Hermite interpolation at sample point gives slightly different results

[VincentCucchietti]

Hello everyone,

I noticed that performing Hermite interpolation at sample point can give slightly different results (~1e-8) which should not happen.

Attached test to reproduce the issue

import org.hipparchus.analysis.interpolation.HermiteInterpolator;
import org.hipparchus.geometry.euclidean.threed.Vector3D;

public class IssueHermiteInterpolatorHipparchus {
    public static void main(String[] args) {

        // GIVEN


        // Data points
        final Vector3D pos1 = new Vector3D(6503514.0,
                                           1239647.0,
                                           -717490.0);

        final Vector3D vel1 = new Vector3D(-873.1600000000001,
                                           8740.42,
                                           -4191.076);

        final Vector3D acc1 = new Vector3D(-8.78857042491286,
                                           -1.6934422560847768,
                                           0.9818410863212799);

        final Vector3D pos2 = new Vector3D(-1.1065513874477834E7,
                                           1.2731407944126774E7,
                                           -5910755.440081692);

        final Vector3D vel2 = new Vector3D(-4415.112289029152,
                                           -154.58334977152364,
                                           159.60303091130456);

        final Vector3D acc2 = new Vector3D(0.7725072019312011,
                                           -0.8888003812990051,
                                           0.41281521337323207);


        // Create interpolator
        final HermiteInterpolator interpolator = new HermiteInterpolator();

        // Add data to interpolator
        interpolator.addSamplePoint(0, pos1.toArray(), vel1.toArray(), acc1.toArray());
        interpolator.addSamplePoint(1, pos2.toArray(), vel2.toArray(), acc2.toArray());

        // WHEN
        // Interpolate at data points
        final double[][] interpolated1 = interpolator.derivatives(0, 2);
        final double[][] interpolated2 = interpolator.derivatives(1, 2);

        // THEN
        // Create equivalent PV
        final Vector3D interpolatedPos1 = new Vector3D(interpolated1[0][0],
                                                       interpolated1[0][1],
                                                       interpolated1[0][2]);
        final Vector3D interpolatedVel1 = new Vector3D(interpolated1[1][0],
                                                       interpolated1[1][1],
                                                       interpolated1[1][2]);
        final Vector3D interpolatedAcc1 = new Vector3D(interpolated1[2][0],
                                                       interpolated1[2][1],
                                                       interpolated1[2][2]);

        final Vector3D interpolatedPos2 = new Vector3D(interpolated2[0][0],
                                                       interpolated2[0][1],
                                                       interpolated2[0][2]);
        final Vector3D interpolatedVel2 = new Vector3D(interpolated2[1][0],
                                                       interpolated2[1][1],
                                                       interpolated2[1][2]);
        final Vector3D interpolatedAcc2 = new Vector3D(interpolated2[2][0],
                                                       interpolated2[2][1],
                                                       interpolated2[2][2]);

        // Show difference with data points
        System.out.println("Difference with PV1");
        System.out.println(pos1.subtract(interpolatedPos1));
        System.out.println(vel1.subtract(interpolatedVel1));
        System.out.println(acc1.subtract(interpolatedAcc1));
        System.out.println();
        System.out.println("Difference with PV2");
        System.out.println(pos2.subtract(interpolatedPos2));
        System.out.println(vel2.subtract(interpolatedVel2));
        System.out.println(acc2.subtract(interpolatedAcc2));
    }
}

Cheers,
Vincent