1 April 2002 Method for aligning any-order polynomial surfaces in three-dimensional space
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Optical Engineering, 41(4), (2002). doi:10.1117/1.1457457
Abstract
A theoretically sound and computationally inexpensive method is proposed for expressing in a canonical form not only quadratic, but any-degree polynomial surfaces, thus enabling the alignment of 3-D objects composed of such surfaces to a standard coordinate system. Furthermore, an analytical proof of the lower upper bound for convergence is presented, by which the efficiency of the proposed method is verified. Experiments are conducted with up to sixth-degree polynomial surfaces, thus demonstrating the method converges to the desired results within a few steps.
Nicolas Alvertos, "Method for aligning any-order polynomial surfaces in three-dimensional space," Optical Engineering 41(4), (1 April 2002). https://doi.org/10.1117/1.1457457
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