Matrix22
#include <Imath/ImathMatrix.h>
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.
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
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));
}
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typedef Matrix22<float> Imath::M22f
2x2 matrix of float
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typedef Matrix22<double> Imath::M22d
2x2 matrix of double
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template<class T>
class Matrix22
2x2 transformation matrix
Direct access to elements
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T x[2][2]
Matrix elements.
Constructors and Assignment
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inline Matrix22(Uninitialized) noexcept
Uninitialized.
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inline constexpr Matrix22() noexcept
Default constructor: initialize to identity.
1 0 0 1
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inline constexpr Matrix22(T a) noexcept
Initialize to scalar constant:
a a a a
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inline constexpr Matrix22(const T a[2][2]) noexcept
Construct from 2x2 array:
a[0][0] a[0][1] a[1][0] a[1][1]
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inline constexpr Matrix22(T a, T b, T c, T d) noexcept
Construct from given scalar values:
a b c d
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inline constexpr Matrix22(const Matrix22 &v) noexcept
Copy constructor.
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template<class S>
inline explicit constexpr Matrix22(const Matrix22<S> &v) noexcept
Construct from Matrix22 of another base type.
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inline constexpr const Matrix22 &operator=(const Matrix22 &v) noexcept
Assignment.
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inline constexpr const Matrix22 &operator=(T a) noexcept
Assignment from scalar.
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~Matrix22() noexcept = default
Destructor.
Compatibility with Sb
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inline T *getValue() noexcept
Return a raw pointer to the array of values.
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inline const T *getValue() const noexcept
Return a raw pointer to the array of values.
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template<class S>
inline void getValue(Matrix22<S> &v) const noexcept
Return the value in v
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template<class S>
constexpr Matrix22 &setValue(const Matrix22<S> &v) noexcept
Set the value.
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template<class S>
constexpr Matrix22 &setTheMatrix(const Matrix22<S> &v) noexcept
Set the value.
Arithmetic and Comparison
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inline constexpr bool operator==(const Matrix22 &v) const noexcept
Equality.
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inline constexpr bool operator!=(const Matrix22 &v) const noexcept
Inequality.
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inline constexpr bool equalWithAbsError(const Matrix22<T> &v, T e) const noexcept
Compare two matrices and test if they are “approximately equal”:
- Returns
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
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inline constexpr bool equalWithRelError(const Matrix22<T> &v, T e) const noexcept
Compare two matrices and test if they are “approximately equal”:
- Returns
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])
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inline constexpr const Matrix22 &operator+=(const Matrix22 &v) noexcept
Component-wise addition.
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inline constexpr const Matrix22 &operator+=(T a) noexcept
Component-wise addition.
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inline constexpr Matrix22 operator+(const Matrix22 &v) const noexcept
Component-wise addition.
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inline constexpr const Matrix22 &operator-=(const Matrix22 &v) noexcept
Component-wise subtraction.
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inline constexpr const Matrix22 &operator-=(T a) noexcept
Component-wise subtraction.
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inline constexpr Matrix22 operator-(const Matrix22 &v) const noexcept
Component-wise subtraction.
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inline constexpr Matrix22 operator-() const noexcept
Component-wise multiplication by -1.
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inline constexpr const Matrix22 &negate() noexcept
Component-wise multiplication by -1.
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inline constexpr const Matrix22 &operator*=(T a) noexcept
Component-wise multiplication.
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inline constexpr Matrix22 operator*(T a) const noexcept
Component-wise multiplication.
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inline constexpr const Matrix22 &operator/=(T a) noexcept
Component-wise division.
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inline constexpr Matrix22 operator/(T a) const noexcept
Component-wise division.
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inline constexpr const Matrix22 &operator*=(const Matrix22 &v) noexcept
Matrix-matrix multiplication.
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inline constexpr Matrix22 operator*(const Matrix22 &v) const noexcept
Matrix-matrix multiplication.
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template<class S>
inline void multDirMatrix(const Vec2<S> &src, Vec2<S> &dst) const noexcept
Vector * matrix multiplication.
- Parameters
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Maniplation
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inline void makeIdentity() noexcept
Set to the identity.
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inline constexpr const Matrix22 &transpose() noexcept
Transpose.
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inline constexpr Matrix22 transposed() const noexcept
Return the transpose.
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inline constexpr const Matrix22 &invert(bool singExc)
Invert in place.
- Parameters
singExc – If true, throw an exception if the matrix cannot be inverted.
- Returns
const reference to this
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inline constexpr const Matrix22 &invert() noexcept
Invert in place.
- Returns
const reference to this
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inline 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.
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inline constexpr Matrix22<T> inverse() const noexcept
Return the inverse, leaving this unmodified.
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inline constexpr T determinant() const noexcept
Determinant.
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inline constexpr T trace() const noexcept
Trace.
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template<class S>
const Matrix22 &setRotation(S r) noexcept
Set matrix to rotation by r (in radians)
- Returns
const referenced to this
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template<class S>
constexpr const Matrix22 &rotate(S r) noexcept
Rotate the given matrix by r (in radians)
- Returns
const referenced to this
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inline constexpr const Matrix22 &setScale(T s) noexcept
Set matrix to scale by given uniform factor.
- Returns
const referenced to this
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template<class S>
constexpr const Matrix22 &setScale(const Vec2<S> &s) noexcept
Set matrix to scale by given vector.
- Returns
const referenced to this
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template<class S>
constexpr const Matrix22 &scale(const Vec2<S> &s) noexcept
- Returns
const referenced to this
Numeric Limits
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static inline constexpr T baseTypeLowest() noexcept
Largest possible negative value.
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static inline constexpr T baseTypeMax() noexcept
Largest possible positive value.
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static inline constexpr T baseTypeSmallest() noexcept
Smallest possible positive value.
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static inline constexpr T baseTypeEpsilon() noexcept
Smallest possible e for which 1+e != 1.
Public Types
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typedef T BaseType
The base type: In templates that accept a parameter V, you can refer to T as V::BaseType
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typedef Vec2<T> BaseVecType
The base vector type.
Public Functions
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inline T *operator[](int i) noexcept
Row access.
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inline const T *operator[](int i) const noexcept
Row access.
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template<class S>
inline constexpr Matrix22<T> &setValue(const Matrix22<S> &v) noexcept
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template<class S>
inline constexpr Matrix22<T> &setTheMatrix(const Matrix22<S> &v) noexcept
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template<class S>
inline const Matrix22<T> &setRotation(S r) noexcept
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template<class S>
inline constexpr const Matrix22<T> &rotate(S r) noexcept
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template<class S>
inline constexpr const Matrix22<T> &setScale(const Vec2<S> &s) noexcept
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template<class S>
inline constexpr const Matrix22<T> &scale(const Vec2<S> &s) noexcept
Public Static Functions
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static inline constexpr unsigned int dimensions() noexcept
Return the number of the row and column dimensions, i.e. 2.
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template<class T>
std::ostream &Imath::operator<<(std::ostream &s, const Matrix22<T> &m)
Stream output, as: (m00 m01 m10 m11)
