Collision calculation for a ball on a curve. It finds the closest point to the ball on the curve and checks if there is a collision between between them.

CurveCollision.java

    public static double curveCollision(Vecteur ballPosition, double ballRadius, Vecteur vitesse, final Vecteur startPoint, final Vecteur controlPoint, final Vecteur endPoint) {
        Vecteur closestPointToBall = getClosestPointToCubicBezier(
                ballPosition, startPoint, controlPoint, endPoint
        );

        double distanceWithBall = Math.sqrt((ballPosition.x - closestPointToBall.x) * (ballPosition.x - closestPointToBall.x) + (ballPosition.y - closestPointToBall.y) * (ballPosition.y - closestPointToBall.y));

        if (distanceWithBall > ballRadius + 10) {
            return 0;
        } else {
            // why such points are colliding with the ball ??? Vecteur(48, 30)
            Vecteur[] base = Geop.base( startPoint, endPoint);
            Vecteur N = base[1];
            double vN = vitesse.produitScalaire(N);
            Vecteur deltaV = N.produit(-3*vN);  // calcul du changement de trajectoire
            vitesse.ajoute(deltaV); // la bille rebondit
            return vN; // HERE WAS RETURN TRUE BEFORE
        }
    }

    /** helper function for curveCollision() **/
    private static Vecteur getClosestPointToCubicBezier(Vecteur base, Vecteur startPoint, Vecteur controlPoint, Vecteur endPoint)  {
        double curveDistanceEstimation = controlPoint.somme(startPoint).somme(endPoint).norme();
        long slices = Math.round(curveDistanceEstimation * CURVE_PRECISION_COEF);
        double tick = 1d / (double) slices;
        double x;
        double y;
        double t;
        Vecteur best = new Vecteur(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
        double bestDistance = Double.POSITIVE_INFINITY;
        double currentDistance;
        for (int i = 0; i <= slices; i++) {
            t = i * tick;
            x = (1 - t) * (1 - t) * startPoint.x + 2 * (1 - t) * t * controlPoint.x + t * t * endPoint.x;
            y = (1 - t) * (1 - t) * startPoint.y + 2 * (1 - t) * t * controlPoint.y + t * t * endPoint.y;

            currentDistance = Math.sqrt((base.x-x)*(base.x-x) + (base.y-y)*(base.y-y));
            if (currentDistance < bestDistance) {
                bestDistance = currentDistance;
                best.x = x;
                best.y = y;
            }
        }
        return best;
    }