插值与逼近混合的三重细分法

Ternary subdivision schemes that blend interpolating and approximating

提出了一种新的四点三重插值曲线细分法和一种含参数的三次B-样条曲线细分法,利用提出的这两种曲线细分方法得到了一种插值与逼近混合的三重曲线细分法。这种混合细分法将插值细分和逼近细分统一为同一格式。给出了这种混合细分法的几何解释,分析了其连续性,并将其推广到曲面情形,提出了四边形网格上的1-9插值曲面细分法和张量积三次B-样条曲面细分法。利用这两种曲面细分法,得到了插值与逼近相混合的三重曲面细分法,并分析了其连续性。数值实例表明,方法是合理有效的。

A new four-point ternary interpolating curve subdivision scheme and a cubic B-spline curve subdivision scheme with parameters are proposed. By using the two proposed methods, a ternary curve subdivision scheme which blends interpolating and approximating is obtained. This blending subdivision scheme can unify the interpolating subdivision and the approximating subdivision. A geometric interpretation of this blending subdivision scheme is given, and its continuity is analyzed. We generalize this method to the surface case. We propose a 1-9 interpolating surface subdivision scheme and a tensor product cubic B-spline surface subdivision scheme on the quadrilateral mesh, and use them to obtain a kind of ternary surface subdivision scheme that blends interpolation and approximation. The continuity of this scheme is analyzed. The numerical example shows that the method is reasonable and effective.