How do I slide smoothly object

I want to make object with 8direction slide smoothly on solid object (walls). I have no idea how to get started with this.

I mean, when object moves onto obstacle, that is not set in angle 90* to him, i want him to move to the most possible way.

Here's one way that works good.

That is some awesome kind of math magic, but i like it because it works. Amazing job, it looks great after some tweaks.