http://stackoverflow.com/questions/817216/is-directx-on-java-possiblehttps://stackoverflow.com/questions/817216/is-directx-on-java-possible
Unless Notch uses JNI, he's not using DirectX. Considering that a lot of JNI code is not portable, and especially since DirectX doesn't exist on Linux and Mac without a lot of work, I'm fairly confident that your don't have to worry about it being your problem. You should be looking more towards OpenGL (if Minecraft uses OpenGL) or your Java Runtime Environment. Type java -version
into a command window to show the version info. They are much more likely to be the culprit.