbsError(const Matrix22<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 Matrix22<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 Matrix22<T> &operator+=(const Matrix22 &v)

Component-wise addition.

constexpr const Matrix22<T> &operator+=(T a)

Component-wise addition.

constexpr Matrix22<T> operator+(const Matrix22 &v) const

Component-wise addition.

constexpr const Matrix22<T> &operator-=(const Matrix22 &v)

Component-wise subtraction.

constexpr const Matrix22<T> &operator-=(T a)

Component-wise subtraction.

constexpr Matrix22<T> operator-(const Matrix22 &v) const

Component-wise subtraction.

constexpr Matrix22<T> operator-() const

Component-wise multiplication by -1.

constexpr const Matrix22<T> &negate()

Component-wise multiplication by -1.

constexpr const Matrix22<T> &operator*=(T a)

Component-wise multiplication.

constexpr Matrix22<T> operator*(T a) const

Component-wise multiplication.

constexpr const Matrix22<T> &operator/=(T a)

Component-wise division.

constexpr Matrix22<T> operator/(T a) const

Component-wise division.

constexpr const Matrix22<T> &operator*=(const Matrix22 &v)

Matrix-matrix multiplication.

constexpr Matrix22<T> operator*(const Matrix22 &v) const

Matrix-matrix multiplication.

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

Vector * matrix multiplication.

Parameters
  • src: Input vector
  • dst: transformed vector

Maniplation

void makeIdentity()

Set to the identity.

constexpr const Matrix22<T> &transpose()

Transpose.

constexpr Matrix22<T> transposed() const

Return the transpose.

constexpr const Matrix22<T> &invert(bool singExc)

Invert in place.

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

constexpr const Matrix22<T> &invert()

Invert in place.

Return
const reference to this

constexpr Matrix22<T> inverse(bool singExc) const

Return the inverse, leaving this unmodified.

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

constexpr Matrix22<T> inverse() const

Return the inverse, leaving this unmodified.

constexpr T determinant() const

Determinant.

template <class S>
const Matrix22 &setRotation(S r)

Set matrix to rotation by r (in radians)

Return
const referenced to this

template <class S>
constexpr const Matrix22 &rotate(S r)

Rotate the given matrix by r (in radians)

Return
const referenced to this

constexpr const Matrix22<T> &setScale(T s)

Set matrix to scale by given uniform factor.

Return
const referenced to this

template <class S>
constexpr const Matrix22 &setScale(const Vec2<S> &s)

Set matrix to scale by given vector.

Return
const referenced to this

template <class S>
constexpr const Matrix22 &scale(const Vec2<S> &s)

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, you can refer to T as V::BaseType

typedef Vec2<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 Matrix22<T> &setValue(const Matrix22<S> &v)
template <class S>
constexpr Matrix22<T> &setTheMatrix(const Matrix22<S> &v)
template <class S>
const Matrix22<T> &setRotation(S r)
template <class S>
constexpr const Matrix22<T> &rotate(S r)
template <class S>
constexpr const Matrix22<T> &setScale(const Vec2<S> &s)
template <class S>
constexpr const Matrix22<T> &scale(const Vec2<S> &s)

Public Static Functions

static constexpr unsigned int dimensions()

Return the number of the row and column dimensions, i.e. 2.

Warning

doxygenfunction: Unable to resolve multiple matches for function “operator<<” with arguments (std::ostream& s, const Matrix22<T>& m) in doxygen xml output for project “Imath” from directory: doxyxml/. 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>&)