The Best Jump Algorithm?

Who's up for a bit of challenge or provide some tips or better code?
I'm having trouble with the math side of doing jumps on the game I'm making.
Can someone please help me out for a while?
My character's jump looks weird, it looks pointy.
There's code here http://codepad.org/SXH4ydz8 where we can start.
There are constraints there.

>>1
Forget it, white people can't jump.

It is np-hard OP, don't bother

>>10
I've seen the original source and they just implemented a basic physics engine: http://en.wikipedia.org/wiki/Standard_Model

The jumping force, air resistance, gravity, etc, just came about naturally as a result.  It's all about emergence bro.