张量积Baskakov-Szász-Mirakjan曲面的构造及性质  

Modeling of Tensor Product Baskakov-Szász-Mirakjan Surfaces and their Properties

作　　者：周国荣 

机构地区：[1]厦门理工学院应用数学学院,福建厦门361024

出　　处：《厦门理工学院学报》2017年第5期83-89,共7页Journal of Xiamen University of Technology

基　　金：国家自然科学基金项目(11626201);厦门理工学院高层次人才项目(YKJ14026R)

摘　　要：根据算子逼近论中的Baskakov算子与Szász-Mirakjan算子,利用Baskakov-Szász-Mirakjan基函数,结合给定的控制顶点构造了张量积Baskakov-Szász-Mirakjan曲面,实现了用有限个控制顶点绘制张量积Baskakov-Szász-Mirakjan曲面,实例验证了此方法的有效性.同时,由基函数的非负性、单位分解性、线性无关性、插值性、导函数公式,推导出张量积Baskakov-Szász-Mirakjan曲面具有仿射不变性、凸包性、非退化性、插值性等主要几何造型性质。According to Baskakov operators and Szász-Mirakjan operators in operator approximation theory,tensor product Baskakov-Szász-Mirakjan surfaces were constructed using Baskakov-Szász-Mirakjan basis functions and several given control vertices, and an example was drawn for verification. From the main properties of Baskakov-Szász-Mirakjanbasic functions we deduced that Baskakov-Szász-Mirakjan surfaces have the main geometric modeling properties,such as affine invariance,convex hull property,non-degeneracy and so on.

关 键 词：张量积曲面 造型方法 BASKAKOV算子 Szász-Mirakjan算子 负次数Bernstein基函数 Poisson基函数 

分 类 号：O174[理学—数学] O177[理学—基础数学]