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TideSDK is capable of extension with modules that can be compiled and included in its runtime. It was written to be extended but I would recommend waiting for TideKit. TideSDK is a bit old and setting up a toolchain could be problematic at this point.
We’ve been investing in a broader vision with TideKit that is getting ready for release. You will be able to extend it with native modules and you won’t need to wait too much longer to see what we’ve been up to. http://youtu.be/aE7gN-d0GhUthat
If you have started anything with TideSDK, you will be able to migrate your code easily to TideKit. The ability to work with with native or JavaScript modularity, and to develop for all screens from a single project code base is where all our efforts have been going.
Note that AppJS was discontinued earlier this year. An alternative is writing C extensions in node through node-webkit. Note that if you are going cross platform on this and you needed OSX as well, you cannot achieve Apple AppStore compliance with node-webkit due to private APIs as a result of its port of webkit.