Lagrange Interpolation and Neville’s Algorithm

Perhaps the easiest way to describe a shape is to select some points on the shape. Given enough data points, the eye has a natural tendency to interpolate smoothly between the data. Here we are going to study this problem mathematically. Given a finite collection of points in affine space, we shall investigate methods for generating polynomial curves and surfaces to go through the points. We begin with schemes for curves and later extend these techniques to surfaces.

2.1 Linear Interpolation

Two points determine a line. Suppose we want the equation of the line P(t) passing through the two points P and Q in affine space. Then we can write


The curve P(t) passes through P at t = 0 ...

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