Bezier Approximation and Pascal’s Triangle
In previous chapters, we used interpolation to specify shape. But interpolation is not always a good way to describe the contour of a curve or surface. To accurately reproduce complicated shapes, we may need to interpolate lots of data. Polynomial interpolation for many points is impractical because the degree of the interpolant can get extremely high, leading to slow and numerically unstable computations. Also polynomial interpolants may oscillate unnecessarily and fail to reproduce the desired shapes (see Figure 5.1). Thus, even if we were to specify more and more points, there is no guarantee that the polynomial interpolants would converge to the curves or surfaces we wish to represent. ...
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