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**Fairing Bézier curves with constraints.**
*(English)*
Zbl 0755.65018

Summary: The generation of a fair, planar Bézier curve is approached as an approximation problem with constraints. The fairness criterion is based on the square of the second derivative norm. The constraints apply to interpolation conditions, end conditions and an integral condition pertaining to the area under the curve. An integer polynomial Bézier curve is constructed using a sufficiently high degree to meet all constraints and retain extra freedom for fairing. The variational problem formulation leads to a nonlinear system of equations, which is solved numerically. The method is illustrated by examples.

### MSC:

65D17 | Computer-aided design (modeling of curves and surfaces) |

### Keywords:

numerical examples; fairing with constraints; second derivative norm; area constraint; variational problem formulation; Bézier curve
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\textit{H. Nowacki} et al., Comput. Aided Geom. Des. 7, No. 1--4, 43--55 (1990; Zbl 0755.65018)

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### References:

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