Pipelined implementation of b-splines and beta-splines for computer graphics and visualization applications

Beta-splines used in visualization techniques differ from b-splines in that they are constructed using geometric continuity constraints instead of parametric derivative constraints. They are piecewise polynomial interpolating functions. We show how to exactly compute the samples of these functions from a sparse set of points. This computation uses only summations, and no multiplications after initial setup, and the summations can be pipelined for hardware implementation. The few multiplications necessary in the setup may be computed much more slowly than the output samples. Next, we show how to adapt this result to interpolate and manipulate curves. This technique consists primarily of summations in pipelined hardware. This new exact discrete implementation is fast, simple, and modular