Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves

In this paper, the geometric Lagrange interpolation of four points by planar cubic Pythagorean-hodograph (PH) curves is studied. It is shown that such an interpolatory curve exists provided that the data polygon, formed by the interpolation points, is convex, and satisfies an additional restriction on its angles. The approximation order is 4. This gives rise to a conjecture that a PH curve of degree n can, under some natural restrictions on data points, interpolate up to n + 1 points. Key words: planar curve, PH curve, geometric interpolation, Lagrange interpolation

• Type: Journal
• Year: 2008
• Where: CAGD
• Authors: Gasper Jaklic, Jernej Kozak, Marjeta Krajnc, Vito Vitrih, Emil Zagar
• Keywords: CAGD 2008, Curve, Geometric Lagrange Interpolation, Lagrange Interpolation