Not sure. Processing is OpenGL meaning that if you use code from this project, you have to make your project GPL too.
But since you seem to rewrite it in C++, it would mean you copy only the API, like they did with ProcessingJS. So I don't know what rules apply here (copyright?).
The best is to contact directly Ben Fry and Casey Reas.

Note: this seems a bit redundant with OpenFrameworks, from what I understood of this software (never tried it). Except perhaps the API would be familiar to Processing users.
I wonder if you really will get a big speed gain...

I will be starting with the canvas soon, but I am unsure if I must focus on OpenGL (every platform) or DirectX (Windows only).

Windows only?! Processing is focused on art programming.
And there are lotsa artists which own Mac machines.
And I'm using Linux now! 

Thank you. I did not know about OpenFrameworks. This is what i was looking for.
I will soon showing some benchmarks to show if C++ is faster/slower.

Thanks, Dippo.

Indeed, http://www.openframeworks.cc/ seems to make a Processing conversion to C++
a little too much redundant!
Moreover, I don't think many Processing folks would abandon garbage collector,
an easy class constructor and start using pointers.

However, if you wanna do that anyways, I've got some alternative ideas.
Rather than using C++ as Open Frameworks got already, why not an unknown gem called D?
Below some references for D language:

http://dlang.org/
http://www.prowiki.org/upload/duser/spec_DMD_1.00.pdf
http://www.informit.com/articles/article.aspx?p=1381876

I still dunno much about it myself. But as far as I've seen, D can be considered 2/3 C++ and 1/3 Java.

C/C++'s similarities:

•     compiles directly to machine code
•     statically typed
•     got main() starting function
•     got pointer variables
•     pass arguments as reference
•     etc.

   
Java's similarities:

•     classes follows single inheritance
•     its class' syntax is almost copycat
•     got garbage collector
•     non-primitive variables are implicit pointers to objects
•     etc.

You could even follow Processing's JS Mode strategy.
Programs can be written in Java. Then a pre-compiler transforms it into a valid D source code.
If a tab is created w/ .d suffix, it is to be interpreted as a raw D code.

Real stumble block is to find an OpenGL framework library in D.
Dunno much; but I believe the most famous libraries are available in D already.

That is so b/c a C++ code uses a very different syntax for classes. And got multi-inheritance too.
On the other hand, most simple C programs can be copy/pasted and be compiled in D.

Well, take a look and tell us what you think about it! 

Yes, i looked into D lang earlier, but decided to not use it because i use 2 websites (stackoverflow & codereview) to get very optimized code. There are not so many people that use the D language on these 2 websites. So if i would get a (simple) problem, then the change is high that i would get stuck because there are not so many followers.
The problem with C++ is that you program on a pile of sand and you put more sand on it. While in Java you build a house, where you begin with the basement and work you way up. There is no line that goes in between these two.

Therefore i was thinking to create my own virtual machine, but this is slow. Look at Java.
Or, create a converter that reads Java Processing code and converts it into C++ code.
Both are complex and does not make it easier for the user if a error occurs. :(

But i do think that D has the potential to become the follow-up for C/C++. If only it has more followers. Unless you can convince me differently. :)

Since a few days i am using SFML (simple and fast media library) with C++, and i must say that it has lots of potential. There are allot of tutorial video's on YouTube about SFML. Please check http://www.youtube.com/watch?v=kAbkFY6lwAY
and skip the first 4 minutes.

Greetings, Dippo.

While we are on suggesting new languages compiling to native binary code: rather than D, not bad but as said not so much used and a bit old already, why not try Google Go? Modern syntax, garbage collected, fast, lot of people use it already, etc.

PhiLho:

While we are on suggesting new languages compiling to native binary code: rather than D...,  why not try Google's Go?

GoToLoop:

Programs can be written in Java. Then a pre-compiler transforms it into a valid D source code.

B/c Java can't be converted into Go w/o some colossal amount of effort. I think it's almost impossible!
So a Processing's Go Mode wouldn't be on par as Java & JavaScript modes are.
And even though there are more folks who code in Go than D,
there are much more coding in Python, Ruby, CoffeeScript, etc.
And we already got Processing implementations for those languages, and they're not used much!

My point isn't about having people programming in Processing + D.
(They would be able to do so by creating a .d prefix named tab).
Rather by sticking in Processing + Java, but having that code compiled directly
into machine code using a more specialized system language for it!

I daresay that converting Processing + Java to D would be much easier than to JavaScript we got! 

El_Dippo:

Since a few days I am using SFML (simple and fast media library) with C++...

There are SFML bindings for many other languages, including D and Java:
http://www.sfml-dev.org/download/bindings.php
https://github.com/Jebbs/DSFML
https://github.com/aldacron/Derelict3/

There's also a translator from Java to D:
http://languagemachine.sourceforge.net/j2d.html

Although I think a more manual approach would be better.