double Function

abstract class Func {

    public abstract double apply(double x);

    public Func scale(double fx, double fy) {
        final Func that = this;
        return new Func() {
            public double apply(double x) {
                return that.apply(x/fx)*fy;
            }
        };
    }
    public Func shift(double dx, double dy) {
        final Func that = this;
        return new Func() {
            public double apply(double x) {
                return that.apply(x-dx)+dy;
            }
        };
    }
    public Func combine(double p, Func other) {
        final Func that = this;
        return new Func() {
            public double apply(double x) {
                if(x <= p) return that.apply(x);
                else return other.apply(x);
            }
        };
    }
    public Func flipX() {
        return scale(-1, 1).shift(1, 0);
    }
    public Func flipY() {
        return scale(1, -1).shift(0, 1);
    }
    public Func flipXY() {
        return scale(-1, -1).shift(1, 1);
    }
    public Func inOut() {
        return scale(0.5, 0.5).combine(
                   0.5,
                   flipXY().scale(0.5, 0.5).shift(0.5, 0.5));
    }
}