spline wavetable generator

From: Claes (Claes@lsipc10.epfl.ch)
Date: Tue Oct 17 2000 - 13:15:31 EDT


Hi,

I'm not sure how the spline wavetable generator should be implemented: (see
page 133 of norm)
for x=x1..xn the number of unknowns is 4(n-1)
the derivatives at the intermediate points are the same: (n-2) equations
in each segment the spline needs to interpolate two points: 2(n-1) equations
the derivative in x1 and xn = 0: 2 equations
(since I do not have enough equations yet, I checked the definition of a
spline, and apparently the derivatives to the order of the degree-1 need to
be equal in the intermediate points:)
the second derivatives at the intermediate points are the same: (n-2)
equations
=>4n-4 unknowns & 4n-4 equations=>ok

Is this the way it should be done ? It surprised me that there was no
mentioning of second derivatives in the norm.
I'm wondering also why in x1 & xn the first derivatives need to be 0 and not
the second derivatives.
I thought a very common spline was a natural interpolating spline, which has
the second & not the first on 0 at these 2 points.

I hope somebody can help me out of this.

Greetings,

Kasper
(a last year exchange student working on SAOL @ the EPFL Switzerland)



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