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Two classes of systolic architectures are presented that are able to compute bicubical B-spline or Bezier polynomial coefficients and carry out polynomial evaluations. Using a pair of full arrays it is possible to compute all the coefficients in parallel, and to evaluate the polynomials for a given surface, as well as provide a speedup factor of more than 1500 compared with the single processor computation. An alternative solution is to partition both tasks into smaller sub-tasks so that a reduced size of the array is required. This allows a reasonable tradeoff between the speed needs and the VLSI implementation requirements to be achieved.