Software to draw on the trackpad I am asking about a software to draw figures and diagrams using the trackpad. I am already aware of Inklet, which works only in conjunction with other software like photoshop. I need another free stand-alone software that does not need other programs pre-installed.
Notability is pretty optimized for the trackpad. Works well if you have an iPad stylus and use it on the trackpad too. Not to mention, iCloud sync and iOS apps to go along with it. Check it out if you haven't had a chance.

If that's not what you're looking for, then maybe Pixelmator is more your cup of tea. It is fully optimized for the Mac as well.

To be honest, when you say "fully optimized for the trackpad," I think you'll find that there isn't much for that. The trackpad is great for a lot of things, but it certainly ain't no Wacom Bamboo tablet. In other words, it may be necessary to understand that the trackpad isn't specifically built for "drawing objects and shapes," although a Wacom tablet is. The programs listed above will certainly get you the desired results without much trouble.

One other thought... If you have an iPad, there are a slew of apps that will allow you to use your iPad as a mouse or a pseudo-trackpad. It may be worth while stopping by your local electronics store, picking up a $10 stylus for an iPad, and using that for drawing instead of the trackpad itself. One example of these apps is Rowmote. I've used it myself for a few years and love it.

Hope all this helps!