Matrix44¶
#include <Imath/ImathMatrix.h>
The Matrix44 class template represents a 4x4 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
matrix44_example ()
{
Imath::M44f M (Imath::UNINITIALIZED); // uninitialized
M.makeIdentity ();
assert (M[0][0] == 1.0f);
assert (M[0][1] == 0.0f);
Imath::M44f Minv = M.inverse ();
Imath::M44f R;
assert (R == Imath::identity44f);
R.rotate (Imath::V3f (0.02f, M_PI / 4, 0.0f));
M = R * M;
Imath::V3f v3 (1.0f, 0.0f, 0.0f);
Imath::V4f v4 (1.0f, 0.0f, 0.0f, 1.0f);
Imath::V3f r3 = v3 * M;
assert (r3.equalWithAbsError (
Imath::V3f (0.707107f, 0.0f, -0.7071070f), 1e-6f));
Imath::V4f r4 = v4 * M;
assert (r4.equalWithAbsError (
Imath::V4f (0.707107f, 0.0f, -0.7071070f, 1.0f), 1e-6f));
}
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template<class T>
class Matrix44¶ 4x4 transformation matrix
Constructors and Assignment
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inline constexpr Matrix44(Uninitialized) noexcept¶
Uninitialized.
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inline constexpr Matrix44() noexcept¶
Default constructor: initialize to identity 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1.
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inline constexpr Matrix44(T a) noexcept¶
Initialize to scalar constant a a a a a a a a a a a a a a a a.
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inline constexpr Matrix44(const T a[4][4]) noexcept¶
Construct from 4x4 array a[0][0] a[0][1] a[0][2] a[0][3] a[1][0] a[1][1] a[1][2] a[1][3] a[2][0] a[2][1] a[2][2] a[2][3] a[3][0] a[3][1] a[3][2] a[3][3].
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inline constexpr Matrix44(T a, T b, T c, T d, T e, T f, T g, T h, T i, T j, T k, T l, T m, T n, T o, T p) noexcept¶
Construct from given scalar values a b c d e f g h i j k l m n o p.
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inline constexpr Matrix44(Matrix33<T> r, Vec3<T> t) noexcept¶
Construct from a 3x3 rotation matrix and a translation vector r r r 0 r r r 0 r r r 0 t t t 1.
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template<class S>
inline explicit constexpr Matrix44(const Matrix44<S> &v) noexcept¶ Construct from Matrix44 of another base type.
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~Matrix44() noexcept = default¶
Destructor.
Compatibility with Sb
Arithmetic and Comparison
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inline constexpr bool equalWithAbsError(const Matrix44<T> &v, T e) const noexcept¶
Compare two matrices and test if they are “approximately equal”:
- Returns:
True if the coefficients of this and
mare 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 Matrix44<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 Matrix44 &operator-=(const Matrix44 &v) noexcept¶
Component-wise subtraction.
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inline constexpr const Matrix44 &operator*=(const Matrix44 &v) noexcept¶
Matrix-matrix multiplication.
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inline constexpr Matrix44 operator*(const Matrix44 &v) const noexcept¶
Matrix-matrix multiplication.
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template<class S>
inline void multVecMatrix(const Vec3<S> &src, Vec3<S> &dst) const noexcept¶ Vector-matrix multiplication: a homogeneous transformation by computing Vec3 (src.x, src.y, src.z, 1) * m and dividing by the result’s third element.
- Parameters:
src – [in] The input vector
dst – [out] The output vector
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template<class S>
inline void multDirMatrix(const Vec3<S> &src, Vec3<S> &dst) const noexcept¶ Vector-matrix multiplication: multiply
srcby the upper left 2x2 submatrix, ignoring the rest of matrix.- Parameters:
src – [in] The input vector
dst – [out] The output vector
Maniplation
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inline void makeIdentity() noexcept¶
Set to the identity matrix.
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inline constexpr const Matrix44 &invert(bool singExc)¶
Invert in place using the determinant.
- 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 Matrix44 &invert() noexcept¶
Invert in place using the determinant.
- Returns:
const reference to this
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inline constexpr Matrix44<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.
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inline constexpr Matrix44<T> inverse() const noexcept¶
Return the inverse using the determinant, leaving this unmodified.
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inline constexpr const Matrix44 &gjInvert(bool singExc)¶
Invert in place using the Gauss-Jordan method.
Significantly slower but more accurate than invert().
- 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 Matrix44 &gjInvert() noexcept¶
Invert in place using the Gauss-Jordan method.
Significantly slower but more accurate than invert().
- Returns:
const reference to this
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inline Matrix44<T> gjInverse(bool singExc) const¶
Return the inverse using the Gauss-Jordan method, leaving this unmodified.
Significantly slower but more accurate than inverse().
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inline Matrix44<T> gjInverse() const noexcept¶
Return the inverse using the Gauss-Jordan method, leaving this unmodified Significantly slower but more accurate than inverse().
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inline constexpr T minorOf(const int r, const int c) const noexcept¶
Calculate the matrix minor of the (r,c) element.
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inline constexpr T fastMinor(const int r0, const int r1, const int r2, const int c0, const int c1, const int c2) const noexcept¶
Build a minor using the specified rows and columns.
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template<class S>
const Matrix44 &setEulerAngles(const Vec3<S> &r) noexcept¶ Set matrix to rotation by XYZ euler angles (in radians)
- Returns:
const referenced to this
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template<class S>
constexpr const Matrix44 &setAxisAngle(const Vec3<S> &ax, S ang) noexcept¶ Set matrix to rotation around given axis by given angle (in radians)
- Returns:
const referenced to this
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template<class S>
const Matrix44 &rotate(const Vec3<S> &r) noexcept¶ Rotate the matrix by XYZ euler angles in r (in radians)
- Returns:
const referenced to this
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inline constexpr const Matrix44 &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 Matrix44 &setScale(const Vec3<S> &s) noexcept¶ Set matrix to scale by given vector.
- Returns:
const referenced to this
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template<class S>
constexpr const Matrix44 &scale(const Vec3<S> &s) noexcept¶ Scale the matrix by s.
- Returns:
const referenced to this
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template<class S>
constexpr const Matrix44 &setTranslation(const Vec3<S> &t) noexcept¶ Set matrix to translation by given vector.
- Returns:
const referenced to this
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template<class S>
constexpr const Matrix44 &translate(const Vec3<S> &t) noexcept¶ Translate the matrix by t.
- Returns:
const referenced to this
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template<class S>
constexpr const Matrix44 &setShear(const Vec3<S> &h) noexcept¶ Set matrix to shear by given vector h.
The resulting matrix
will shear x for each y coord. by a factor of h[0] ;
will shear x for each z coord. by a factor of h[1] ;
will shear y for each z coord. by a factor of h[2] .
- Returns:
const referenced to this
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template<class S>
constexpr const Matrix44 &setShear(const Shear6<S> &h) noexcept¶ Set matrix to shear by given factors.
The resulting matrix
will shear x for each y coord. by a factor of h.xy ;
will shear x for each z coord. by a factor of h.xz ;
will shear y for each z coord. by a factor of h.yz ;
will shear y for each x coord. by a factor of h.yx ;
will shear z for each x coord. by a factor of h.zx ;
will shear z for each y coord. by a factor of h.zy .
- Returns:
const referenced to this
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template<class S>
constexpr const Matrix44 &shear(const Vec3<S> &h) noexcept¶ Shear the matrix by given vector.
The composed matrix will be
shear*this, where the shear matrix …will shear x for each y coord. by a factor of h[0] ;
will shear x for each z coord. by a factor of h[1] ;
will shear y for each z coord. by a factor of h[2] .
- Returns:
const referenced to this
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template<class S>
constexpr const Matrix44 &shear(const Shear6<S> &h) noexcept¶ Shear the matrix by the given factors.
The composed matrix will be
shear*this, where the shear matrix …will shear x for each y coord. by a factor of h.xy ;
will shear x for each z coord. by a factor of h.xz ;
will shear y for each z coord. by a factor of h.yz ;
will shear y for each x coord. by a factor of h.yx ;
will shear z for each x coord. by a factor of h.zx ;
will shear z for each y coord. by a factor of h.zy .
- Returns:
const referenced to this
Numeric Limits
Public Types
Public Functions
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. 4.
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inline constexpr Matrix44(Uninitialized) noexcept¶
