摘要
根据微分几何理论,给出一种可展曲面上G2连续的曲线插值算法。构造一等距对应将可展曲面展成平面,从而将原问题转化为通常的平面上的曲线插值问题。在R2上利用二次三角B样条曲线插值型值点列,无需反算控制顶点,证明了所得的可展曲面上的插值曲线是G2连续的。理论推导和实例均表明,该算法具有推广应用的广阔前景。
According to the basic principles of differential geometry, a new algorithm for constructing G^2 continuous interpolation curve on developable surface is presented. Constructing an isometric correspondence, and then, the developable surface will be developed into plane. Therefore, the original problem can be ended into the construction of interpolation curve in R^2 generally. The quadratic trigonometric B spline curve is used to interpolate the given points in R^2, without calculating the control points. And it proves that the interpolation curve on the developable surface is G^2 continuous. Theoretical deduction and experimentation show that such an algorithm is effective and produces good results.
出处
《计算机工程与设计》
CSCD
北大核心
2009年第11期2803-2805,共3页
Computer Engineering and Design
关键词
可展曲面
等距对应
插值曲线
样条曲线
测地曲率
developable surface
isometric correspondence
interpolation curve
spline curve
geodesic curvature
