OpenVDB  5.2.0
Public Types | Public Member Functions | Static Public Member Functions | Protected Attributes | Related Functions | List of all members
Mat3< T > Class Template Reference

3x3 matrix class. More...

#include <Mat3.h>

Inherits Mat< 3, T >.

Public Types

using value_type = T
 Data type held by the matrix. More...
 
using ValueType = T
 
using MyBase = Mat< 3, T >
 
enum  SIZE_
 

Public Member Functions

 Mat3 ()
 Trivial constructor, the matrix is NOT initialized. More...
 
 Mat3 (const Quat< T > &q)
 
template<typename Source >
 Mat3 (Source a, Source b, Source c, Source d, Source e, Source f, Source g, Source h, Source i)
 Constructor given array of elements, the ordering is in row major form: More...
 
template<typename Source >
 Mat3 (const Vec3< Source > &v1, const Vec3< Source > &v2, const Vec3< Source > &v3, bool rows=true)
 
template<typename Source >
 Mat3 (Source *a)
 
 Mat3 (const Mat< 3, T > &m)
 Copy constructor. More...
 
template<typename Source >
 Mat3 (const Mat3< Source > &m)
 Conversion constructor. More...
 
 Mat3 (const Mat4< T > &m)
 Conversion from Mat4 (copies top left) More...
 
void setRow (int i, const Vec3< T > &v)
 Set ith row to vector v. More...
 
Vec3< T > row (int i) const
 Get ith row, e.g. Vec3d v = m.row(1);. More...
 
void setCol (int j, const Vec3< T > &v)
 Set jth column to vector v. More...
 
Vec3< T > col (int j) const
 Get jth column, e.g. Vec3d v = m.col(0);. More...
 
T * asPointer ()
 
const T * asPointer () const
 
T & operator() (int i, int j)
 
operator() (int i, int j) const
 
void setRows (const Vec3< T > &v1, const Vec3< T > &v2, const Vec3< T > &v3)
 Set the rows of this matrix to the vectors v1, v2, v3. More...
 
void setColumns (const Vec3< T > &v1, const Vec3< T > &v2, const Vec3< T > &v3)
 Set the columns of this matrix to the vectors v1, v2, v3. More...
 
void setSymmetric (const Vec3< T > &vdiag, const Vec3< T > &vtri)
 Set diagonal and symmetric triangular components. More...
 
void setSkew (const Vec3< T > &v)
 Set the matrix as cross product of the given vector. More...
 
void setToRotation (const Quat< T > &q)
 Set this matrix to the rotation matrix specified by the quaternion. More...
 
void setToRotation (const Vec3< T > &axis, T angle)
 Set this matrix to the rotation specified by axis and angle. More...
 
void setZero ()
 Set this matrix to zero. More...
 
void setIdentity ()
 Set this matrix to identity. More...
 
template<typename Source >
const Mat3operator= (const Mat3< Source > &m)
 Assignment operator. More...
 
bool eq (const Mat3 &m, T eps=1.0e-8) const
 Return true if this matrix is equivalent to m within a tolerance of eps. More...
 
Mat3< T > operator- () const
 Negation operator, for e.g. m1 = -m2;. More...
 
template<typename S >
const Mat3< T > & operator*= (S scalar)
 Multiplication operator, e.g. M = scalar * M;. More...
 
template<typename S >
const Mat3< T > & operator+= (const Mat3< S > &m1)
 Add each element of the given matrix to the corresponding element of this matrix. More...
 
template<typename S >
const Mat3< T > & operator-= (const Mat3< S > &m1)
 Subtract each element of the given matrix from the corresponding element of this matrix. More...
 
template<typename S >
const Mat3< T > & operator*= (const Mat3< S > &m1)
 Multiply this matrix by the given matrix. More...
 
Mat3 cofactor () const
 Return the cofactor matrix of this matrix. More...
 
Mat3 adjoint () const
 Return the adjoint of this matrix, i.e., the transpose of its cofactor. More...
 
Mat3 transpose () const
 returns transpose of this More...
 
Mat3 inverse (T tolerance=0) const
 
det () const
 Determinant of matrix. More...
 
trace () const
 Trace of matrix. More...
 
Mat3 snapBasis (Axis axis, const Vec3< T > &direction)
 
template<typename T0 >
Vec3< T0 > transform (const Vec3< T0 > &v) const
 
template<typename T0 >
Vec3< T0 > pretransform (const Vec3< T0 > &v) const
 
Mat3 timesDiagonal (const Vec3< T > &diag) const
 Treat diag as a diagonal matrix and return the product of this matrix with diag (from the right). More...
 
std::string str (unsigned indentation=0) const
 
void write (std::ostream &os) const
 
void read (std::istream &is)
 
absMax () const
 Return the maximum of the absolute of all elements in this matrix. More...
 
bool isNan () const
 True if a Nan is present in this matrix. More...
 
bool isInfinite () const
 True if an Inf is present in this matrix. More...
 
bool isFinite () const
 True if no Nan or Inf values are present. More...
 
bool isZero () const
 True if all elements are exactly zero. More...
 
T * operator[] (int i)
 
const T * operator[] (int i) const
 

Static Public Member Functions

static const Mat3< T > & identity ()
 Predefined constant for identity matrix. More...
 
static const Mat3< T > & zero ()
 Predefined constant for zero matrix. More...
 
static Mat3 symmetric (const Vec3< T > &vdiag, const Vec3< T > &vtri)
 Return a matrix with the prescribed diagonal and symmetric triangular components. More...
 
static unsigned numRows ()
 
static unsigned numColumns ()
 
static unsigned numElements ()
 

Protected Attributes

mm [SIZE *SIZE]
 

Related Functions

(Note that these are not member functions.)

template<typename T0 , typename T1 >
bool operator== (const Mat3< T0 > &m0, const Mat3< T1 > &m1)
 Equality operator, does exact floating point comparisons. More...
 
template<typename T0 , typename T1 >
bool operator!= (const Mat3< T0 > &m0, const Mat3< T1 > &m1)
 Inequality operator, does exact floating point comparisons. More...
 
template<typename S , typename T >
Mat3< typename promote< S, T >::type > operator* (S scalar, const Mat3< T > &m)
 Multiply each element of the given matrix by scalar and return the result. More...
 
template<typename S , typename T >
Mat3< typename promote< S, T >::type > operator* (const Mat3< T > &m, S scalar)
 Multiply each element of the given matrix by scalar and return the result. More...
 
template<typename T0 , typename T1 >
Mat3< typename promote< T0, T1 >::type > operator+ (const Mat3< T0 > &m0, const Mat3< T1 > &m1)
 Add corresponding elements of m0 and m1 and return the result. More...
 
template<typename T0 , typename T1 >
Mat3< typename promote< T0, T1 >::type > operator- (const Mat3< T0 > &m0, const Mat3< T1 > &m1)
 Subtract corresponding elements of m0 and m1 and return the result. More...
 
template<typename T , typename MT >
Vec3< typename promote< T, MT >::type > operator* (const Mat3< MT > &_m, const Vec3< T > &_v)
 Multiply _m by _v and return the resulting vector. More...
 
template<typename T , typename MT >
Vec3< typename promote< T, MT >::type > operator* (const Vec3< T > &_v, const Mat3< MT > &_m)
 Multiply _v by _m and return the resulting vector. More...
 
template<typename T , typename MT >
Vec3< T > & operator*= (Vec3< T > &_v, const Mat3< MT > &_m)
 Multiply _v by _m and replace _v with the resulting vector. More...
 

Detailed Description

template<typename T>
class openvdb::v5_2::math::Mat3< T >

3x3 matrix class.

Member Typedef Documentation

using MyBase = Mat<3, T>
using value_type = T

Data type held by the matrix.

using ValueType = T

Member Enumeration Documentation

enum SIZE_
inherited

Constructor & Destructor Documentation

Mat3 ( )
inline

Trivial constructor, the matrix is NOT initialized.

Mat3 ( const Quat< T > &  q)
inline

Constructor given the quaternion rotation, e.g. Mat3f m(q); The quaternion is normalized and used to construct the matrix

Mat3 ( Source  a,
Source  b,
Source  c,
Source  d,
Source  e,
Source  f,
Source  g,
Source  h,
Source  i 
)
inline

Constructor given array of elements, the ordering is in row major form:

a b c
d e f
g h i
Mat3 ( const Vec3< Source > &  v1,
const Vec3< Source > &  v2,
const Vec3< Source > &  v3,
bool  rows = true 
)
inline

Construct matrix from rows or columns vectors (defaults to rows for historical reasons)

Mat3 ( Source *  a)
inline

Constructor given array of elements, the ordering is in row major form:
a[0] a[1] a[2]
a[3] a[4] a[5]
a[6] a[7] a[8]

Mat3 ( const Mat< 3, T > &  m)
inline

Copy constructor.

Mat3 ( const Mat3< Source > &  m)
inlineexplicit

Conversion constructor.

Mat3 ( const Mat4< T > &  m)
inlineexplicit

Conversion from Mat4 (copies top left)

Member Function Documentation

T absMax ( ) const
inlineinherited

Return the maximum of the absolute of all elements in this matrix.

Mat3 adjoint ( ) const
inline

Return the adjoint of this matrix, i.e., the transpose of its cofactor.

T* asPointer ( )
inline
const T* asPointer ( ) const
inline
Mat3 cofactor ( ) const
inline

Return the cofactor matrix of this matrix.

Vec3<T> col ( int  j) const
inline

Get jth column, e.g. Vec3d v = m.col(0);.

T det ( ) const
inline

Determinant of matrix.

bool eq ( const Mat3< T > &  m,
eps = 1.0e-8 
) const
inline

Return true if this matrix is equivalent to m within a tolerance of eps.

static const Mat3<T>& identity ( )
inlinestatic

Predefined constant for identity matrix.

Mat3 inverse ( tolerance = 0) const
inline

returns inverse of this

Exceptions
ArithmeticErrorif singular
bool isFinite ( ) const
inlineinherited

True if no Nan or Inf values are present.

bool isInfinite ( ) const
inlineinherited

True if an Inf is present in this matrix.

bool isNan ( ) const
inlineinherited

True if a Nan is present in this matrix.

bool isZero ( ) const
inlineinherited

True if all elements are exactly zero.

static unsigned numColumns ( )
inlinestaticinherited
static unsigned numElements ( )
inlinestaticinherited
static unsigned numRows ( )
inlinestaticinherited
T& operator() ( int  i,
int  j 
)
inline

Alternative indexed reference to the elements Note that the indices are row first and column second. e.g. m(0,0) = 1;

T operator() ( int  i,
int  j 
) const
inline

Alternative indexed constant reference to the elements, Note that the indices are row first and column second. e.g. float f = m(1,0);

const Mat3<T>& operator*= ( scalar)
inline

Multiplication operator, e.g. M = scalar * M;.

Multiply each element of this matrix by scalar.

const Mat3<T>& operator*= ( const Mat3< S > &  m1)
inline

Multiply this matrix by the given matrix.

const Mat3<T>& operator+= ( const Mat3< S > &  m1)
inline

Add each element of the given matrix to the corresponding element of this matrix.

Mat3<T> operator- ( ) const
inline

Negation operator, for e.g. m1 = -m2;.

const Mat3<T>& operator-= ( const Mat3< S > &  m1)
inline

Subtract each element of the given matrix from the corresponding element of this matrix.

const Mat3& operator= ( const Mat3< Source > &  m)
inline

Assignment operator.

T* operator[] ( int  i)
inline

Array style reference to ith row e.g. m[1][2] = 4;

const T* operator[] ( int  i) const
inline

Array style reference to ith row e.g. m[1][2] = 4;

Vec3<T0> pretransform ( const Vec3< T0 > &  v) const
inline

Return the transformed vector by transpose of this matrix. This function is equivalent to pre-multiplying the matrix.

void read ( std::istream &  is)
inlineinherited
Vec3<T> row ( int  i) const
inline

Get ith row, e.g. Vec3d v = m.row(1);.

void setCol ( int  j,
const Vec3< T > &  v 
)
inline

Set jth column to vector v.

void setColumns ( const Vec3< T > &  v1,
const Vec3< T > &  v2,
const Vec3< T > &  v3 
)
inline

Set the columns of this matrix to the vectors v1, v2, v3.

void setIdentity ( )
inline

Set this matrix to identity.

void setRow ( int  i,
const Vec3< T > &  v 
)
inline

Set ith row to vector v.

void setRows ( const Vec3< T > &  v1,
const Vec3< T > &  v2,
const Vec3< T > &  v3 
)
inline

Set the rows of this matrix to the vectors v1, v2, v3.

void setSkew ( const Vec3< T > &  v)
inline

Set the matrix as cross product of the given vector.

void setSymmetric ( const Vec3< T > &  vdiag,
const Vec3< T > &  vtri 
)
inline

Set diagonal and symmetric triangular components.

void setToRotation ( const Quat< T > &  q)
inline

Set this matrix to the rotation matrix specified by the quaternion.

The quaternion is normalized and used to construct the matrix. Note that the matrix is transposed to match post-multiplication semantics.

void setToRotation ( const Vec3< T > &  axis,
angle 
)
inline

Set this matrix to the rotation specified by axis and angle.

The axis must be unit vector

void setZero ( )
inline

Set this matrix to zero.

Mat3 snapBasis ( Axis  axis,
const Vec3< T > &  direction 
)
inline

This function snaps a specific axis to a specific direction, preserving scaling. It does this using minimum energy, thus posing a unique solution if basis & direction arent parralel. Direction need not be unit.

std::string str ( unsigned  indentation = 0) const
inlineinherited
Returns
string representation of matrix Since output is multiline, optional indentation argument prefixes each newline with that much white space. It does not indent the first line, since you might be calling this inline:

cout << "matrix: " << mat.str(7)

matrix: [[1 2] [3 4]]

static Mat3 symmetric ( const Vec3< T > &  vdiag,
const Vec3< T > &  vtri 
)
inlinestatic

Return a matrix with the prescribed diagonal and symmetric triangular components.

Mat3 timesDiagonal ( const Vec3< T > &  diag) const
inline

Treat diag as a diagonal matrix and return the product of this matrix with diag (from the right).

T trace ( ) const
inline

Trace of matrix.

Vec3<T0> transform ( const Vec3< T0 > &  v) const
inline

Return the transformed vector by this matrix. This function is equivalent to post-multiplying the matrix.

Mat3 transpose ( ) const
inline

returns transpose of this

void write ( std::ostream &  os) const
inlineinherited
static const Mat3<T>& zero ( )
inlinestatic

Predefined constant for zero matrix.

Friends And Related Function Documentation

bool operator!= ( const Mat3< T0 > &  m0,
const Mat3< T1 > &  m1 
)
related

Inequality operator, does exact floating point comparisons.

Mat3< typename promote< S, T >::type > operator* ( scalar,
const Mat3< T > &  m 
)
related

Multiply each element of the given matrix by scalar and return the result.

Mat3< typename promote< S, T >::type > operator* ( const Mat3< T > &  m,
scalar 
)
related

Multiply each element of the given matrix by scalar and return the result.

Vec3< typename promote< T, MT >::type > operator* ( const Mat3< MT > &  _m,
const Vec3< T > &  _v 
)
related

Multiply _m by _v and return the resulting vector.

Vec3< typename promote< T, MT >::type > operator* ( const Vec3< T > &  _v,
const Mat3< MT > &  _m 
)
related

Multiply _v by _m and return the resulting vector.

Vec3< T > & operator*= ( Vec3< T > &  _v,
const Mat3< MT > &  _m 
)
related

Multiply _v by _m and replace _v with the resulting vector.

Mat3< typename promote< T0, T1 >::type > operator+ ( const Mat3< T0 > &  m0,
const Mat3< T1 > &  m1 
)
related

Add corresponding elements of m0 and m1 and return the result.

Mat3< typename promote< T0, T1 >::type > operator- ( const Mat3< T0 > &  m0,
const Mat3< T1 > &  m1 
)
related

Subtract corresponding elements of m0 and m1 and return the result.

bool operator== ( const Mat3< T0 > &  m0,
const Mat3< T1 > &  m1 
)
related

Equality operator, does exact floating point comparisons.

Member Data Documentation

T mm[SIZE *SIZE]
protectedinherited

The documentation for this class was generated from the following file: