Matrix.java
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package com.itextpdf.kernel.geom;
import java.util.Arrays;
/**
* Keeps all the values of a 3 by 3 matrix and allows you to do some math with matrices.
*
* <p>
* Transformation matrix in PDF is a special case of a 3 by 3 matrix
* <br>{@code [a b 0]}
* <br>{@code [c d 0]}
* <br>{@code [e f 1]}
*
* <p>
* In its most general form, this matrix is specified by six numbers, usually in the form of an array containing six
* elements {@code [a b c d e f]}. It can represent any linear transformation from one coordinate system to
* another. Here the most common transformations:
* <ul>
* <li>Translations shall be specified as {@code [1 0 0 1 Tx Ty]}, where {@code Tx} and {@code Ty} shall be the
* distances to translate the origin of the coordinate system in the horizontal and vertical dimensions, respectively.
* <li>Scaling shall be obtained by {@code [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 {@code Sx} and {@code Sy} units,
* respectively, in the previous coordinate system.
* <li>Rotations shall be produced by {@code [Rc Rs -Rs Rc 0 0]}, where {@code Rc = cos(q)} and {@code Rs = sin(q)}
* which has the effect of rotating the coordinate system axes by an angle {@code q} counterclockwise.
* <li>Skew shall be specified by {@code [1 Wx Wy 1 0 0]}, where {@code Wx = tan(a)} and {@code Wy = tan(b)} which
* skews the x-axis by an angle {@code a} and the y-axis by an angle {@code b}.
* </ul>
*
* <p>
* For more information see PDF Specification ISO 32000-1 section 8.3.
*/
public class Matrix {
/** The row=1, col=1 position ('a') in the matrix. */
public static final int I11 = 0;
/** The row=1, col=2 position ('b') in the matrix. */
public static final int I12 = 1;
/** The row=1, col=3 position (always 0 for 2D) in the matrix. */
public static final int I13 = 2;
/** The row=2, col=1 position ('c') in the matrix. */
public static final int I21 = 3;
/** The row=2, col=2 position ('d') in the matrix. */
public static final int I22 = 4;
/** The row=2, col=3 position (always 0 for 2D) in the matrix. */
public static final int I23 = 5;
/** The row=3, col=1 ('e', or X translation) position in the matrix. */
public static final int I31 = 6;
/** The row=3, col=2 ('f', or Y translation) position in the matrix. */
public static final int I32 = 7;
/** The row=3, col=3 position (always 1 for 2D) in the matrix. */
public static final int I33 = 8;
/**
* The values inside the matrix (the identity matrix by default).
*
* <p>
* For reference, the indexes are as follows:
* <br>I11 I12 I13
* <br>I21 I22 I23
* <br>I31 I32 I33
*/
private final float[] vals = new float[]{
1,0,0,
0,1,0,
0,0,1
};
/**
* Constructs a new Matrix with identity.
*/
public Matrix() {
}
/**
* Constructs a matrix that represents translation.
*
* @param tx x-axis translation
* @param ty y-axis translation
*/
public Matrix(float tx, float ty) {
vals[I31] = tx;
vals[I32] = ty;
}
/**
* Creates a Matrix with 9 specified entries.
*
* @param e11 element at position (1,1)
* @param e12 element at position (1,2)
* @param e13 element at position (1,3)
* @param e21 element at position (2,1)
* @param e22 element at position (2,2)
* @param e23 element at position (2,3)
* @param e31 element at position (3,1)
* @param e32 element at position (3,2)
* @param e33 element at position (3,3)
*/
public Matrix(float e11, float e12, float e13, float e21, float e22, float e23, float e31, float e32, float e33){
vals[I11] = e11;
vals[I12] = e12;
vals[I13] = e13;
vals[I21] = e21;
vals[I22] = e22;
vals[I23] = e23;
vals[I31] = e31;
vals[I32] = e32;
vals[I33] = e33;
}
/**
* Creates a Matrix with 6 specified entries.
* The third column will always be [0 0 1]
* (row, column)
*
* @param a element at (1,1)
* @param b element at (1,2)
* @param c element at (2,1)
* @param d element at (2,2)
* @param e element at (3,1)
* @param f element at (3,2)
*/
public Matrix(float a, float b, float c, float d, float e, float f){
vals[I11] = a;
vals[I12] = b;
vals[I13] = 0;
vals[I21] = c;
vals[I22] = d;
vals[I23] = 0;
vals[I31] = e;
vals[I32] = f;
vals[I33] = 1;
}
/**
* Gets a specific value inside the matrix.
*
* <p>
* For reference, the indeces are as follows:
* <br>I11 I12 I13
* <br>I21 I22 I23
* <br>I31 I32 I33
*
* @param index an array index corresponding with a value inside the matrix
* @return the value at that specific position.
*/
public float get(int index){
return vals[index];
}
/**
* multiplies this matrix by 'b' and returns the result.
* See <a href="http://en.wikipedia.org/wiki/Matrix_multiplication">Matrix_multiplication</a>
*
* @param by The matrix to multiply by
* @return the resulting matrix
*/
public Matrix multiply(Matrix by){
Matrix rslt = new Matrix();
float[] a = vals;
float[] b = by.vals;
float[] c = rslt.vals;
c[I11] = a[I11]*b[I11] + a[I12]*b[I21] + a[I13]*b[I31];
c[I12] = a[I11]*b[I12] + a[I12]*b[I22] + a[I13]*b[I32];
c[I13] = a[I11]*b[I13] + a[I12]*b[I23] + a[I13]*b[I33];
c[I21] = a[I21]*b[I11] + a[I22]*b[I21] + a[I23]*b[I31];
c[I22] = a[I21]*b[I12] + a[I22]*b[I22] + a[I23]*b[I32];
c[I23] = a[I21]*b[I13] + a[I22]*b[I23] + a[I23]*b[I33];
c[I31] = a[I31]*b[I11] + a[I32]*b[I21] + a[I33]*b[I31];
c[I32] = a[I31]*b[I12] + a[I32]*b[I22] + a[I33]*b[I32];
c[I33] = a[I31]*b[I13] + a[I32]*b[I23] + a[I33]*b[I33];
return rslt;
}
/**
* Adds a matrix from this matrix and returns the results.
*
* @param arg the matrix to subtract from this matrix
* @return a Matrix object
*/
public Matrix add(Matrix arg){
Matrix rslt = new Matrix();
float[] a = vals;
float[] b = arg.vals;
float[] c = rslt.vals;
c[I11] = a[I11]+b[I11];
c[I12] = a[I12]+b[I12];
c[I13] = a[I13]+b[I13];
c[I21] = a[I21]+b[I21];
c[I22] = a[I22]+b[I22];
c[I23] = a[I23]+b[I23];
c[I31] = a[I31]+b[I31];
c[I32] = a[I32]+b[I32];
c[I33] = a[I33]+b[I33];
return rslt;
}
/**
* Subtracts a matrix from this matrix and returns the results.
*
* @param arg the matrix to subtract from this matrix
* @return a Matrix object
*/
public Matrix subtract(Matrix arg){
Matrix rslt = new Matrix();
float[] a = vals;
float[] b = arg.vals;
float[] c = rslt.vals;
c[I11] = a[I11]-b[I11];
c[I12] = a[I12]-b[I12];
c[I13] = a[I13]-b[I13];
c[I21] = a[I21]-b[I21];
c[I22] = a[I22]-b[I22];
c[I23] = a[I23]-b[I23];
c[I31] = a[I31]-b[I31];
c[I32] = a[I32]-b[I32];
c[I33] = a[I33]-b[I33];
return rslt;
}
/**
* Computes the determinant of the matrix.
*
* @return the determinant of the matrix
*/
public float getDeterminant(){
// ref http://en.wikipedia.org/wiki/Determinant
// note that in PDF, I13 and I23 are always 0 and I33 is always 1
// so this could be simplified/faster
return vals[I11] * vals[I22] * vals[I33]
+ vals[I12] * vals[I23] * vals[I31]
+ vals[I13] * vals[I21] * vals[I32]
- vals[I11] * vals[I23] * vals[I32]
- vals[I12] * vals[I21] * vals[I33]
- vals[I13] * vals[I22] * vals[I31];
}
/**
* Checks equality of matrices.
*
* @param obj the other Matrix that needs to be compared with this matrix.
* @return true if both matrices are equal
* @see java.lang.Object#equals(java.lang.Object)
*/
@Override
public boolean equals(Object obj) {
if (!(obj instanceof Matrix))
return false;
return Arrays.equals(vals, ((Matrix) obj).vals);
}
/**
* Generates a hash code for this object.
*
* @return the hash code of this object
* @see java.lang.Object#hashCode()
*/
@Override
public int hashCode() {
return Arrays.hashCode(vals);
}
/**
* Generates a String representation of the matrix.
*
* @return the values, delimited with tabs and newlines.
* @see java.lang.Object#toString()
*/
@Override
public String toString() {
return vals[I11] + "\t" + vals[I12] + "\t" + vals[I13] + "\n" +
vals[I21] + "\t" + vals[I22] + "\t" + vals[I23] + "\n" +
vals[I31] + "\t" + vals[I32] + "\t" + vals[I33];
}
}