AffineTransform : Java Glossary

AffineTransform

java.awt.geom.AffineTransform is a class that represents a PostScript-like co-ordinate transformation i.e. a 3 × 3 matrix multiplication. It lets you rotate around an anchor point, translate the axes and shear (change the x and y scaling). Using negative scale factors, you can flip (reflect around the x or y axis). The transform converts an x,y co-ordinate to a new x',y' co-ordinate.

[ x']   [  m00  m01  m02  ] [ x ]   [ m00 * x + m01 * y + m02 ]
[ y'] = [  m10  m11  m12  ] [ y ] = [ m10 * x + m11 * y + m12 ]
[ 1 ]   [   0    0    1   ] [ 1 ]   [               1         ]

Though AffineTransform is often associated with drawing, it is not tied in any way to the Graphics class. It is purely mathematical.

Tips	Rotating Images
Manual Use	Learning More
Drawing	Links
Mouse Co-ordinates

Tips

Watch out: rotate is cumulative but setToRotation is not. Don’t forget to call Graphics2.setTransform after every change to your AffineTransform. It pays to learn how to use Graphics2D and AffineTransform. It is much simpler to draw something simple on a simple grid and transform it than it is to compute all the transformed points on the natural grid yourself. Angles are in radians are points are in the current transformed user co-ordinate system. Best to just experiment drawing lines on a Canvas till you get the hang of it before tackling your real project.

Graphics.drawImage will do a simple scale for you, often inadvertently. You don’t need an AffineTransform for that.

Manual Use of AffineTransform

The basic idea is this. A transform maps every point x,y onto a new point, by a combination of rotation, scaling, translation and mirroring. You can manually transform a point like this:

Drawing with AffineTransform

You can also simply plug an AffineTransform into your Graphics2D object. Then you can specify simple co-ordinates and the drawing will appear in transformed co-ordinates. Note that with Graphics2D, your co-ordinates are doubles not ints.

Correcting Mouse Co-ordinates

The catch is, the mouse knows nothing about your transforms. You need to convert mouse screen co-ordinates to your user-co-ordinates. This is the inverse of what you normally do, namely converting convenient user co-ordinates to pixel display co-ordinates. For this, you need the inverse of your transform.

You can learn more with a Google search.

Rotating Images

Rotating Images is a tad trickier than you might expect. The code snippet below will show you how it is done.

The tricks:

AffineTransform has no flip method to turn an Image upside down. Use scale( 1.0, -1.0 ) instead.
AffineTransform has no mirror method to reverse an image left to right. Use scale( -1.0, 1.0 ) instead.
If you are rotating by multiples of 90 degrees, you will get faster and more accurate results if you use quadrantRotate().
If you scale or rotate, the Image will spin around the upper left corner of the Image and disappear off the screen. You must first move the origin to the center of the image, do your rotation, then move it back.
Try writing yourself a training program that just draws coloured rectangles. Experiment with various combinations of transforms until you see the effects, stage by stage.

Rotating is trickier than you might suppose. Run this program and follow through the steps to make sure you can follow what happens at each stage.

Learning More

Sun’s JDK Technote Guide on 2D : available:

on the web at java.sun.com
in the current JDK 1.6.0_17 on your local Windows J: drive.

Sun’s Javadoc on AffineTransform class : available:

on the web at java.sun.com
in the current JDK 1.6.0_17 or in the old JDK 1.5.0_22 on your local Windows J: drive.

Sun’s Javadoc on Graphics2D class : available:

on the web at java.sun.com
in the current JDK 1.6.0_17 or in the old JDK 1.5.0_22 on your local Windows J: drive.

co-ordinates
Graphics object
Java 2D
point
resolution

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