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This paper presents a geometric interpolation method for curve approximation in R3 space. Given a curve, the new method is to find an approximation Bézier curve of degree 4 tangent with the given curve at the two end points and at an inner point as well. The resulting Bézier curve is explicitly expressed in the parameters of the tangent inner point of both the given curve and the approximation curve. We prove that the approximation order of the new method is 6, which is the optimal approximation order in the traditional conjecture. © 2010 CAD Solutions, LLC.

Geometric Interpolation Method inR3Space with Optimal Approximation Order