Polynomial Curve Constructions
Polynomial interpolation is a fundamental concept for all of CAGD. Although its uses are limited to low degrees, the basic concept still needs to be understood in order to develop new algorithms. If the amount of data is too large for interpolation to be successful, one uses approximation methods instead.
7.1 Aitken’s Algorithm
A common problem in curve design is point data interpolation: from data points pi with corresponding parameter values ti, find a curve that passes through the pi.1 One of the oldest techniques to solve this problem is to find an interpolating polynomial through the given points. That polynomial must satisfy the interpolatory constraints
Several algorithms exist for this problem—any textbook ...
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