Having access to low level layers doesn't necessarily give more possibilities, particularly in the field of graphics, which is more about abstract notions (geometry, algorithms) than hardware access.
Beside, when needed, Java can use C/C++ libraries, via JNI or JNA to access said hardware: that's how we can use OpenGL, graphics tablets, etc.
I have no experience in the field, but in the Exhibition section, you can see people doing wonders in OpenGL by accessing it directly (rather than via the simplified interface offered by Processing).

If you search Matlab on the forum, I am pretty sure you will find some libraries and/or code too.

"I have the impression that it is going to require quite a bit of hardwork to code graphical output algorithms"
Yes, but that's what Processing is about: to do this hard work for you (eg. drawing Bézier curves), to simplify usage of graphics.
Of course, you will find similar graphics libraries in C++ as well (people often mention OpenFrameworks).

"don't large Java applets tend to be a little slow?"
Java fans claim that Java can be as fast as C++ (once the Jit compiler kicked in) or even faster! At least on carefully designed programs that doesn't make lot of garbage to collect...

Note: if you aim at making applets (running in the browser), Processing is the way to go...

If you meant applets as "small programs" and don't care about running in browsers, Processing has still has an advantage over C++: it is highly portable, you can download a compiled sketch (Processing program) and run it whatever your platform (Mac, Linux, Windows...), while you must compile a C++ program on your computer to make it work. Or distribute lot of binaries. Or at least one for Windows, where compilers are not available out of the box, unlike Unix systems.

Lastly, I would say you wouldn't loose time by learning Processing: the base concepts are quite universal in graphics programming, it is easy and fun to learn, with fast feedback loop (code, click Run and see the result: the save & compile phase is hidden).
And it has a helpful forum!
If really you hit a performance bottleneck (once eliminated newbies' errors like loading a file on each frame...), you might switch to C++, but what you have learned won't be lost.