A NEW METHOD OF INTERPOLATION AND SMOOTH CURVE FITTING BASED ON LOCAL PROCEDURES
A NEW METHOD OF INTERPOLATION AND SMOOTH CURVE FITTING BASED ON LOCAL PROCEDURES
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DOI：
10.1145/321607.321609
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发表时间：
1970-01-01
影响因子：
2.5
通讯作者：
AKIMA, H
中科院分区：
文献类型：
--
作者：
AKIMA, H
发展了一种新的数学方法，用于从平面上给定的数据点集进行插补，并将光滑曲线拟合到这些点上。这种方法是这样设计的，即合成的曲线将通过给定点，并将看起来平滑和自然。它基于由一组多项式组成的分段函数，每个多项式至多三次，适用于给定点的连续区间。在这种方法中，曲线的斜率是在每个给定点局部确定的，而表示一对给定点之间曲线的一部分的每个多项式由这些点的坐标和斜率来确定。比较表明，用该方法绘制的曲线比用其他数学方法绘制的曲线更接近于手工绘制的曲线。
A new mathematical method is developed for interpolation from a given set of data points in a plane and for fitting a smooth curve to the points. This method is devised in such a way that the resultant curve will pass through the given points and will appear smooth and natural. It is based on a piecewise function composed of a set of polynomials, each of degree three, at most, and applicable to successive intervals of the given points. In this method, the slope of the curve is determined at each given point locally, and each polynomial representing a portion of the curve between a pair of given points is determined by the coordinates of and the slopes at the points. Comparison indicates that the curve obtained by this new method is closer to a manually drawn curve than those drawn by other mathematical methods.