![]() Now the spline function f( x) = p 0( x) for x in the interval, f( x) = p 1( x) for x in the interval and f( x) = p 2( x) for x in the interval. We see from Figure 1, for example, that the second of the spline polynomials is Cellsįigure 2 – Representative formulas from Figure 1 ![]() We show how to calculate these parameters in the rest of the figure.įigure 2 displays some of the representative formulas in Figure 1. ![]() The coefficients for the three cubic polynomials p 0, p 1 and p 2 are shown in range B16:E18 of Figure 1. ExampleĮxample 1: Create a spline curve that passes through the four points in range B4:C7 of Figure 1. Proof: See Derivation of Spline Polynomials. Now define U = to be an n+1 × n+1 matrix where i, j = 0, …, n andĪnd define B = and V = to be n+1 × 1 matrices where the v i are as defined above and B is defined by P i( x) = a i( x–x i) 3 + b i( x–x i) 2 + c i( x–x i) + d iīased on h i = x i +1 – x i and k i = y i +1 – y i. The b i coefficients are defined via matrix operations as follows. Property 1: The polynomials that we are seeking can be defined by In particular, we seek n cubic polynomials p 0, …, p n -1 so that f( x) = p i( x) for all x in the interval. Thus, we seek a smooth function f( x) so that f( x i) = y i for all i. ![]() Spline fitting or spline interpolation is a way to draw a smooth curve through n+1 points ( x 0, y 0), …, ( x n,y n).
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