Curve defined as [Lx(t), Ly(t), Lz(t)] where L?(t) are Lagrange's interpolation polynomials. Lx(t) crosses points (ti, xi) (i = 0..ControlPoints.Count-1) where ti = TBegin + i/(ControlPoints.Count-1) * (TEnd-TBegin) and xi = ControlPoints[i, 0]. Similarly for Ly and Lz.
Later note: in fact, you can override ControlPointT to define function "ti" as you like.