CAJ | 학술논문

本文构造了一种基于函数值的带形状参数的(3,2)1阶有理插值样条曲面，并研究该曲面中诸如边界插值、极限、解析和正则等性质。引入双八次九阶矩阵表示的凸性判别函数，推导了判定插值曲面凸性的充要条件。根据该条件给出数值实例，展示如何适当选取参数实现曲面的局部保凸控制。特别发现这种插值曲面的凸性在某些点处即使型值是凸的数据也是相对刚性的。
본문구조료일충기우함수치적대형상삼수적(3,2)1계유리삽치양조곡면，병연구해곡면중제여변계삽치、겁한、해석화정칙등성질。인입쌍팔차구계구진표시적철성판별함수，추도료판정삽치곡면철성적충요조건。근거해조건급출수치실례，전시여하괄당선취삼수실현곡면적국부보철공제。특별발현저충삽치곡면적철성재모사점처즉사형치시철적수거야시상대강성적。
In this paper, a rational interpolating spline surface with parameters of order (3, 2)1 is constructed based on function values. Some properties are studied for the rational spline interpolating surface and its basic functions, for example, boundaries, limits, analysis and canonical. A matrix representation with 9-order coe?cient matrix and 8-degree bibariate polynomial vector function is introduced as identification of the functional convexity. The necessary and su?cient condition for the rational interpolation surface to be local convex is derived. According to the condition, examples are prensented to show how to choose the parameters and to change shapes of the surfaces. Particularly, it is found that the convexity of the interpolation surface is relatively rigid at certain points even if the interpolated data is convex.