Geometric interpolation by planar cubic polynomial curves
Computer Aided Geometric Design
An Interpolation Method That Minimizes an Energy Integral of Fractional Order
Computer Mathematics
Planar cubic G1 interpolatory splines with small strain energy
Journal of Computational and Applied Mathematics
Interpolation Scheme for Planar Cubic G2 Spline Curves
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Lagrange geometric interpolation by rational spatial cubic Bézier curves
Computer Aided Geometric Design
An approach to geometric interpolation by Pythagorean-hodograph curves
Advances in Computational Mathematics
Construction of low degree rational motions
Journal of Computational and Applied Mathematics
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In this paper, geometric interpolation by parametric polynomial curves is considered. Discussion is focused on the case where the number of interpolated points is equal to r + 2, and n=r denotes the degree of the interpolating polynomial curve. The interpolation takes place in $\mathbb R^d$ with d=n. Even though the problem is nonlinear, simple necessary and sufficient conditions for existence of the solution are stated. These conditions are entirely geometric and do not depend on the asymptotic analysis. Furthermore, they provide an efficient and stable way to the numeric solution of the problem.