杨军, 王青燕. 基于Lupas q-拟Bernstein算子的G2样条曲线[J]. 南昌航空大学学报(自然科学版), 2018, 32(4): 24-31. DOI: 10.3969/j.issn.1001-4926.2018.04.004
引用本文: 杨军, 王青燕. 基于Lupas q-拟Bernstein算子的G2样条曲线[J]. 南昌航空大学学报(自然科学版), 2018, 32(4): 24-31. DOI: 10.3969/j.issn.1001-4926.2018.04.004
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YANG Jun, WANG Qing-yan. G2 Spline Curves Based on Lupas q-analogue of Bernstein Operator[J]. Journal of nanchang hangkong university(Natural science edition), 2018, 32(4): 24-31. DOI: 10.3969/j.issn.1001-4926.2018.04.004
Citation: YANG Jun, WANG Qing-yan. G2 Spline Curves Based on Lupas q-analogue of Bernstein Operator[J]. Journal of nanchang hangkong university(Natural science edition), 2018, 32(4): 24-31. DOI: 10.3969/j.issn.1001-4926.2018.04.004
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基于Lupas q-拟Bernstein算子的G2样条曲线

G2 Spline Curves Based on Lupas q-analogue of Bernstein Operator

    摘要
  • 摘要: 为增加自由型曲线形状调控能力，以Lupas q-Bernstein算子的性质为基础，给出了Lupas q-拟Bezier曲线的新性质；进一步，在控制顶点给定的情况下，通过引入新的形状参数获取额外自由度，对分段Lupas q-Bezier曲线进行光滑拼接构造G2样条曲线。特别地，当选取特殊形状参数时，曲线可退化为Gamma样条曲线。理论分析和计算实例表明G2样条曲线较Gamma样条曲线在形状控制方面具有更多的灵活性。

     

    Abstract: To improve the shape control ability of freeform curves, based on the properties of the Lupas q-Bernstein operator, new properties of the Lupas q-Bezier curve are given. Further, additional degrees of freedom are obtained by introducing new shape parameters for given control points, and a G2 spline curve is constructed by joining piecewise Lupas q-Bezier curves smoothly. In particular, when the shape parameters are selected specially, the curve degenerates into the Gamma spline curve. Theoretical analysis and calculation examples show that the G2 spline curve has more flexibility in shape control than the Gamma spline curve.

     

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