GJK collision detection implementation from 2D to 3D

I apologize for the length of this question and give a pre-emptive thanks for anyone who reads through this!

So i've spent the last few days going over the GJK algorithm. I understand the general concepts behind it, and understand the most of the nitty gritties of its implementation in 2D thanks to the wonderful article by William Bittle at http://www.codezealot.org/archives/88 .

I've implemented his pseudo code (found at the end of the article) into my own c++ project, however i want to make a 3D implementation. My weakness comes into using the dot products to test the voronoi regions and the tripleProducts to get perpandicular lines. But im trying to read up more on that.

My problem comes down to the containsOrigin function. I开发者_如何学JAVAm having trouble visualizing and accounting for the new voronoi regions that the z axis adds. I just can't seem to wrap my head around how to determine which regions contains the origin. I assume there is 4 I have to account for, each extending from the triangular planes that the comprise the 4 faces of the tetrahedron simplex. If the origin is not within any of those regions, then it is contained, and we have a collision.

How do i go about testing if it is contained in a particular voronoi region/ which triangular face is pointing in the direction of the origin?

The current 2D algorithm checks if a triangle is made, if not, then the simplex is a line and it finds the 3rd point. I assume the 3D algorithm with check if a tetrahedron is made, if not, then it will check for a triangle, if true then it will to find a 4th point to make a tetrahedron(how would i get this? using a normal in direction of origin?). If i trangle isnt made, it will find a 3rd point to make a triangle (do i still use triple product for this like in 2D?).

Any suggestions, outlines, resources, code augmentations, comments are much appretiated.

Depending on what result you expect from the GJK algorithm you might want to look at this nice tutorial from Molly Rocket: https://mollyrocket.com/849

Be aware though that his implementation only outputs intersection? yes/no. But it might be a nice start.