Matrix2< T > Class Template Reference
Detailed Description
template<typename T>
class cy::Matrix2< T >
class cy::Matrix2< T >
2x2 matrix class.
Its data stores 4-value array of column-major matrix elements. You can use Matrix2 with Vec2<T> to transform 2D points.
#include <cyMatrix.h>
Public Member Functions | |
Constructors | |
| Matrix2 () | |
| Default constructor. | |
| template<typename TT > | |
| Matrix2 (const Matrix2< TT > &matrix) | |
| Copy constructor for different types. | |
| Matrix2 (T const *values) | |
| Initialize the matrix using an array of 4 values. | |
| Matrix2 (T v) | |
| Initialize the matrix as identity scaled by v. | |
| Matrix2 (Vec2< T > const &x, Vec2< T > const &y) | |
| Initialize the matrix using two vectors as columns. | |
| Matrix2 (Matrix3< T > const &m) | |
| Default constructor. | |
| Matrix2 (Matrix34< T > const &m) | |
| Default constructor. | |
| Matrix2 (Matrix4< T > const &m) | |
| Default constructor. | |
| Matrix2 (T c00, T c01, T c10, T c11) | |
| 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 4. | |
| void | Set (T const *values) |
| Set Matrix using an array of 4 values. | |
| void | Set (Vec2< T > const &x, Vec2< T > const &y) |
| Set Matrix using two vectors as columns. | |
| void | SetIdentity () |
| Converts the matrix to an identity matrix. | |
| void | SetTensorProduct (Vec2< T > const &v0, Vec2< 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) |
| Sets a scale matrix. | |
| void | SetScale (Vec2< T > const &scale) |
| Sets a scale matrix. | |
| void | SetRotation (T angle) |
| Set a rotation matrix by angle. | |
| void | SetRotation (T sinAngle, T cosAngle) |
| Set a rotation matrix by cos and sin of angle. | |
| void | SetCartesianFrameX (Vec2< T > const &x) |
| Sets a Cartesian coordinate frame using the given x direction. x must be a unit vector. | |
| void | SetCartesianFrameY (Vec2< T > const &y) |
| Sets a Cartesian coordinate frame using the given y direction. y must be a unit vector. | |
Set Row, Column, or Diagonal | |
| void | SetRow (int ri, T x, T y) |
| Sets a row of the matrix. | |
| void | SetRow (int ri, Vec2< T > const &v) |
| Sets a row of the matrix. | |
| void | SetColumn (int ci, T x, T y) |
| Sets a column of the matrix. | |
| void | SetColumn (int ci, Vec2< T > const &v) |
| Sets a column of the matrix. | |
| void | SetDiagonal (T xx, T yy) |
| Sets the diagonal values of the matrix. | |
| void | SetDiagonal (Vec2< T > const &p) |
| Sets the diagonal values of the matrix. | |
| void | SetDiagonal (T const *values) |
| Sets the diagonal values of the matrix. | |
Get Row, Column, or Diagonal | |
| Vec2< T > * | Columns () |
| Returns a row of the matrix. | |
| Vec2< T > const * | Columns () const |
| Returns a row of the matrix. | |
| Vec2< T > & | Column (int ci) |
| Returns a row of the matrix. | |
| Vec2< T > const & | Column (int ci) const |
| Returns a row of the matrix. | |
| Vec2< T > | GetRow (int ri) const |
| Returns a row of the matrix. | |
| Vec2< T > | GetDiagonal () const |
| Returns the diagonal of the matrix. | |
| Matrix2 | GetRotation () const |
| Returns the rotation portion of the transformation. | |
| Matrix2 | GetScale () const |
| Returns the scale portion of the transformation. The returned matrix is symmetric, but not necessarily diagonal, and it can include non-uniform scale. | |
| T | GetAvrgScale () const |
| Returns the average scale factor. | |
| void | GetComponents (Matrix2< T > &scale, Matrix2< T > &rotation) const |
| Returns separate transformation components. | |
Comparison Operators | |
| bool | operator== (Matrix2 const &right) const |
| compare equal | |
| bool | operator!= (Matrix2 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 | |
| Matrix2 | operator- () const |
| negative matrix | |
| Matrix2 | operator* (T const value) const |
| multiply matrix by a value | |
| Matrix2 | operator/ (T const value) const |
| divide matrix by a value | |
| Matrix2 | operator+ (Matrix2 const &right) const |
| add two Matrices | |
| Matrix2 | operator- (Matrix2 const &right) const |
| subtract one Matrix2 from another | |
| Matrix2 | operator* (Matrix2 const &right) const |
| < multiply a matrix with another | |
| Vec2< T > | operator* (Vec2< T > const &p) const |
| negative matrix | |
| Matrix2 | operator+ (T value) const |
| add a value times identity matrix | |
| Matrix2 | operator- (T value) const |
| subtract a value times identity matrix | |
ND Transform Methods | |
| void | Transform (Vec< T, N > &p) const |
| Transforms the given vector by multiplying it with the matrix. | |
Assignment Operators | |
| Matrix2 const & | operator+= (Matrix2 const &right) |
| add two Matrices modify this | |
| Matrix2 const & | operator-= (Matrix2 const &right) |
| subtract one Matrix2 from another matrix and modify this matrix | |
| Matrix2 const & | operator*= (Matrix2 const &right) |
| multiply a matrix with another matrix and modify this matrix | |
| Matrix2 const & | operator*= (T const value) |
| multiply a matrix with a value modify this matrix | |
| Matrix2 const & | operator/= (T const value) |
| divide the matrix by a value modify the this matrix | |
| Matrix2 const & | operator+= (T const value) |
| add a value times identity matrix | |
| Matrix2 const & | operator-= (T const value) |
| subtract a value times identity matrix | |
Other Methods | |
| void | Transpose () |
| Transpose this matrix. | |
| Matrix2 | GetTranspose () const |
| < Returns the transpose of this matrix | |
| Vec2< T > | TransposeMult (Vec2< T > const &p) const |
| Multiply the give vector with the transpose of the matrix. | |
| Matrix2 | TransposeMult (Matrix2 const &right) const |
| < Multiply a matrix by the transpose of this one (i.e. this^T * right). | |
| Matrix2 | MultTranspose (Matrix2 const &right) const |
| < Multiply the transpose of a matrix by this one (i.e. this * right^T). | |
| Matrix2 | TransposeMultSelf () const |
| Multiply the transpose of this matrix with itself (i.e. this^T * this). | |
| Matrix2 | MultSelfTranspose () const |
| Multiply the matrix with its transpose (i.e. this * this^T). | |
| T | GetTrace () const |
| return the Trace of this matrix | |
| T | GetDeterminant () const |
| Get the determinant of this matrix. | |
| void | Invert () |
| Transpose this matrix. | |
| Matrix2 | GetInverse () const |
| < Get the inverse of this matrix | |
| void | Normalize () |
| Removes the scale component of the matrix by normalizing each column. 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. | |
| 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. | |
| Vec2< T > | GetEigenvalues () const |
| Returns the eigenvalues of the matrix. The eigenvalues are ordered, such that the first one is larger. | |
| Vec2< T > | GetEigenvectors (Vec2< T > &evec0, Vec2< T > &evec1, T tollerance=T(0.0001)) const |
| Returns the eigenvalues and sets the given vectors as the eigenvectors of the matrix. The eigenvalues are ordered, such that the first one is larger. The given tollerance is used for checking whether the eigenvalues are the same. | |
| void | SingularValueDecomposition (Matrix2< T > &U, Vec2< T > &S, Matrix2< T > &V) |
| Singular value decomposition (SVD). Returns the SVD of the matrix, where U and V are orthogonal matrices and S is the diagonal elements of a diagonal matrix (including zeros), such that this matrix A = U S V^T. | |
Static Public Member Functions | |
Static Methods | |
| static Matrix2 | Identity () |
| Returns an identity matrix. | |
| static Matrix2 | Rotation (T angle) |
| Returns a rotation matrix by angle in radians. | |
| static Matrix2 | Rotation (T cosAngle, T sinAngle) |
| Returns a rotation matrix by cos and sin of the rotation angle. | |
| static Matrix2 | Scale (T uniformScale) |
| Returns a uniform scale matrix. | |
| static Matrix2 | Scale (T scaleX, T scaleY) |
| Returns a scale matrix. | |
| static Matrix2 | Scale (Vec2< T > const &scale) |
| Returns a scale matrix. | |
| static Matrix2 | TensorProduct (Vec2< T > const &v0, Vec2< T > const &v1) |
| Returns the tensor product (outer product) matrix of two vectors. | |
Public Attributes | |
| T | cell [4] |
| Elements of the matrix are column-major: | 0 2 | | 1 3 | . | |
Friends | |
| Matrix2 | operator* (T value, Matrix2 const &right) |
| multiply matrix by a value | |
| Matrix2 | operator+ (T value, Matrix2 const &right) |
| add a value times identity matrix to a matrix | |
| Matrix2 | operator- (T value, Matrix2 const &right) |
| subtract matrix from a value times identity matrix | |
| Matrix2 | Inverse (Matrix2 const &m) |
| return the inverse of the matrix | |