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HallsofIvy

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If f(x) is the "quadratic spline" that is given by

[itex]f(x)= x^2[/itex] for [itex]0\le x\le 2[/itex], [itex]f(x)= 2x^2- 4x+ 4[/itex] for [itex]2\le x\le 3[/itex], etc. then x= 2 or, more properly, the point (2, 4) is a "knot".

Typically one wants a spline that interpolates given values. Often the knots are chosen at the "interpolation points" but not always.

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"Knots" are the points where the "pieces" change. That is, where the formula changes.

Assume a B-spline with n+1 control points (0 to n) & d control points per curve(polynomial of degree (d-1)). The text says that B-Splines are defined only in the interval from knot value u

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HallsofIvy

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What you can do is add the "not a knot" condition- you require that the polynomials in the first two intervals at each end be exactly the same. That is, that two "knots" are, in fact,

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