The DataPoints command retrieves the interpolated data points from a POLYINTERP structure.

The POLYINTERP structure is created using the PolynomialInterpolation command or the CubicSpline command.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right)\:$

$\mathrm{xy}≔\left[\left[0\,1\right]\,\left[\frac{1}{2}\,1\right]\,\left[1\,\frac{11}{10}\right]\,\left[\frac{3}{2}\,\frac{3}{4}\right]\,\left[2\,\frac{7}{8}\right]\,\left[\frac{5}{2}\,\frac{9}{10}\right]\,\left[3\,\frac{11}{10}\right]\,\left[\frac{7}{2}\,1\right]\right]$

$\mathrm{xy}≔\left[\left[0\,1\right]\,\left[\frac{1}{2}\,1\right]\,\left[1\,\frac{11}{10}\right]\,\left[\frac{3}{2}\,\frac{3}{4}\right]\,\left[2\,\frac{7}{8}\right]\,\left[\frac{5}{2}\,\frac{9}{10}\right]\,\left[3\,\frac{11}{10}\right]\,\left[\frac{7}{2}\,1\right]\right]$

$\mathrm{p1}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xy}\,\mathrm{independentvar}=x\,\mathrm{method}=\mathrm{lagrange}\right)\:$

$\mathrm{DataPoints}\left(\mathrm{p1}\right)$

$\left[\left[0\,1\right]\,\left[\frac{1}{2}\,1\right]\,\left[1\,\frac{11}{10}\right]\,\left[\frac{3}{2}\,\frac{3}{4}\right]\,\left[2\,\frac{7}{8}\right]\,\left[\frac{5}{2}\,\frac{9}{10}\right]\,\left[3\,\frac{11}{10}\right]\,\left[\frac{7}{2}\,1\right]\right]$

$\mathrm{p2}≔\mathrm{CubicSpline}\left(\mathrm{xy}\,\mathrm{independentvar}=x\right)\:$

$\mathrm{DataPoints}\left(\mathrm{p2}\right)$

$\left[\left[0\,1\right]\,\left[\frac{1}{2}\,1\right]\,\left[1\,\frac{11}{10}\right]\,\left[\frac{3}{2}\,\frac{3}{4}\right]\,\left[2\,\frac{7}{8}\right]\,\left[\frac{5}{2}\,\frac{9}{10}\right]\,\left[3\,\frac{11}{10}\right]\,\left[\frac{7}{2}\,1\right]\right]$