3次Hermite曲线逼近Conic曲线段有关性质

利用Hermite多项式逼近法研究使用3次Hermite曲线逼近有理Conic曲线段的方法,推导3次Hermite曲线与Conic曲线段在端点处具有G2连续性、在中点具有G1连续性、保形几何属性需要满足的条件以及误差函数计算公式,通过多组不同类型的对比试验进一步证明了所述的关于用3次Hermite曲线逼近Conic曲线段有关性质的有效性.

Relevant Properties of Approximation to Conic Sections with Cubic Hermite Curves

By the Hermite polynomicals method,an approach to approximate Conic sections in the form of a rational Bezier curve with Hermite polynomial curves is studied.The property condition of constructed Hermite polynomial curve such as G-continuity with the Conic section at the end points and G-continuity at the parametric mid-point and shape-preserving has been proposed.Explicit error bound is also derived and discussed.The validity of the proposed method for approximating Conic sections with Hermite polynomial curves is further proved through multiples sets of different types of comparative tests.