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Cubic Spline 三次样条曲线

System Model

For a group of certain points \((x_{0,1},x_{0,2},\cdots,x_{0,m}),(x_{1,1},x_{1,2},\cdots,x_{1,m}), (x_{2,1},x_{2,2},\cdots,x_{2,m}), \cdots, (x_{n,1},x_{n,2},\cdots,x_{n,m})\), we want to find a smooth enough curve that passes all these points to achieve the interpolation goal. To do so, we can use piecewise cubic functions to fitting the points.