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Journal for Geometry and Graphics 09 (2005), No. 1, 067--075
Copyright Heldermann Verlag 2005

Blending curves

Albert Wiltsche
Institute of Geometry, University of Technology, Kopernikusgasse 24, 8010 Graz, Austria


Two arbitrarily given curves $k_1(t)$ and $k_2(t)$ are blended to a third curve $b(t)$ so that $b$ joins $k_1$ and $k_2$ in given points $A_1$ and $B_2$ $C^l$- and $C^m$-continuously, respectively. In order to meet this objective we use polynomial functions $\alpha_{lm}(t)$ for the blending process. The Casteljau algorithm for curves is used in a special way to build the blended curve $b(t)$. Furthermore we can use our construction to generate interpolating spline curves.

Keywords: Spline curves, Hermite interpolation, interpolation.

MSC: 68U05

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