摘要
函数曲线的积分问题在工业领域中占有极其重要的地位,非均匀有理B样条(NURBS)方法,是STEP国际标准中关于工业产品几何定义的唯一数学方法。但是关于NURBS曲线的积分问题一直没有得到很好的解决,这使得NURBS曲线的应用大大地打了折扣。本文首次提出了一种解决三次NURBS曲线积分问题的高精度数值方法,给出了包括面积、面积矩、惯性矩、曲线长度等的积分公式的例子,并对这种方法应用于船舶静力性能计算做了一定程度的研究。
The integral of curve in industry field is important. NURBS is the only mathematic method about geometric definition of industrial product in the STEP international standard, but there is still no good solution for the integral of NURBS curve. For the first time, this paper presents a high precision numerical method for the integral of cubic NURBS curve. In the first place, authors write the equation of point＇s X-coordinate and Y-coordinate with de Boor algorithm, then construct different formulas such as area, area moment, inertia moment, curvets length and so on. Though these formulasf contents are different, they belong to the same type. At last, the outcome is gotten by calculating these formulas with a numerical method-Romberg algorithm. Also, this paper performs a study on the application of the method in ship static calculation.
出处
《中国造船》
EI
CSCD
北大核心
2006年第1期78-83,共6页
Shipbuilding of China
