JavaFX interpolator for a line of best fit through a set of points.

BestFitSplineDemo.java

import javafx.animation.*;
import javafx.application.Application;
import javafx.scene.* ;
import javafx.scene.paint.*;
import javafx.scene.shape.*;
import javafx.stage.Stage;
import javafx.util.Duration;

public class BestFitSplineDemo extends Application {

  private static final Duration CYCLE_TIME = Duration.seconds(7);

  private static final int PLOT_SIZE = 500;
  private static final int N_SEGS    = PLOT_SIZE / 10;

  public void start(Stage stage) {
    Path path = new Path();
    path.setStroke(Color.DARKGREEN);

    final Interpolator pathInterpolator = new BestFitSplineInterpolator(
      new double[] { 0.0, 0.25, 0.5, 0.75, 1.0 },
      new double[] { 0.0, 0.5,  0.3, 0.8,  0.0 }
    );

    // interpolated spline function plot.
    plotSpline(path, pathInterpolator, true);

    // animated dot moving along the plot according to a distance over time function.
    final Interpolator timeVsDistanceInterpolator = new BestFitSplineInterpolator(
        new double[] { 0.0, 0.25, 0.5, 0.75, 1.0 },
        new double[] { 0.0, 0.1,  0.4, 0.85, 1.0 }
    );

    Circle dot = new Circle(5, Color.GREENYELLOW);
    PathTransition transition = new PathTransition(CYCLE_TIME, path, dot);
    transition.setInterpolator(timeVsDistanceInterpolator);
    transition.setAutoReverse(true);
    transition.setCycleCount(PathTransition.INDEFINITE);
    transition.play();

    // show a light grey path representing the distance over time.
    Path timeVsDistancePath = new Path();
    timeVsDistancePath.setStroke(Color.DIMGRAY.darker());
    timeVsDistancePath.getStrokeDashArray().setAll(15d, 10d, 5d, 10d);
    plotSpline(timeVsDistancePath, timeVsDistanceInterpolator, true);

    stage.setScene(
      new Scene(
        new Group(
          timeVsDistancePath,
          path,
          dot
        ),
        Color.rgb(35,39,50)
      )
    );
    stage.show();
  }

  // plots an interpolated curve in segments along a path
  // if invert is true then y=0 will be in the bottom left, otherwise it is in the top right
  private void plotSpline(Path path, Interpolator pathInterpolator, boolean invert) {
    final double y0 = pathInterpolator.interpolate(0, PLOT_SIZE, 0);
    path.getElements().addAll(
      new MoveTo(0, invert ? PLOT_SIZE - y0 : y0)
    );

    for (int i = 0; i < N_SEGS; i++) {
      final double frac = (i + 1.0) / N_SEGS;
      final double x = frac * PLOT_SIZE;
      final double y = pathInterpolator.interpolate(0, PLOT_SIZE, frac);
      path.getElements().add(new LineTo(x, invert ? PLOT_SIZE - y : y));
    }
  }

  public static void main(String[] args) { launch(args); }
}

BestFitSplineInterpolator.java

import javafx.animation.Interpolator;
import org.apache.commons.math3.analysis.interpolation.SplineInterpolator;
import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
 
public class BestFitSplineInterpolator extends Interpolator {
 
  final PolynomialSplineFunction f;
 
  BestFitSplineInterpolator(double[] x, double[] y) {
    f = new SplineInterpolator().interpolate(x, y);
  }
 
  @Override protected double curve(double t) {
    return f.value(t);
  }
}

Answer to JavaFX forum question: Using more than 2 control points in Interpolater.Spline

This interpolator differs a little from the Interpolator.SPLINE interpolator that comes with JavaFX.
Instead of control points which bend the curve but do not lie on the curve, the interpolator takes a set of points and plots a curve of best fit directly through the points.

Relies on apache commons math 3.2