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在工业设计和反求工程中,曲线是形状设计和数据拟合的重要对象。曲线的光顺性对最终产品的外观质量有着直接影响。文章利用文献[1]构造出带有参数调配函数的模型,用其生成三次C-Bézier曲线。在能量法的基础上,研究了控制参数α对这种新曲线形态的影响,通过调整α和控制顶点使得曲线的能量最小,得到最优的光顺逼近曲线。通过最小二乘法和非线性泛函的极小值优化计算,对平面数据点进行光顺逼近,达到光顺的目的。该算法既可以对曲线进行全局光顺又可以进行局部光顺。最后给出了由数据拟合的C-Bézier曲线光顺的实例。
In industrial design and reverse engineering, the curve is an important object of shape design and data fitting. The smoothness of the curve has a direct effect on the appearance quality of the final product. In this paper, the paper [1] is used to construct a model with parameter fitting function, which is used to generate cubic C-Bézier curves. Based on the energy method, the influence of the control parameter α on the shape of this new curve is studied. By adjusting α and controlling the vertex, the curve energy is minimized, and the optimal smoothing approximation curve is obtained. Through least-squares method and nonlinear functional minimum optimization calculation, the plane data points smoothing approach, to achieve the purpose of smooth. The algorithm can both smooth the curve globally and partially smooth. Finally, an example of smoothing of C-Bézier curves fitted by data is given.