带形状参数三角B样条曲线曲面及其应用

摘要

Aiming at the construction of spline curves and surfaces and its application in image zooming,we constructed in trigonometric function space {1,t ,sint ,cost ,sin2 t ,cos2 t }a kind of trigonometric B-spline basis function with shape parameter,and defined the corresponding trigonometric B-spline curves and surfaces,the properties of the trigonometric B-spline curves and surfaces and the effect of parameter in adjusting the shapes of curves and surfaces were also analysed.We broadened the value of shape parameter and constructed the trigonometric B-spline interpolation curves and surfaces which satisfy C2 continuity and can directly interpolate the given control vertices,and applied these interpolation surfaces to image zooming.Examples illustrated that the trigonometric B-spline curves and surfaces constructed in the paper had good application in curves and surfaces modelling and image zooming.%针对样条曲线曲面构造及其在图像放缩中的应用问题，在三角函数空间｛1，t ，sint ，cost ，sin2 t ，cos2 t ｝中构造一类带有形状参数的三角 B 样条基函数，并定义相应的三角 B 样条曲线和曲面，分析该曲线曲面的性质以及形状参数对曲线曲面形状的调节作用。拓宽形状参数的取值，构造了满足 C2连续且可以直接插值控制顶点的三角 B 样条插值曲线和曲面，并将其应用于图像放缩中。实例说明了所构造的三角 B 样条曲线曲面在曲线曲面造型和图像放缩方面有较好应用。