Matrix4< T > Class Template Reference
Detailed Description
template<typename T>
class cy::Matrix4< T >
class cy::Matrix4< T >
4x4 matrix class.
Its data stores 16-value array of column-major matrix elements. I chose column-major format to be compatible with OpenGL You can use Matrix4 with Vec3<T> and Vec4<T> to transform 3D and 4D points.
#include <cyMatrix.h>
Public Member Functions | |
Constructors | |
| Matrix4 () | |
| Default constructor. | |
| template<typename TT > | |
| Matrix4 (Matrix4< TT > const &matrix) | |
| Copy constructor for different types. | |
| Matrix4 (T const *values) | |
| Initialize the matrix using an array of 9 values. | |
| Matrix4 (T v) | |
| Initialize the matrix as identity scaled by v. | |
| Matrix4 (Vec3< T > const &x, Vec3< T > const &y, Vec3< T > const &z, Vec3< T > const &pos) | |
| Initialize the matrix using x,y,z vectors and coordinate center. | |
| Matrix4 (Vec4< T > const &x, Vec4< T > const &y, Vec4< T > const &z, Vec4< T > const &w) | |
| Initialize the matrix using x,y,z vectors as columns. | |
| Matrix4 (Matrix34< T > const &m) | |
| Default constructor. | |
| Matrix4 (Matrix3< T > const &m) | |
| Default constructor. | |
| Matrix4 (Matrix2< T > const &m) | |
| Default constructor. | |
| Matrix4 (Matrix3< T > const &m, Vec3< T > const &pos) | |
| Default constructor. | |
| Matrix4 (T c00, T c01, T c02, T c03, T c10, T c11, T c12, T c13, T c20, T c21, T c22, T c23, T c30, T c31, T c32, T c33) | |
| Constructor using row-major order for initialization. | |
Set & Get Methods | |
| void | Zero () |
| Set all the values as zero. | |
| bool | IsZero () const |
| Returns true if the matrix is exactly zero. | |
| bool | IsFinite () const |
| Returns true if all components are finite real numbers. | |
| void | Get (T *values) |
| Copies the matrix cell to the given values array of size 16. | |
| void | Set (T const *values) |
| Set Matrix using an array of 16 values. | |
| void | Set (Vec3< T > const &x, Vec3< T > const &y, Vec3< T > const &z, Vec3< T > const &pos) |
| Set matrix using x,y,z column vectors and coordinate center. | |
| void | Set (Vec4< T > const &x, Vec4< T > const &y, Vec4< T > const &z, Vec4< T > const &w) |
| Set matrix using x,y,z,w column vectors. | |
| void | SetIdentity () |
| Converts the matrix to an identity matrix. | |
| void | SetTensorProduct (Vec4< T > const &v0, Vec4< T > const &v1) |
| Set all the values as zero. | |
Affine transformations | |
| void | SetScale (T uniformScale) |
| Sets a uniform scale matrix. | |
| void | SetScale (T scaleX, T scaleY, T scaleZ, T scaleW=T(1)) |
| Sets a scale matrix. | |
| void | SetScale (Vec3< T > const &scale) |
| Sets a scale matrix. | |
| void | SetRotationX (T angle) |
| Set as rotation matrix around x axis. | |
| void | SetRotationX (T sinAngle, T cosAngle) |
| Set as rotation matrix around x axis by cos and sin of angle. | |
| void | SetRotationY (T angle) |
| Set as rotation matrix around y axis. | |
| void | SetRotationY (T sinAngle, T cosAngle) |
| Set as rotation matrix around y axis by cos and sin of angle. | |
| void | SetRotationZ (T angle) |
| Set as rotation matrix around z axis. | |
| void | SetRotationZ (T sinAngle, T cosAngle) |
| Set as rotation matrix around z axis by cos and sin of angle. | |
| void | SetRotationXYZ (T angleX, T angleY, T angleZ) |
| Set as rotation matrix around x, y, and then z axes ( Rz * Ry * Rx ) | |
| void | SetRotationZYX (T angleX, T angleY, T angleZ) |
| Set as rotation matrix around z, y, and then x axes ( Rx * Ry * Rz ) | |
| void | SetRotation (Vec3< T > const &axis, T angle) |
| Set a rotation matrix about the given axis by angle. | |
| void | SetRotation (Vec3< T > const &axis, T sinAngle, T cosAngle) |
| Set a rotation matrix about the given axis by cos and sin of angle. | |
| void | SetRotation (Vec3< T > const &from, Vec3< T > const &to) |
| Set a rotation matrix that sets [from] unit vector to [to] unit vector. | |
| void | SetTranslation (Vec3< T > const &move) |
| Sets a translation matrix with no rotation or scale. | |
| void | AddTranslation (Vec3< T > const &move) |
| Adds a translation to the matrix. | |
| void | SetTranslationComponent (Vec3< T > const &move) |
| Sets the translation component of the matrix. | |
| void | SetNoTranslation () |
| Sets the translation component of the matrix to zero. | |
| void | SetView (Vec3< T > const &pos, Vec3< T > const &target, Vec3< T > const &up) |
| Set view matrix using position, target and approximate up vector. | |
| void | SetCartesianFrameXY (Vec3< T > const &x, Vec3< T > const &y_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0))) |
| Sets a Cartesian coordinate frame using the given x direction, an approximate y direction, and a translation. x must be a unit vector. | |
| void | SetCartesianFrameXZ (Vec3< T > const &x, Vec3< T > const &z_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0))) |
| Sets a Cartesian coordinate frame using the given x direction, an approximate z direction, and a translation. x must be a unit vector. | |
| void | SetCartesianFrameYX (Vec3< T > const &y, Vec3< T > const &x_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0))) |
| Sets a Cartesian coordinate frame using the given y direction, an approximate x direction, and a translation. y must be a unit vector. | |
| void | SetCartesianFrameYZ (Vec3< T > const &y, Vec3< T > const &z_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0))) |
| Sets a Cartesian coordinate frame using the given y direction, an approximate z direction, and a translation. y must be a unit vector. | |
| void | SetCartesianFrameZX (Vec3< T > const &z, Vec3< T > const &x_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0))) |
| Sets a Cartesian coordinate frame using the given z direction, an approximate x direction, and a translation. z must be a unit vector. | |
| void | SetCartesianFrameZY (Vec3< T > const &z, Vec3< T > const &y_approx, Vec3< T > const &trans=Vec3< T >(T(0), T(0), T(0))) |
| Sets a Cartesian coordinate frame using the given z direction, an approximate y direction, and a translation. z must be a unit vector. | |
| void | SetPerspective (T fov, T aspect, T znear, T zfar) |
| Set a project matrix with field of view in radians. | |
| void | SetPerspectiveTan (T tan_fov_2, T aspect, T znear, T zfar) |
| Set a project matrix with the tangent of the half field of view (tan_fov_2) | |
Set Row, Column, or Diagonal | |
| void | SetRow (int ri, T x, T y, T z, T w) |
| Sets a row of the matrix. | |
| void | SetRow (int ri, Vec4< T > const &v) |
| Sets a row of the matrix. | |
| void | SetColumn (int ci, T x, T y, T z, T w) |
| Sets a column of the matrix. | |
| void | SetColumn (int ci, Vec4< T > const &v) |
| Sets a column of the matrix. | |
| void | SetDiagonal (T xx, T yy, T zz, T ww=1) |
| Sets the diagonal values of the matrix. | |
| void | SetDiagonal (Vec4< T > const &p) |
| Sets the diagonal values of the matrix. | |
| void | SetDiagonal (Vec3< T > const &p) |
| Sets the diagonal values of the matrix. | |
| void | SetDiagonal (T const *values) |
| Sets the 4 diagonal values of the matrix. | |
Get Row, Column, or Diagonal | |
| Vec4< T > * | Columns () |
| Returns a row of the matrix. | |
| Vec4< T > const * | Columns () const |
| Returns a row of the matrix. | |
| Vec4< T > & | Column (int ci) |
| Returns a row of the matrix. | |
| Vec4< T > const & | Column (int ci) const |
| Returns a row of the matrix. | |
| Vec3< T > & | Column3 (int ci) |
| Returns a row of the matrix. | |
| Vec3< T > const & | Column3 (int ci) const |
| Returns a row of the matrix. | |
| Vec4< T > | GetRow (int ri) const |
| Returns a row of the matrix. | |
| Vec4< T > | GetDiagonal () const |
| Returns the diagonal of the matrix. | |
Get Sub-matrix cell | |
| Matrix34< T > | GetSubMatrix34 () const |
| Returns the 3x4 portion of the matrix. | |
| Matrix3< T > | GetSubMatrix3 () const |
| Returns the 3x3 portion of the matrix. | |
| Matrix2< T > | GetSubMatrix2 () const |
| Returns the 2x2 portion of the matrix. | |
| Vec3< T > | GetTranslation () const |
| Returns the translation component of the matrix. | |
| Matrix3< T > | GetRotation () const |
| Returns the rotation portion of the transformation. | |
| Matrix3< T > | GetScale () const |
| Returns the scale portion of the transformation. | |
| T | GetAvrgScale () const |
| Returns the average scale factor of the 3 by 3 sub-matrix. | |
| void | GetComponents (Matrix3< T > &scale, Matrix3< T > &rotation, Vec3< T > &translation) const |
| Returns separate transformation components. | |
Comparison Operators | |
| bool | operator== (Matrix4 const &right) const |
| compare equal | |
| bool | operator!= (Matrix4 const &right) const |
| compare not equal | |
Access Operators | |
| T & | operator() (int ri, int ci) |
| subscript operator | |
| T const & | operator() (int ri, int ci) const |
| constant subscript operator | |
| T & | operator[] (int i) |
| subscript operator | |
| T const & | operator[] (int i) const |
| constant subscript operator | |
Unary and Binary Operators | |
| Matrix4 | operator- () const |
| negative matrix | |
| Matrix4 | operator* (T const value) const |
| multiply matrix by a value | |
| Matrix4 | operator/ (T const value) const |
| divide matrix by a value | |
| Matrix4 | operator+ (Matrix4 const &right) const |
| add two Matrices | |
| Matrix4 | operator- (Matrix4 const &right) const |
| subtract one Matrix4 from another | |
| Matrix4 | operator* (Matrix4 const &right) const |
| < multiply a matrix with another | |
| Matrix4 | operator* (Matrix34< T > const &right) const |
| < multiply a matrix with another | |
| Matrix4 | operator* (Matrix3< T > const &right) const |
| < multiply a matrix with another | |
| Vec4< T > | operator* (Vec3< T > const &p) const |
| negative matrix | |
| Vec4< T > | operator* (Vec4< T > const &p) const |
| negative matrix | |
Transform Methods | |
| void | Transform (Vec4< T > &p) const |
| Transforms the given vector by multiplying it with the matrix. | |
| Vec4< T > | VectorTransform (Vec3< T > const &p) const |
| Transforms the vector by multiplying it with the matrix, ignoring the translation component. | |
Assignment Operators | |
| Matrix4 const & | operator+= (Matrix4 const &right) |
| add two Matrices modify this | |
| Matrix4 const & | operator-= (Matrix4 const &right) |
| subtract one Matrix4 from another matrix and modify this matrix | |
| Matrix4 const & | operator*= (Matrix4 const &right) |
| multiply a matrix with another matrix and modify this matrix | |
| Matrix4 const & | operator*= (Matrix34< T > const &right) |
| multiply a matrix with another matrix and modify this matrix | |
| Matrix4 const & | operator*= (Matrix3< T > const &right) |
| multiply a matrix with another matrix and modify this matrix | |
| Matrix4 const & | operator*= (T const value) |
| multiply a matrix with a value modify this matrix | |
| Matrix4 const & | operator/= (T const value) |
| divide the matrix by a value modify the this matrix | |
Other Methods | |
| void | Transpose () |
| < Return the transpose of this matrix | |
| Matrix4 | GetTranspose () const |
| < Return the transpose of this matrix | |
| Vec4< T > | TransposeMult (Vec3< T > const &p) const |
| Multiply the give vector with the transpose of the matrix. | |
| Vec4< T > | TransposeMult (Vec4< T > const &p) const |
| Multiply the give vector with the transpose of the matrix. | |
| Matrix4 | TransposeMult (Matrix4 const &right) const |
| < Multiply a matrix by the transpose of this one (i.e. this^T * right). | |
| Matrix4 | MultTranspose (Matrix4 const &right) const |
| < Multiply the transpose of a matrix by this one (i.e. this * right^T). | |
| Matrix4 | TransposeMultSelf () const |
| Multiply the transpose of this matrix with itself (i.e. this^T * this). | |
| Matrix4 | MultSelfTranspose () const |
| Multiply the matrix with its transpose (i.e. this * this^T). | |
| T | GetTrace () const |
| < Return the transpose of this matrix | |
| T | GetDeterminant () const |
| < Get the determinant of this matrix | |
| void | Invert () |
| Invert this matrix. | |
| Matrix4 | GetInverse () const |
| < Get the inverse of this matrix | |
| void | Normalize () |
| Removes the scale component of the matrix by normalizing each column of the 3x3 sub-matrix. The resulting matrix can contain shear, if it originally contained non-uniform scale and rotation. | |
| void | OrthogonalizeX () |
| Orthogonalizes the matrix and removes the scale component, preserving the x direction. | |
| void | OrthogonalizeY () |
| Orthogonalizes the matrix and removes the scale component, preserving the y direction. | |
| void | OrthogonalizeZ () |
| Orthogonalizes the matrix and removes the scale component, preserving the z direction. | |
| bool | IsIdentity (T tollerance=T(0.0001)) const |
| Returns if the matrix is identity within the given error tollerance. | |
| bool | IsSymmetric (T tollerance=T(0.0001)) const |
| Returns if the matrix is symmetric within the given error tollerance. | |
| bool | IsDiagonal (T tollerance=T(0.0001)) const |
| Returns if the matrix is diagonal. | |
Static Public Member Functions | |
Static Methods | |
| static Matrix4 | Identity () |
| Returns an identity matrix. | |
| static Matrix4 | View (Vec3< T > const &pos, Vec3< T > const &target, Vec3< T > const &up) |
| Returns a view matrix using position, target and approximate up vector. | |
| static Matrix4 | RotationX (T angle) |
| Returns a rotation matrix around x axis by angle in radians. | |
| static Matrix4 | RotationY (T angle) |
| Returns a rotation matrix around y axis by angle in radians. | |
| static Matrix4 | RotationZ (T angle) |
| Returns a rotation matrix around z axis by angle in radians. | |
| static Matrix4 | Rotation (Vec3< T > const &axis, T angle) |
| Returns a rotation matrix about the given axis by angle in radians. | |
| static Matrix4 | Rotation (Vec3< T > const &axis, T cosAngle, T sinAngle) |
| Returns a rotation matrix about the given axis by cos and sin of the rotation angle. | |
| static Matrix4 | Rotation (Vec3< T > const &from, Vec3< T > const &to) |
| Returns a rotation matrix that sets [from] unit vector to [to] unit vector. | |
| static Matrix4 | RotationXYZ (T angleX, T angleY, T angleZ) |
| Returns a rotation matrix around x, y, and then z axes by angle in radians (Rz * Ry * Rx) | |
| static Matrix4 | RotationZYX (T angleX, T angleY, T angleZ) |
| Returns a rotation matrix around z, y, and then x axes by angle in radians (Rx * Ry * Rz) | |
| static Matrix4 | Scale (T uniformScale) |
| Returns a uniform scale matrix. | |
| static Matrix4 | Scale (T scaleX, T scaleY, T scaleZ, T scaleW=T(1)) |
| Returns a scale matrix. | |
| static Matrix4 | Scale (Vec3< T > const &scale) |
| Returns a scale matrix. | |
| static Matrix4 | Translation (Vec3< T > const &move) |
| Returns a translation matrix with no rotation or scale. | |
| static Matrix4 | Perspective (T fov, T aspect, T znear, T zfar) |
| Returns a project matrix with field of view in radians. | |
| static Matrix4 | PerspectiveTan (T tan_fov_2, T aspect, T znear, T zfar) |
| Returns a project matrix with the tangent of the half field of view (tan_fov_2) | |
| static Matrix4 | TensorProduct (Vec4< T > const &v0, Vec4< T > const &v1) |
| Returns the tensor product (outer product) matrix of two vectors. | |
Public Attributes | |
| T | cell [16] |
| Elements of the matrix are column-major: | 0 4 8 12 | | 1 5 9 13 | | 2 6 10 14 | | 3 7 11 15 | . | |
Friends | |
| Matrix4 | operator* (T value, Matrix4 const &right) |
| multiply matrix by a value | |
| Matrix4 | Inverse (Matrix4 const &m) |
| return the inverse of the matrix | |
| Matrix4 | operator* (Matrix34< T > const &left, Matrix4 const &right) |
| multiply a 4x4 matrix with a 3x4 matrix, treating it as a 4x4 matrix with last row 0,0,0,1 | |