In MonoGame, how would I handle collisions and physics between two non-rectangular Texture2Ds? Obviously, since this is a game, speed is crucial. What are my options?
Here's one such example of algorithms.
http://www.codeproject.com/Articles/15573/D-Polygon-Collision-Detection
There are examples littered all over the web.
Essentially you want to check a BIG space around your object and you don't do more accurate checking until objects are more likely to be colliding with one another.