How is a 3D spline represented in a pp form?

Hi,

I'm trying to understand how the pp form is used to construct a spline curve with 3 dimensions.

So, with just 1 dimension it looks like each break indicates the start point of each piece in the x dimension, and coefs represent the 4 coefficients of the cubic polynomial to be drawn between the current break and the next break.

However, with 3 dimensions there are 3 rows of coefficients for each break, so I assume those are the coefficients for the polynomials in the X-Y, X-Z and Y-Z planes. However, in this case I don't really understand what each break means. I guess they represent the distance along the spline in some way, but I'm not sure.

So my question is essentially how does each break translate to the start and end location of each piece of the spline?

I'm asking because I want to export the breaks and coefs to plot in openGL within C#

Sorry if this is unclear, or the answer is obvious, I think my understanding of splines is probably flawed at a fundamental level, but any answers you could give would be appreciated!