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pdftron::Common::Matrix2D Class Reference

#include <Matrix2D.h>

+ Inheritance diagram for pdftron::Common::Matrix2D:

Public Member Functions

 Matrix2D (double a=1, double b=0, double c=0, double d=1, double h=0, double v=0)
 
 Matrix2D (const Matrix2D &m)
 
Matrix2Doperator= (const Matrix2D &m)
 
void Set (double a, double b, double c, double d, double h, double v)
 
void Concat (double a, double b, double c, double d, double h, double v)
 
Matrix2Doperator*= (const Matrix2D &m)
 
Matrix2D operator* (const Matrix2D &m) const
 
bool operator== (const Matrix2D &m) const
 
bool operator!= (const Matrix2D &m) const
 
PDF::Point Mult (const PDF::Point &pt) const
 
void Mult (double &in_out_x, double &in_out_y) const
 
Matrix2D Inverse () const
 
void Translate (double h, double v)
 
void Scale (double h, double v)
 

Static Public Member Functions

static Matrix2D ZeroMatrix ()
 
static Matrix2D IdentityMatrix ()
 
static Matrix2D RotationMatrix (const double angle)
 

Detailed Description

2D Matrix

A Matrix2D object represents a 3x3 matrix that, in turn, represents an affine transformation. A Matrix2D object stores only six of the nine numbers in a 3x3 matrix because all 3x3 matrices that represent affine transformations have the same third column (0, 0, 1).

Affine transformations include rotating, scaling, reflecting, shearing, and translating. In PDFNet, the Matrix2D class provides the foundation for performing affine transformations on vector drawings, images, and text.

A transformation matrix specifies the relationship between two coordinate spaces. By modifying a transformation matrix, objects can be scaled, rotated, translated, or transformed in other ways.

A transformation matrix in PDF is specified by six numbers, usually in the form of an array containing six elements. In its most general form, this array is denoted [a b c d h v]; The following table lists the arrays that specify the most common transformations:

  • Translations are specified as [1 0 0 1 tx ty], where tx and ty are the distances to translate the origin of the coordinate system in the horizontal and vertical dimensions, respectively.
  • Scaling is obtained by [sx 0 0 sy 0 0]. This scales the coordinates so that 1 unit in the horizontal and vertical dimensions of the new coordinate system is the same size as sx and sy units, respectively, in the previous coordinate system.
  • Rotations are produced by [cos(A) sin(A) -sin(A) cos(A) 0 0], which has the effect of rotating the coordinate system axes by an angle 'A' counterclockwise.
  • Skew is specified by [1 tan(A) tan(B) 1 0 0], which skews the x axis by an angle A and the y axis by an angle B.

Matrix2D elements are positioned as follows : | m_a m_b 0 | | m_c m_d 0 | | m_h m_v 1 |

A single Matrix2D object can store a single transformation or a sequence of transformations. The latter is called a composite transformation. The matrix of a composite transformation is obtained by multiplying (concatenating) the matrices of the individual transformations. Because matrix multiplication is not commutative-the order in which matrices are multiplied is significant. For example, if you first rotate, then scale, then translate, you get a different result than if you first translate, then rotate, then scale.

For more information on properties of PDF matrices please refer to PDF Reference Manual (Sections 4.2 'Coordinate Systems' and 4.2.3 'Transformation Matrices')

* The following sample illustrates how to use Matrix2D in order to position
* an image on the page. Note that PDFNet uses the same convention of matrix
* multiplication used in PostScript and OpenGL.
*
* Element element = eb.CreateImage(Image(...));
* double deg2rad = 3.1415926535 / 180.0;
*
* Matrix2D mtx = Matrix2D(1, 0, 0, 1, 0, 200); // Translate
* mtx *= Matrix2D(300, 0, 0, 200, 0, 0); // Scale
* mtx *= Matrix2D::RotationMatrix( 90 * deg2rad ); // Rotate
* element.GetGState().SetTransform(mtx);
* writer.WritePlacedElement(element);
*
* The following sample sample illustrates how to use Matrix2D in order to calculate
* absolute positioning for the text on the page.
* ...
* Matrix2D text_mtx = text_element.GetTextMatrix();
* double x, y;
* for (CharIterator itr = text_element.GetCharIterator(); itr.HasNext(); itr.Next()) {
* x = itr.Current().x; // character positioning information
* y = itr.Current().y;
* // Get current transformation matrix (CTM)
* Matrix2D ctm = text_element.GetCTM();
*
* // To get the absolute character positioning information concatenate current
* // text matrix with CTM and then multiply relative positioning coordinates with
* // the resulting matrix.
* Matrix2D mtx = ctm * text_mtx;
* mtx.Mult(x, y);
* }
*

Definition at line 103 of file Matrix2D.h.

Constructor & Destructor Documentation

pdftron::Common::Matrix2D::Matrix2D ( double  a = 1,
double  b = 0,
double  c = 0,
double  d = 1,
double  h = 0,
double  v = 0 
)

Creates and initializes a Matrix object based on six numbers that define an affine transformation.

Parameters
athe matrix element in the first row, first column.
bthe matrix element in the first row, second column.
cthe matrix element in the second row, first column.
dthe matrix element in the second row, second column.
hthe matrix element in the third row, first column.
vthe matrix element in the third row, second column.

when none the arguments are specified, an identity matrix is created.

pdftron::Common::Matrix2D::Matrix2D ( const Matrix2D m)

Copy constructor.

Member Function Documentation

void pdftron::Common::Matrix2D::Concat ( double  a,
double  b,
double  c,
double  d,
double  h,
double  v 
)

The Concat method updates this matrix with the product of itself and another matrix specified through an argument list.

Parameters
athe matrix element in the first row, first column.
bthe matrix element in the first row, second column.
cthe matrix element in the second row, first column.
dthe matrix element in the second row, second column.
hthe matrix element in the third row, first column.
vthe matrix element in the third row, second column.
static Matrix2D pdftron::Common::Matrix2D::IdentityMatrix ( )
static

Create identity matrix (1 0 0 1 0 0)

Matrix2D pdftron::Common::Matrix2D::Inverse ( ) const
Returns
If this matrix is invertible, the Inverse method returns its inverse matrix.
PDF::Point pdftron::Common::Matrix2D::Mult ( const PDF::Point pt) const

Transform/multiply the point (in_out_x, in_out_y) using this matrix

void pdftron::Common::Matrix2D::Mult ( double &  in_out_x,
double &  in_out_y 
) const
bool pdftron::Common::Matrix2D::operator!= ( const Matrix2D m) const
inline

The inequality operator determines whether the elements of this matrix are not equal to the elements of another matrix.

Parameters
AMatrix object that is compared with this Matrix object.
Returns
A boolean regarding whether two matrices are different.

Definition at line 189 of file Matrix2D.h.

Matrix2D pdftron::Common::Matrix2D::operator* ( const Matrix2D m) const

Multiplies this matrix with another matrix and return the result in a new matrix.

Returns
a matrix representing the product of this matrix and given matrix 'm'.
Matrix2D& pdftron::Common::Matrix2D::operator*= ( const Matrix2D m)

The multiply method updates this matrix with the product of itself and another matrix.

Parameters
mA matrix used to update this matrix
Returns
updated this matrix representing the product of this matrix and given matrix 'm'.
Matrix2D& pdftron::Common::Matrix2D::operator= ( const Matrix2D m)

Assignment operator.

bool pdftron::Common::Matrix2D::operator== ( const Matrix2D m) const

The equality operator determines whether the elements of this matrix are equal to the elements of another matrix.

Parameters
mA Matrix object that is compared with this Matrix object.
Returns
A boolean regarding whether two matrices are the same.
static Matrix2D pdftron::Common::Matrix2D::RotationMatrix ( const double  angle)
static
Returns
A rotation matrix for a given angle.
Parameters
anglethe angle of rotation in radians. Positive values specify clockwise rotation.
void pdftron::Common::Matrix2D::Scale ( double  h,
double  v 
)

The Scale method updates this matrix with the product of itself and a scaling matrix.

Parameters
hthe horizontal scale factor.
vthe vertical scale factor
Returns
updated this matrix
void pdftron::Common::Matrix2D::Set ( double  a,
double  b,
double  c,
double  d,
double  h,
double  v 
)

The Set method sets the elements of this matrix.

Parameters
athe matrix element in the first row, first column.
bthe matrix element in the first row, second column.
cthe matrix element in the second row, first column.
dthe matrix element in the second row, second column.
hthe matrix element in the third row, first column.
vthe matrix element in the third row, second column.
void pdftron::Common::Matrix2D::Translate ( double  h,
double  v 
)

The Translate method updates this matrix with the product of itself and a translation matrix (i.e. it is equivalent to this.m_h += h; this.m_v += v).

Parameters
hthe horizontal component of the translation.
vthe vertical component of the translation.
Returns
updated this matrix
static Matrix2D pdftron::Common::Matrix2D::ZeroMatrix ( )
static

Create zero matrix (0 0 0 0 0 0)


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