带形状参数三角B样条曲线曲面及其应用  

TRIGONOMETRIC B-SPLINE CURVES AND SURFACES WITH SHAPE PARAMETER AND ITS APPLICATION

作　　者：陈素根[1] 汪志华[1] 赵正俊[1] 

机构地区：[1]安庆师范学院数学与计算科学学院,安徽安庆246133

出　　处：《计算机应用与软件》2015年第10期78-81,共4页Computer Applications and Software

基　　金：国家自然科学基金项目(11326052);安徽省高等学校自然科学研究项目(KJ2012B088;KJ2012B089)

摘　　要：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。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.

关 键 词：计算机应用 三角 B 样条 插值样条 图像放缩 形状参数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]