B-spline Curvefitting - Maple Programming Help

B-spline Curvefitting

 Description Define a B-spline curve using specified data points. This produces a parametric curve.

Enter a list of data points.

 > $\left[\left[{-5}{,}{5}\right]{,}\left[{0}{,}{2}\right]{,}\left[{2}{,}{-1}\right]{,}\left[{4}{,}{0}\right]\right]$
 $\left[\left[{-}{5}{,}{5}\right]{,}\left[{0}{,}{2}\right]{,}\left[{2}{,}{-}{1}\right]{,}\left[{4}{,}{0}\right]\right]$ (1)

Specify the independent variable, and then define the B-spline curve.

 > $b:=\mathrm{CurveFitting}\left[\mathrm{BSplineCurve}\right]\left(,{v}\right)$
 ${b}{:=}\left[{{}\begin{array}{cc}{0}& {v}{<}{0}\\ {-}\frac{{5}}{{6}}{}{{v}}^{{3}}& {v}{<}{1}\\ \frac{{5}}{{3}}{-}\frac{{5}}{{2}}{}{v}{-}\frac{{5}}{{2}}{}{\left({v}{-}{1}\right)}^{{2}}{+}\frac{{5}}{{2}}{}{\left({v}{-}{1}\right)}^{{3}}& {v}{<}{2}\\ {-}\frac{{10}}{{3}}{+}{5}{}{\left({v}{-}{2}\right)}^{{2}}{-}\frac{{13}}{{6}}{}{\left({v}{-}{2}\right)}^{{3}}& {v}{<}{3}\\ {-}{11}{+}\frac{{7}}{{2}}{}{v}{-}\frac{{3}}{{2}}{}{\left({v}{-}{3}\right)}^{{2}}{+}\frac{{1}}{{2}}{}{\left({v}{-}{3}\right)}^{{3}}& {v}{<}{4}\\ {-}{6}{-}{\left({v}{-}{4}\right)}^{{3}}{+}{2}{}{v}& {v}{<}{5}\\ {8}{-}{v}{-}{3}{}{\left({v}{-}{5}\right)}^{{2}}{+}\frac{{5}}{{3}}{}{\left({v}{-}{5}\right)}^{{3}}& {v}{<}{6}\\ \frac{{38}}{{3}}{-}{2}{}{v}{+}{2}{}{\left({v}{-}{6}\right)}^{{2}}{-}\frac{{2}}{{3}}{}{\left({v}{-}{6}\right)}^{{3}}& {v}{<}{7}\\ {0}& {7}{\le }{v}\end{array}{,}{{}\begin{array}{cc}{0}& {v}{<}{0}\\ \frac{{5}}{{6}}{}{{v}}^{{3}}& {v}{<}{1}\\ {-}\frac{{5}}{{3}}{+}\frac{{5}}{{2}}{}{v}{+}\frac{{5}}{{2}}{}{\left({v}{-}{1}\right)}^{{2}}{-}\frac{{13}}{{6}}{}{\left({v}{-}{1}\right)}^{{3}}& {v}{<}{2}\\ \frac{{5}}{{3}}{-}{4}{}{\left({v}{-}{2}\right)}^{{2}}{+}\frac{{4}}{{3}}{}{\left({v}{-}{2}\right)}^{{3}}{+}{v}& {v}{<}{3}\\ {11}{-}{3}{}{v}{+}\frac{{2}}{{3}}{}{\left({v}{-}{3}\right)}^{{3}}& {v}{<}{4}\\ \frac{{11}}{{3}}{-}{v}{+}{2}{}{\left({v}{-}{4}\right)}^{{2}}{-}\frac{{5}}{{6}}{}{\left({v}{-}{4}\right)}^{{3}}& {v}{<}{5}\\ {-}\frac{{8}}{{3}}{+}\frac{{1}}{{2}}{}{v}{-}\frac{{1}}{{2}}{}{\left({v}{-}{5}\right)}^{{2}}{+}\frac{{1}}{{6}}{}{\left({v}{-}{5}\right)}^{{3}}& {v}{<}{6}\\ {0}& {6}{\le }{v}\end{array}{,}{v}{=}{3}{..}{4}\right]$ (2)
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