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

  • Constructor Summary

    Constructors
    Constructor
    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
    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 Details

    • I11

      public static final int I11
      The row=1, col=1 position ('a') in the matrix.
      See Also:

    • I12

      public static final int I12
      The row=1, col=2 position ('b') in the matrix.
      See Also:

    • I13

      public static final int I13
      The row=1, col=3 position (always 0 for 2D) in the matrix.
      See Also:

    • I21

      public static final int I21
      The row=2, col=1 position ('c') in the matrix.
      See Also:

    • I22

      public static final int I22
      The row=2, col=2 position ('d') in the matrix.
      See Also:

    • I23

      public static final int I23
      The row=2, col=3 position (always 0 for 2D) in the matrix.
      See Also:

    • I31

      public static final int I31
      The row=3, col=1 ('e', or X translation) position in the matrix.
      See Also:

    • I32

      public static final int I32
      The row=3, col=2 ('f', or Y translation) position in the matrix.
      See Also:

    • I33

      public static final int I33
      The row=3, col=3 position (always 1 for 2D) in the matrix.
      See Also:

  • Constructor Details

    • 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 Details

    • 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:

    • 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:

    • 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: