This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
With JavaFX, you can easily implement the 3 transformer sliders by binding properties of any objects to the slider values. So, to hook up a rectangle to 3 sliders that control angle, scale, and shear you use the transforms property:
Any Node (including UI controls) can be transformed.
You can also provide effects, animation, and manipulate a 2D graphics space.
You can still leverage your Java knowledge, since calling Java APIs is totally transparent.
JavaFX is easy to learn and its declarative style makes code concise and easy to read, as the above example hopefully shows.
I would urge you to check out JavaFX and see if you like it!