AffineTransform : Java Glossary

[ 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         ]

Tips

• Watch out: setToRotation is not cumulative. Graphics2.setTransform replaces the transform. It does not append the transform to the existing transforms.
• 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
• Points are in the current transformed user coordinate 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 coordinates and the drawing will appear in transformed coordinates. Note that with Graphics2D, your coordinates are doubles not ints.

Correcting Mouse Co-ordinates

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

You can learn more with a Google search.

Rotating Images

• 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.
• the Y axis grows down. This in confusing if you are familiar with Cartesian coordinates that mathematics uses.
• 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 spot you want to rotate around, the image, do your rotation, then move the origin to some more suitable location. You will need some translation before the rotation, after or both. The corrections you need to move the origin after the rotate cause brain ache. It is not immediately obvious whether you want negative or positive translations and whether you should apply them in the x or y direction. Any error results in a blank image. If you want to solve the problem by brute force, you can try all 32 combinations of rotation direction, positive or negative correction and whether you apply in the x or y direction. And that does not even count the magnitude of the correction. Imagine you had a little X made of wire with x and y axes labelled that you could plop down over drawing at the origin. Imagine spinning the X in clockwise or counter-clockwise direction. Then make your origin correction in terms of the directions on the arms of the spinned X rather than in terms of the final image. Making such an X out of a paper clip and with coloured tip made with a Sharpie, that you place over your paper drawings will help immensely to grok the notion of rotating the axes.
• A positive translate moves the origin right and down. Think of translate as moving the origin, not moving objects.
• A positive rotate() rotates the clockwise around the origin, and negative counter clockwise. quadrantRotate() measures in 90 degree increments. rotate() measures in radians.
• Try writing yourself a training program that just draws coloured asymmetrical shapes. Experiment with various combinations of transforms until you see the effects, stage by stage.
• When you finally get around to drawing something in your virtual coordinate system, logically the various transforms are computed starting with the most recently applied working back to the device coordinate system.
• Beware of transform(). It applies transforms out of order.

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