Interpolating B-Spline Curves with Boundary Conditions
A B-spline curve is determined by interpolation points and the tangent vectors at both ends. There can be four to 12 locators; new ones are added at the end.
The control points of the nonuniform cubic B-spline curve are determined from the interpolation points and the boundary conditions. The first and last two control points are so-called phantom points, which are determined by the first-order boundary conditions. The computational method can be applied to three-dimensional curves, too.
B. K. Choi, W. S. Yoo, and C. S. Lee, "Matrix Representation for NURB Curves and Surfaces," Computer-Aided Design, 22(4), 1990 pp. 235–239.
G. E. Farin, Curves and Surfaces for Computer-Aided Geometric Design, San Diego, CA: Academic Press, 1988.