Abstract
In this paper, the problem of geometric interpolation of space data is considered. Cubic polynomial parametric curve is supposed to interpolate five points in three dimensional space. It is a case of a more general problem, i.e., the conjecture about the number of points in \(\mathbb{R}\)d which can be interpolated by parametric polynomial curve of degree n. The necessary and sufficient conditions are found which assure the existence and the uniqueness of the interpolating polynomial curve.
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