Curve design with rational Pythagorean-hodograph curves
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- Pottmann, H. Adv Comput Math (1995) 3: 147. doi:10.1007/BF03028365
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The dual Bézier representation offers a simple and efficient constructive approach to rational curves with rational offsets (rational PH curves). Based on the dual form, we develop geometric algorithms for approximating a given curve with aG2 piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation andG2 Hermite interpolation. The solution involves rational PH curves of algebraic class 4; these curves and important special cases are studied in detail.