Class Matrix2D

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 :

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.multiply(Matrix2D(300, 0, 0, 200, 0, 0));    // Scale
mtx.multiply(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 postitioning coordinates with the resulting matrix.

Matrix2D mtx = ctm.multiply(text_mtx);
mtx.multPoint(x, y);

Inheritance

System.Object

Matrix2D

Implements

System.IDisposable

Inherited Members

System.Object.Equals(System.Object)

System.Object.Equals(System.Object, System.Object)

System.Object.GetHashCode()

System.Object.GetType()

System.Object.MemberwiseClone()

System.Object.ReferenceEquals(System.Object, System.Object)

System.Object.ToString()

Namespace: pdftron.Common

Assembly: PDFTronDotNet.dll

Syntax

public class Matrix2D : IDisposable

Constructors

Matrix2D()

Creates an identity matrix

Declaration

public Matrix2D()

Matrix2D(Matrix2D)

Create a matrix and initialize it with values from another matrix

Declaration

public Matrix2D(Matrix2D m)

Parameters

Type	Name	Description
Matrix2D	m	matrix to initialize

Matrix2D(Double, Double, Double, Double, Double, Double)

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

Declaration

public Matrix2D(double a, double b, double c, double d, double h, double v)

Parameters

Type	Name	Description
System.Double	a	the matrix element in the first row, first column.
System.Double	b	the matrix element in the first row, second column.
System.Double	c	the matrix element in the second row, first column.
System.Double	d	the matrix element in the second row, second column.
System.Double	h	the matrix element in the third row, first column.
System.Double	v	the matrix element in the third row, second column.

Properties

m_a

the matrix element in the first row, first column.

Declaration

public double m_a { get; set; }

Property Value

Type	Description
System.Double

m_b

the matrix element in the first row, second column

Declaration

public double m_b { get; set; }

Property Value

Type	Description
System.Double

m_c

the matrix element in the second row, first column

Declaration

public double m_c { get; set; }

Property Value

Type	Description
System.Double

m_d

the matrix element in the second row, second column.

Declaration

public double m_d { get; set; }

Property Value

Type	Description
System.Double

m_h

the matrix element in the third row, first column.

Declaration

public double m_h { get; set; }

Property Value

Type	Description
System.Double

m_v

the matrix element in the third row, second column.

Declaration

public double m_v { get; set; }

Property Value

Type	Description
System.Double

Methods

Concat(Double, Double, Double, Double, Double, Double)

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

Declaration

public void Concat(double a, double b, double c, double d, double h, double v)

Parameters

Type	Name	Description
System.Double	a	the matrix element in the first row, first column.
System.Double	b	the matrix element in the first row, second column.
System.Double	c	the matrix element in the second row, first column.
System.Double	d	the matrix element in the second row, second column.
System.Double	h	the matrix element in the third row, first column.
System.Double	v	the matrix element in the third row, second column.

Dispose()

Declaration

public void Dispose()

Dispose(Boolean)

Declaration

protected virtual void Dispose(bool disposing)

Parameters

Type	Name	Description
System.Boolean	disposing

Finalize()

Releases all resources used by the Matrix2D

Declaration

protected void Finalize()

IdentityMatrix()

Create identity matrix {1 0 0 1 0 0}.

Declaration

public static Matrix2D IdentityMatrix()

Returns

Type	Description
Matrix2D	the identity matrix

Inverse()

If this matrix is invertible, the Inverse method returns its inverse matrix.

Declaration

public Matrix2D Inverse()

Returns

Type	Description
Matrix2D	inverse of the matrix

Mult(ref Double, ref Double)

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

Declaration

public void Mult(ref double in_out_x, ref double in_out_y)

Parameters

Type	Name	Description
System.Double	in_out_x	x coordinate of the result point
System.Double	in_out_y	y coordinate of the result point

op_Assign(Matrix2D)

assign value from another matrix

Declaration

public Matrix2D op_Assign(Matrix2D rm)

Parameters

Type	Name	Description
Matrix2D	rm	another matrix

Returns

Type	Description
Matrix2D	matrix with value from `rm`

RotationMatrix(Double)

Rotation matrix.

Declaration

public static Matrix2D RotationMatrix(double angle)

Parameters

Type	Name	Description
System.Double	angle	the angle of rotation in radians. Positive values specify clockwise rotation.

Returns

Type	Description
Matrix2D	A rotation matrix for a given angle.

Scale(Double, Double)

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

Declaration

public Matrix2D Scale(double x, double y)

Parameters

Type	Name	Description
System.Double	x	the horizontal scale factor.
System.Double	y	the vertical scale factor

Returns

Type	Description
Matrix2D	translated matrix

Set(Matrix2D)

set value to given matrix

Declaration

public void Set(Matrix2D p)

Parameters

Type	Name	Description
Matrix2D	p	matrix value for the created matrix

Set(Double, Double, Double, Double, Double, Double)

The Set method sets the elements of this matrix.

Declaration

public void Set(double a, double b, double c, double d, double h, double v)

Parameters

Type	Name	Description
System.Double	a	the matrix element in the first row, first column.
System.Double	b	the matrix element in the first row, second column.
System.Double	c	the matrix element in the second row, first column.
System.Double	d	the matrix element in the second row, second column.
System.Double	h	the matrix element in the third row, first column.
System.Double	v	the matrix element in the third row, second column.

Translate(Double, Double)

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).

Declaration

public Matrix2D Translate(double x, double y)

Parameters

Type	Name	Description
System.Double	x	the horizontal component of the translation.
System.Double	y	the vertical component of the translation.

Returns

Type	Description
Matrix2D	translated matrix

ZeroMatrix()

Create zero matrix (0 0 0 0 0 0).

Declaration

public static Matrix2D ZeroMatrix()

Returns

Type	Description
Matrix2D	zero matrix

Operators

Equality(Matrix2D, Matrix2D)

check if two matrices are equal

Declaration

public static bool operator ==(Matrix2D lm, Matrix2D rm)

Parameters

Type	Name	Description
Matrix2D	lm	left matrix
Matrix2D	rm	right matrix

Returns

Type	Description
System.Boolean	true, if both matrices are equal. false, otherwise.

Inequality(Matrix2D, Matrix2D)

check if two matrices are inequal

Declaration

public static bool operator !=(Matrix2D lm, Matrix2D rm)

Parameters

Type	Name	Description
Matrix2D	lm	left matrix
Matrix2D	rm	right matrix

Returns

Type	Description
System.Boolean	true, if both matrices are not equal, false, otherwise.

Multiply(Matrix2D, Matrix2D)

multiply two matrices

Declaration

public static Matrix2D operator *(Matrix2D lm, Matrix2D rm)

Parameters

Type	Name	Description
Matrix2D	lm	left matrix
Matrix2D	rm	right matrix

Returns

Type	Description
Matrix2D	multiplication result matrix

Implements

System.IDisposable