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Hermite Interpolation by Pythagorean Hodograph Quintics
1995
Mathematics of Computation
The Pythagorean hodograph (PH) curves are polynomial parametric curves {x(t), y(t)} whose hodograph (derivative) components satisfy the Pythagorean condition x'2(t)+y'2(t) = a2(t) for some polynomial a(t). Thus, unlike polynomial curves in general, PH curves have arc lengths and offset curves that admit exact rational representations. The lowest-order PH curves that are sufficiently flexible for general interpolation/approximation problems are the quintics. While the PH quintics are capable of
doi:10.2307/2153373
fatcat:p45qeoad2rawfhktxr7nej3q5m