TCB-Splines

I have a question regarding the endtangents of TCB-Splines. Since the equation for the outgoing tangent involves the endpoint BEFORE the current, how would you find the tangent of the very first point (because a point before the first does not exist)? Similarly, the final incoming tangent requires a point after (which does not exist). Any help would be greatly appriciated. Thanks

Oh, PS: I’m not using them for animation, so creating a loop (and setting the last vector to the “before the first” and the first vector to the “after the last” will not work). Just thought I’d clarify that now.