References
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@ -24,3 +24,11 @@
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url = "http://opensource.org/licenses/Zlib",
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url = "http://opensource.org/licenses/Zlib",
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urldate = "2015-03-12"
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urldate = "2015-03-12"
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}
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}
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@online{spline,
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author="Jana Proch\'azkov\'a",
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title="DERIVATIVE OF B-SPLINE FUNCTION",
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url="http://mat.fsv.cvut.cz/gcg/sbornik/prochazkova.pdf",
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urldate="2015-03-12"
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}
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@ -35,3 +35,5 @@ The \texttt{prime} member function computes the derivative like this
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$$C'(t) = \sum_{i=0}^m N_i^{\prime n} (t) P_i $$
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$$C'(t) = \sum_{i=0}^m N_i^{\prime n} (t) P_i $$
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with
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with
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$$ N_i^{\prime n}(t) = \frac{n}{t_{i+n}-t_{i}}N_i^{n-1}(t) - \frac{n}{t_{i+n+1}-t_{i+1}}N_{i+1}^{n-1}(t)$$
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$$ N_i^{\prime n}(t) = \frac{n}{t_{i+n}-t_{i}}N_i^{n-1}(t) - \frac{n}{t_{i+n+1}-t_{i+1}}N_{i+1}^{n-1}(t)$$
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These formulas have been taken from the reference \cite{spline}.
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