Matrix2D Class

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')

Examples

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.

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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.

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...
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)

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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.

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

Inheritance Hierarchy

SystemObject
pdftron.CommonMatrix2D

Namespace: pdftron.Common
Assembly: pdftron (in pdftron.dll) Version: 255.255.255.255

Syntax

C++

JavaScript

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public sealed class Matrix2D : IClosable

Public NotInheritable Class Matrix2D
	Implements IClosable

public ref class Matrix2D sealed : IClosable

pdftron.Common.Matrix2D = function();

Type.createClass(
	'pdftron.Common.Matrix2D',
	null,
	Windows.Foundation.IClosable);

The Matrix2D type exposes the following members.

Constructors

	Name	Description
	Matrix2D	Creates an identity matrix
	Matrix2D(Matrix2D)	Creates a matrix and initialize it with values from another matrix.
	Matrix2D(Double, Double, Double, Double, Double, Double)	Creates a Matrix object based on six numbers that define an affine transformation.

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Properties

	Name	Description
	m_a	The matrix element in the first row, first column.
	m_b	The matrix element in the first row, second column
	m_c	The matrix element in the second row, first column
	m_d	The matrix element in the second row, second column.
	m_h	The matrix element in the third row, first column.
	m_v	The matrix element in the third row, second column.

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Methods

	Name	Description
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	Concat	Updates this matrix with the product of itself and another matrix specified through an argument list.
	Equals	Determines whether the specified Object is equal to the current Object. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	IdentityMatrix	Creates an identity matrix. {1 0 0 1 0 0}.
	Inverse	If this matrix is invertible, the Inverse method returns its inverse matrix.
	Mult(DoubleRef, DoubleRef)	Transform/multiply the point (in_out_x, in_out_y) using this matrix.
	Mult(Matrix2D, Matrix2D)	Multiply two matrices.
	RotationMatrix	Creates a rotation matrix.
	Scale	The Scale method updates this matrix with the product of itself and a scaling matrix. (i.e. it is equivalent to this.m_a = h; this.m_d = v).
	Set(Matrix2D)	Sets value to given matrix.
	Set(Double, Double, Double, Double, Double, Double)	Sets the elements of this matrix.
	ToString	Returns a string that represents the current object. (Inherited from Object.)
	Translate	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).
	ZeroMatrix	Creates a zero matrix (0 0 0 0 0 0).

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Reference

pdftron.Common Namespace