Fits a Cubic Bezier curve and allows you to treat it as y = f(x)

CubicBezierCurve.java

import java.util.HashMap;
import java.util.Map;

/**
 * @author kabram.
 *
 */
public class CubicBezierCurve {

    private Point p0, p1, p2, p3;
    private final Map<Double, Double> precomputed = new HashMap<>();


    public void setEndPoints(Point start, Point end) {
        p0 = start;
        p3 = end;
    }


    public void setControlPoints(Point c1, Point c2) {
        p1 = c1;
        p2 = c2;
    }


    public double get(double x, double precision) {
        if (precomputed.containsKey(x)) {
            return precomputed.get(x);
        } else {
            double t = (x - p0.x) / (p3.x - p0.x);
            double x1 = getX(t);
            double left = 0.0;
            double right = 1.0;
            while (Math.abs(x1 - x) > precision) {
                if (x1 < x) {
                    left = t;
                } else {
                    right = t;
                }
                t = (left + right) / 2.0;
                x1 = getX(t);
            }
            return getY(t);
        }
    }


    private double getY(double t) {
        double t2 = Math.pow(t, 2);
        double t3 = Math.pow(t, 3);
        double a = Math.pow(1 - t, 3);
        double b = 3.0 * (t - 2.0 * t2 + t3);
        double c = 3.0 * (t2 - t3);
        double d = t3;

        return a * p0.y + b * p1.y + c * p2.y + d * p3.y;
    }


    private double getX(double t) {
        double t2 = Math.pow(t, 2);
        double t3 = Math.pow(t, 3);
        double a = Math.pow(1 - t, 3);
        double b = 3.0 * (t - 2.0 * t2 + t3);
        double c = 3.0 * (t2 - t3);
        double d = t3;

        return a * p0.x + b * p1.x + c * p2.x + d * p3.x;
    }


    /**
     * @param step Pre-compute values base on step value of x from start.x to end.x.
     */
    public void precompute(double step, double precision) {
        double x = p0.x;
        while (x <= p3.x * Math.signum(step)) {
            precomputed.put(x, get(x, precision));
            x += step;
        }
    }


    public static void main(String[] args) {
        CubicBezierCurve curve = new CubicBezierCurve();

        curve.setEndPoints(new Point(0, 10), new Point(20, 0));
        curve.setControlPoints(new Point(0, 6), new Point(12, 0));
        System.out.println(curve.get(0.18, 0.001));
    }

    public static class Point {

        double x;
        double y;


        public Point() {
            super();
        }


        public Point(double x, double y) {
            super();
            this.x = x;
            this.y = y;
        }


        public static Point xy(double x, double y) {
            return new Point(x, y);
        }
    }

}