Matrix.java
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.pdfbox.util;
import org.apache.pdfbox.cos.COSArray;
import org.apache.pdfbox.cos.COSFloat;
import org.apache.pdfbox.cos.COSNumber;
import java.awt.geom.AffineTransform;
import java.awt.geom.Point2D;
import java.util.Arrays;
import org.apache.pdfbox.cos.COSBase;
/**
* This class will be used for matrix manipulation.
*
* @author Ben Litchfield
*/
public final class Matrix implements Cloneable
{
public static final int SIZE = 9;
private float[] single;
/**
* Constructor. This produces an identity matrix.
*/
public Matrix()
{
// a b 0
// c d 0
// tx ty 1
// note: hx and hy are reversed vs.the PDF spec as we use AffineTransform's definition x and y shear
// sx hy 0
// hx sy 0
// tx ty 1
single = new float[] { 1, 0, 0, 0, 1, 0, 0, 0, 1 };
}
/**
* Constructor. This produces a matrix with the given array as data.
* The source array is not copied or cloned.
*/
private Matrix(float[] src)
{
single = src;
}
/**
* Creates a matrix from a 6-element (a b c d e f) COS array.
*
* @param array source array, elements must be or extend COSNumber
*/
private Matrix(COSArray array)
{
single = new float[SIZE];
single[0] = ((COSNumber)array.getObject(0)).floatValue();
single[1] = ((COSNumber)array.getObject(1)).floatValue();
single[3] = ((COSNumber)array.getObject(2)).floatValue();
single[4] = ((COSNumber)array.getObject(3)).floatValue();
single[6] = ((COSNumber)array.getObject(4)).floatValue();
single[7] = ((COSNumber)array.getObject(5)).floatValue();
single[8] = 1;
}
/**
* Creates a transformation matrix with the given 6 elements. Transformation matrices are
* discussed in 8.3.3, "Common Transformations" and 8.3.4, "Transformation Matrices" of the PDF
* specification. For simple purposes (rotate, scale, translate) it is recommended to use the
* static methods below.
*
* Produces the following matrix:
* a b 0
* c d 0
* e f 1
*
* @see Matrix#getRotateInstance(double, float, float)
* @see Matrix#getScaleInstance(float, float)
* @see Matrix#getTranslateInstance(float, float)
*
* @param a the X coordinate scaling element (m00) of the 3x3 matrix
* @param b the Y coordinate shearing element (m10) of the 3x3 matrix
* @param c the X coordinate shearing element (m01) of the 3x3 matrix
* @param d the Y coordinate scaling element (m11) of the 3x3 matrix
* @param e the X coordinate translation element (m02) of the 3x3 matrix
* @param f the Y coordinate translation element (m12) of the 3x3 matrix
*/
public Matrix(float a, float b, float c, float d, float e, float f)
{
single = new float[SIZE];
single[0] = a;
single[1] = b;
single[3] = c;
single[4] = d;
single[6] = e;
single[7] = f;
single[8] = 1;
}
/**
* Creates a matrix with the same elements as the given AffineTransform.
* @param at matrix elements will be initialize with the values from this affine transformation, as follows:
*
* scaleX shearY 0
* shearX scaleY 0
* transX transY 1
*
*/
public Matrix(AffineTransform at)
{
single = new float[SIZE];
single[0] = (float)at.getScaleX();
single[1] = (float)at.getShearY();
single[3] = (float)at.getShearX();
single[4] = (float)at.getScaleY();
single[6] = (float)at.getTranslateX();
single[7] = (float)at.getTranslateY();
single[8] = 1;
}
/**
* Convenience method to be used when creating a matrix from unverified data. If the parameter
* is a COSArray with at least six numbers, a Matrix object is created from the first six
* numbers and returned. If not, then the identity Matrix is returned.
*
* @param base a COS object, preferably a COSArray with six numbers.
*
* @return a Matrix object.
*/
public static Matrix createMatrix(COSBase base)
{
if (!(base instanceof COSArray))
{
return new Matrix();
}
COSArray array = (COSArray) base;
if (array.size() < 6)
{
return new Matrix();
}
for (int i = 0; i < 6; ++i)
{
if (!(array.getObject(i) instanceof COSNumber))
{
return new Matrix();
}
}
return new Matrix(array);
}
/**
* Create an affine transform from this matrix's values.
*
* @return An affine transform with this matrix's values.
*/
public AffineTransform createAffineTransform()
{
return new AffineTransform(
single[0], single[1], // m00 m10 = scaleX shearY
single[3], single[4], // m01 m11 = shearX scaleY
single[6], single[7] ); // m02 m12 = tx ty
}
/**
* This will get a matrix value at some point.
*
* @param row The row to get the value from.
* @param column The column to get the value from.
*
* @return The value at the row/column position.
*/
public float getValue( int row, int column )
{
return single[row*3+column];
}
/**
* This will set a value at a position.
*
* @param row The row to set the value at.
* @param column the column to set the value at.
* @param value The value to set at the position.
*/
public void setValue( int row, int column, float value )
{
single[row*3+column] = value;
}
/**
* Return a single dimension array of all values in the matrix.
*
* @return The values of this matrix.
*/
public float[][] getValues()
{
float[][] retval = new float[3][3];
retval[0][0] = single[0];
retval[0][1] = single[1];
retval[0][2] = single[2];
retval[1][0] = single[3];
retval[1][1] = single[4];
retval[1][2] = single[5];
retval[2][0] = single[6];
retval[2][1] = single[7];
retval[2][2] = single[8];
return retval;
}
/**
* Concatenates (premultiplies) the given matrix to this matrix.
*
* @param matrix The matrix to concatenate.
*/
public void concatenate(Matrix matrix)
{
single = checkFloatValues(multiplyArrays(matrix.single, single));
}
/**
* Translates this matrix by the given vector.
*
* @param vector 2D vector
*/
public void translate(Vector vector)
{
translate(vector.getX(), vector.getY());
}
/**
* Translates this matrix by the given amount.
*
* @param tx x-translation
* @param ty y-translation
*/
public void translate(float tx, float ty)
{
single[6] += tx * single[0] + ty * single[3];
single[7] += tx * single[1] + ty * single[4];
single[8] += tx * single[2] + ty * single[5];
checkFloatValues(single);
}
/**
* Scales this matrix by the given factors.
*
* @param sx x-scale
* @param sy y-scale
*/
public void scale(float sx, float sy)
{
single[0] *= sx;
single[1] *= sx;
single[2] *= sx;
single[3] *= sy;
single[4] *= sy;
single[5] *= sy;
checkFloatValues(single);
}
/**
* Rotates this matrix by the given factors.
*
* @param theta The angle of rotation measured in radians
*/
public void rotate(double theta)
{
concatenate(Matrix.getRotateInstance(theta, 0, 0));
}
/**
* This method multiplies this Matrix with the specified other Matrix, storing the product in a
* new instance. It is allowed to have (other == this).
*
* @param other the second operand Matrix in the multiplication; required
* @return the product of the two matrices.
*/
public Matrix multiply(Matrix other)
{
return new Matrix(checkFloatValues(multiplyArrays(single, other.single)));
}
private float[] checkFloatValues(float[] values)
{
if (!Float.isFinite(values[0]) || !Float.isFinite(values[1]) || !Float.isFinite(values[2])
|| !Float.isFinite(values[3]) || !Float.isFinite(values[4]) || !Float.isFinite(values[5])
|| !Float.isFinite(values[6]) || !Float.isFinite(values[7]) || !Float.isFinite(values[8]))
throw new IllegalArgumentException("Multiplying two matrices produces illegal values");
return values;
}
private float[] multiplyArrays(float[] a, float[] b)
{
float[] c = new float[SIZE];
c[0] = a[0] * b[0] + a[1] * b[3] + a[2] * b[6];
c[1] = a[0] * b[1] + a[1] * b[4] + a[2] * b[7];
c[2] = a[0] * b[2] + a[1] * b[5] + a[2] * b[8];
c[3] = a[3] * b[0] + a[4] * b[3] + a[5] * b[6];
c[4] = a[3] * b[1] + a[4] * b[4] + a[5] * b[7];
c[5] = a[3] * b[2] + a[4] * b[5] + a[5] * b[8];
c[6] = a[6] * b[0] + a[7] * b[3] + a[8] * b[6];
c[7] = a[6] * b[1] + a[7] * b[4] + a[8] * b[7];
c[8] = a[6] * b[2] + a[7] * b[5] + a[8] * b[8];
return c;
}
/**
* Transforms the given point by this matrix.
*
* @param point point to transform
*/
public void transform(Point2D point)
{
float x = (float)point.getX();
float y = (float)point.getY();
float a = single[0];
float b = single[1];
float c = single[3];
float d = single[4];
float e = single[6];
float f = single[7];
point.setLocation(x * a + y * c + e, x * b + y * d + f);
}
/**
* Transforms the given point by this matrix.
*
* @param x x-coordinate
* @param y y-coordinate
*/
public Point2D.Float transformPoint(float x, float y)
{
float a = single[0];
float b = single[1];
float c = single[3];
float d = single[4];
float e = single[6];
float f = single[7];
return new Point2D.Float(x * a + y * c + e, x * b + y * d + f);
}
/**
* Transforms the given point by this matrix.
*
* @param vector 2D vector
*/
public Vector transform(Vector vector)
{
float a = single[0];
float b = single[1];
float c = single[3];
float d = single[4];
float e = single[6];
float f = single[7];
float x = vector.getX();
float y = vector.getY();
return new Vector(x * a + y * c + e, x * b + y * d + f);
}
/**
* Convenience method to create a scaled instance.
*
* Produces the following matrix:
* x 0 0
* 0 y 0
* 0 0 1
*
* @param x The xscale operator.
* @param y The yscale operator.
* @return A new matrix with just the x/y scaling
*/
public static Matrix getScaleInstance(float x, float y)
{
return new Matrix(x, 0, 0, y, 0, 0);
}
/**
* Convenience method to create a translating instance.
*
* Produces the following matrix:
* 1 0 0
* 0 1 0
* x y 1
*
* @param x The x translating operator.
* @param y The y translating operator.
* @return A new matrix with just the x/y translating.
*/
public static Matrix getTranslateInstance(float x, float y)
{
return new Matrix(1, 0, 0, 1, x, y);
}
/**
* Convenience method to create a rotated instance.
*
* @param theta The angle of rotation measured in radians
* @param tx The x translation.
* @param ty The y translation.
* @return A new matrix with the rotation and the x/y translating.
*/
public static Matrix getRotateInstance(double theta, float tx, float ty)
{
float cosTheta = (float)Math.cos(theta);
float sinTheta = (float)Math.sin(theta);
return new Matrix(cosTheta, sinTheta, -sinTheta, cosTheta, tx, ty);
}
/**
* Produces a copy of the first matrix, with the second matrix concatenated.
*
* @param a The matrix to copy.
* @param b The matrix to concatenate.
*/
public static Matrix concatenate(Matrix a, Matrix b)
{
return b.multiply(a);
}
/**
* Clones this object.
* @return cloned matrix as an object.
*/
@Override
public Matrix clone()
{
return new Matrix(single.clone());
}
/**
* Returns the x-scaling factor of this matrix. This is calculated from the scale and shear.
*
* @return The x-scaling factor.
*/
public float getScalingFactorX()
{
/*
* BM: if the trm is rotated, the calculation is a little more complicated
*
* The rotation matrix multiplied with the scaling matrix is:
* ( x 0 0) ( cos sin 0) ( x*cos x*sin 0)
* ( 0 y 0) * (-sin cos 0) = (-y*sin y*cos 0)
* ( 0 0 1) ( 0 0 1) ( 0 0 1)
*
* So, if you want to deduce x from the matrix you take
* M(0,0) = x*cos and M(0,1) = x*sin and use the theorem of Pythagoras
*
* sqrt(M(0,0)^2+M(0,1)^2) =
* sqrt(x2*cos2+x2*sin2) =
* sqrt(x2*(cos2+sin2)) = <- here is the trick cos2+sin2 is one
* sqrt(x2) =
* abs(x)
*/
if (Float.compare(single[1], 0.0f) != 0)
{
return (float) Math.sqrt(Math.pow(single[0], 2) +
Math.pow(single[1], 2));
}
return single[0];
}
/**
* Returns the y-scaling factor of this matrix. This is calculated from the scale and shear.
*
* @return The y-scaling factor.
*/
public float getScalingFactorY()
{
if (Float.compare(single[3], 0.0f) != 0)
{
return (float) Math.sqrt(Math.pow(single[3], 2) +
Math.pow(single[4], 2));
}
return single[4];
}
/**
* Returns the x-scaling element of this matrix.
*
* @see #getScalingFactorX()
*/
public float getScaleX()
{
return single[0];
}
/**
* Returns the y-shear element of this matrix.
*/
public float getShearY()
{
return single[1];
}
/**
* Returns the x-shear element of this matrix.
*/
public float getShearX()
{
return single[3];
}
/**
* Returns the y-scaling element of this matrix.
*
* @see #getScalingFactorY()
*/
public float getScaleY()
{
return single[4];
}
/**
* Returns the x-translation element of this matrix.
*/
public float getTranslateX()
{
return single[6];
}
/**
* Returns the y-translation element of this matrix.
*/
public float getTranslateY()
{
return single[7];
}
/**
* Returns a COS array which represent the geometric relevant
* components of the matrix. The last column of the matrix is ignored,
* only the first two columns are returned. This is analog to the
* Matrix(COSArray) constructor.
*/
public COSArray toCOSArray()
{
COSArray array = new COSArray();
array.add(new COSFloat(single[0]));
array.add(new COSFloat(single[1]));
array.add(new COSFloat(single[3]));
array.add(new COSFloat(single[4]));
array.add(new COSFloat(single[6]));
array.add(new COSFloat(single[7]));
return array;
}
@Override
public String toString()
{
return "[" +
single[0] + "," +
single[1] + "," +
single[3] + "," +
single[4] + "," +
single[6] + "," +
single[7] + "]";
}
@Override
public int hashCode()
{
return Arrays.hashCode(single);
}
@Override
public boolean equals(Object obj)
{
if (this == obj)
{
return true;
}
if (obj == null)
{
return false;
}
if (getClass() != obj.getClass())
{
return false;
}
return Arrays.equals(this.single, ((Matrix) obj).single);
}
}