Catmull-Rom Splines

I have tried, but I genuinely don't understand how the equations work here.  Could someone possibly slowly slowly walk me through the equations here: http://www.mvps.org/directx/articles/catmull/

I guess what i really need to know is that given a set of given points, how do I work through the equations necessary to create the catmull-rom spline which passes through them.  Any help would be greatly appreciated.

That far-RHS matrix got some serious attention with the ugly stick, I've got no clue as to how it would miraculously transform your point matrix + the t matrix into an accurate curve that represents your discretised data, but oh well.
The most important thing to note here is that the equation you get is valid only for one interval of t (0.0 to 1.0 in the example). Also, the only points used are the two either side, nothing else matters for that interval. If you're plotting over, say, 0.0 to 3.0, you'll need a total of 6 points.
For interval 0.0 to 1.0, plug in the first 4 points, then for interval 1.0 to 2.0, use the next 'window' of 4 points, but this time take them one step along, ie: points P1 to P4 from the example. Repeat ad nauseum until you've got all the curve you need.

OP here, Thanks for your help, turns out my brain decided to go AWOL for a second on me.

or: OP here, nm i figured it out.