CAJ | 학술논문

给出两类均匀结点情形下二阶三角B-样条基函数的定义，分析它们的构造过程，性质，并分别用其生成二阶三角B-样条函数和二阶三角B-样条曲线。其中第一类曲线是三点分段的，即由前后相继3个控制点决定一段曲线，与二阶B-样条曲线类似，第二类曲线是四点分段的，即由前后相继4个控制点决定一段曲线，与三阶B-样条曲线类似。讨论这两类曲线的性质及它们之间的关系。针对第一类曲线，还给出了重结点情形下基函数的定义并分析了这种情形下曲线的情况。将第一类二阶三角B-样条曲线与一阶三角B-样条曲线进行了对比，得出相同结点向量下，二阶三角B-样条曲线更加接近控制多边形的结论。
급출량류균균결점정형하이계삼각B-양조기함수적정의，분석타문적구조과정，성질，병분별용기생성이계삼각B-양조함수화이계삼각B-양조곡선。기중제일류곡선시삼점분단적，즉유전후상계3개공제점결정일단곡선，여이계B-양조곡선유사，제이류곡선시사점분단적，즉유전후상계4개공제점결정일단곡선，여삼계B-양조곡선유사。토론저량류곡선적성질급타문지간적관계。침대제일류곡선，환급출료중결점정형하기함수적정의병분석료저충정형하곡선적정황。장제일류이계삼각B-양조곡선여일계삼각B-양조곡선진행료대비，득출상동결점향량하，이계삼각B-양조곡선경가접근공제다변형적결론。
Two kinds of quadratic trigonometric B-spline basis functions with uniform knot vectors are presented in this paper ,their constructions and properties are analyzed .These two kinds of functions can be used to construct trigonometric B-spline functions and trigonometric B-spline curves .Every segment of the first kind of curves is determined by three control points w hen every segment of the second kind of curves is determined by four control points .The properties of the two kinds of curves and the relationship between them are discussed .The cases of multiple knots of the first kind of basis functions are defined ,and we show how the curves like in this situation .The comparisons of the one order trigonometric B-spline curves and the quadratic trigonometric spline curves are presented in this paper .We came to a conclusion that the quadratic trigonometric B-spline curves are closer to the con-trol polygon than the one order trigonometric B-spline curves .