Constructing a spline curve that interpolates an ordered sequence of points is a relatively simple matter, involving only the solution of tridiagonal linear systems. Constructing a spline surface that interpolates an array of points is a much more challenging problem — such a surface comprises a network of “patches,” and we must guarantee second—order continuity along the common boundary curves of every pair of adjacent patches. Attempting to formulate and solve systems of equations that express these continuity constraints is an exceedingly cumbersome and unrewarding task. However, we shall see below that the expression of spline functions in terms of spline bases offers an elegant and easily—implemented solution to this problem.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Spline Basis Functions. In: Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. Geometry and Computing, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73398-0_15
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DOI: https://doi.org/10.1007/978-3-540-73398-0_15
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