com.itextpdf.kernel.geom

Class Matrix

java.lang.Object

com.itextpdf.kernel.geom.Matrix

public class Matrix
extends Object

Keeps all the values of a 3 by 3 matrix and allows you to do some math with matrices.

Transformation matrix in PDF is a special case of a 3 by 3 matrix
[a b 0]
[c d 0]
[e f 1]

In its most general form, this matrix is specified by six numbers, usually in the form of an array containing six elements [a b c d e f]. It can represent any linear transformation from one coordinate system to another. Here the most common transformations:

• Translations shall be specified as [1 0 0 1 Tx Ty], where Tx and Ty shall be the distances to translate the origin of the coordinate system in the horizontal and vertical dimensions, respectively.
• Scaling shall be 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 shall be produced by [Rc Rs -Rs Rc 0 0], where Rc = cos(q) and Rs = sin(q) which has the effect of rotating the coordinate system axes by an angle q counterclockwise.
• Skew shall be specified by [1 Wx Wy 1 0 0], where Wx = tan(a) and Wy = tan(b) which skews the x-axis by an angle a and the y-axis by an angle b.

For more information see PDF Specification ISO 32000-1 section 8.3.

Field Summary

Fields

Modifier and Type	Field and Description
static int	I11 The row=1, col=1 position ('a') in the matrix.
static int	I12 The row=1, col=2 position ('b') in the matrix.
static int	I13 The row=1, col=3 position (always 0 for 2D) in the matrix.
static int	I21 The row=2, col=1 position ('c') in the matrix.
static int	I22 The row=2, col=2 position ('d') in the matrix.
static int	I23 The row=2, col=3 position (always 0 for 2D) in the matrix.
static int	I31 The row=3, col=1 ('e', or X translation) position in the matrix.
static int	I32 The row=3, col=2 ('f', or Y translation) position in the matrix.
static int	I33 The row=3, col=3 position (always 1 for 2D) in the matrix.

Constructor Summary

Constructors

Constructor and Description
Matrix() Constructs a new Matrix with identity.
Matrix(float tx, float ty) Constructs a matrix that represents translation.
Matrix(float a, float b, float c, float d, float e, float f) Creates a Matrix with 6 specified entries.
Matrix(float e11, float e12, float e13, float e21, float e22, float e23, float e31, float e32, float e33) Creates a Matrix with 9 specified entries.

Method Summary

Modifier and Type	Method and Description
Matrix	add(Matrix arg) Adds a matrix from this matrix and returns the results.
boolean	equals(Object obj) Checks equality of matrices.
float	get(int index) Gets a specific value inside the matrix.
float	getDeterminant() Computes the determinant of the matrix.
int	hashCode() Generates a hash code for this object.
Matrix	multiply(Matrix by) multiplies this matrix by 'b' and returns the result.
Matrix	subtract(Matrix arg) Subtracts a matrix from this matrix and returns the results.
String	toString() Generates a String representation of the matrix.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

I11

public static final int I11

The row=1, col=1 position ('a') in the matrix.

See Also:

Constant Field Values

I12

public static final int I12

The row=1, col=2 position ('b') in the matrix.

See Also:

Constant Field Values

I13

public static final int I13

The row=1, col=3 position (always 0 for 2D) in the matrix.

See Also:

Constant Field Values

I21

public static final int I21

The row=2, col=1 position ('c') in the matrix.

See Also:

Constant Field Values

I22

public static final int I22

The row=2, col=2 position ('d') in the matrix.

See Also:

Constant Field Values

I23

public static final int I23

The row=2, col=3 position (always 0 for 2D) in the matrix.

See Also:

Constant Field Values

I31

public static final int I31

The row=3, col=1 ('e', or X translation) position in the matrix.

See Also:

Constant Field Values

I32

public static final int I32

The row=3, col=2 ('f', or Y translation) position in the matrix.

See Also:

Constant Field Values

I33

public static final int I33

The row=3, col=3 position (always 1 for 2D) in the matrix.

See Also:

Constant Field Values

Constructor Detail

Matrix

public Matrix()

Constructs a new Matrix with identity.

Matrix

public Matrix(float tx,
              float ty)

Constructs a matrix that represents translation.

Parameters:

tx - x-axis translation

ty - y-axis translation

Matrix

public Matrix(float e11,
              float e12,
              float e13,
              float e21,
              float e22,
              float e23,
              float e31,
              float e32,
              float e33)

Creates a Matrix with 9 specified entries.

Parameters:

e11 - element at position (1,1)

e12 - element at position (1,2)

e13 - element at position (1,3)

e21 - element at position (2,1)

e22 - element at position (2,2)

e23 - element at position (2,3)

e31 - element at position (3,1)

e32 - element at position (3,2)

e33 - element at position (3,3)

Matrix

public Matrix(float a,
              float b,
              float c,
              float d,
              float e,
              float f)

Creates a Matrix with 6 specified entries. The third column will always be [0 0 1] (row, column)

Parameters:

a - element at (1,1)

b - element at (1,2)

c - element at (2,1)

d - element at (2,2)

e - element at (3,1)

f - element at (3,2)

Method Detail

get

public float get(int index)

Gets a specific value inside the matrix.

For reference, the indeces are as follows:
I11 I12 I13
I21 I22 I23
I31 I32 I33

Parameters:

index - an array index corresponding with a value inside the matrix

Returns:

the value at that specific position.

multiply

public Matrix multiply(Matrix by)

multiplies this matrix by 'b' and returns the result. See Matrix_multiplication

Parameters:

by - The matrix to multiply by

Returns:

the resulting matrix

add

public Matrix add(Matrix arg)

Adds a matrix from this matrix and returns the results.

Parameters:

arg - the matrix to subtract from this matrix

Returns:

a Matrix object

subtract

public Matrix subtract(Matrix arg)

Subtracts a matrix from this matrix and returns the results.

Parameters:

arg - the matrix to subtract from this matrix

Returns:

a Matrix object

getDeterminant

public float getDeterminant()

Computes the determinant of the matrix.

Returns:

the determinant of the matrix

equals

public boolean equals(Object obj)

Checks equality of matrices.

Overrides:

equals in class Object

Parameters:

obj - the other Matrix that needs to be compared with this matrix.

Returns:

true if both matrices are equal

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Generates a hash code for this object.

Overrides:

hashCode in class Object

Returns:

the hash code of this object

See Also:

Object.hashCode()

toString

public String toString()

Generates a String representation of the matrix.

Overrides:

toString in class Object

Returns:

the values, delimited with tabs and newlines.

See Also:

Object.toString()