【摘要】 为使构造的曲线兼顾代数多项式空间和三角多项式空间的优点,利用加权思想,提出一种ωλμ-TC-Bézier曲线。将代数多项式空间的三次Bernstein基函数和三角多项式空间的三次类Bernstein基函数相结合,得到新的基函数并分析其性质;在该基函数的基础上,给出相应曲线的定义和性质;给出曲线的大量案例。结果表明,形状参数及加权思想的融入使ωλμ-TC-Bézier曲线在具有Bézier曲线实用性质的同时还具有灵活的形状可调性,能够精确地表示地抛物线弧、椭圆弧及圆弧等二次曲线。大量的分析以及实例结果表明,结合加权思想构造的ωλμ-TC-Bézier曲线在曲线设计中十分有效。更多还原

【Abstract】 To make constructed curve have the advantages of the algebraic polynomial space and the triangular polynomial space,aωλμ-TC-Bézier curve was proposed using the idea of weighting.A new base function and its properties were analyzed by combining the cubic Bernstein base function of algebraic polynomial space and cubic class Bernstein base function of trigonometric polynomial space.The definition and properties of corresponding curves were given on the basis of the new base function.A large number of cases of curves was given.The results show that the integration of shape parameters and weighting ideas makes theωλμ-TC-Bézier curve has not only the practical properties of Bézier curve,but flexible shape adjustability,and it can accurately represent the conic curves such as parabola arc,elliptical arc and arc.A large number of analysis and examples show that theωλμ-TC-Bézier curve constructed with the weighting idea is very effective in curve design.更多还原