Piecewise linear splines

[zyda res acct]

I am trying to convert a data file consisting of polygon vertices
into a file containing the coefficients of a parametric polynomial
function of order 1. In other words, polygon data to parametric 
piecewise linear curve. Given:
1) N: The number of segments,
2) T(1),...,T(N+1): The endpoints and the breakpoints separating
   the polynomial segments,

3) The coordinates of the points in the i-th segment of the curve
   are given by the following polynomials:

	X(u) = AX(i) + BX(i) * s

	Y(u) = AY(i) + BY(i) * s

	Z(u) = AZ(i) + BZ(i) * s

where
	T(i) <= u <= T(i + 1), i = 1,...,N
	s = u - T(i)

My question is how do I get the values for the coefficients A(i),B(i),
i = 1,...,N representing the spline in each of the N segments?

Thanks,

	gd