Hilberts Space-filling Curves in Java

Question

I am trying to create a simple Java applet which should display generated Hilberts Curves in Java. I mixed up my code and some from a book, and now I got stuck. I dont get the display I want to get.

Here is the whole code :

    import java.awt.*;
    import javax.swing.*;
    import java.awt.event.*;
    
    //Defining classes 
    public class HilbertCurves extends JApplet {
        //Declare data fields
        private JTextField OrderTextfield = new JTextField("0",5);
        private HilbertCurve  hilbertCurvePanel = new HilbertCurve();
        
        //Constructors
        public HilbertCurves() {
        //Creating a panel object
        JPanel panel = new JPanel();
        panel.add(new JLabel("Enter the order : "));
        panel.add(OrderTextfield);
        
        OrderTextfield.setHorizontalAlignment(SwingConstants.RIGHT);
        
        //Adding panel to the app
        add(hilbertCurvePanel);
        add(panel, BorderLayout.SOUTH);
        OrderTextfield.addActionListener(new ActionListener(){
        public void actionPerformed(ActionEvent e){
        hilbertCurvePanel.setOrder(Integer.parseInt(OrderTextfield.getText()));
            }
        });
        }
        
        
        private static class HilbertCurve extends JPanel {
        //Declare variables
            private int length;
            private int order=1;
            private int a,b;
            
        //For order
            public void setOrder(int order){
            this.order=order;
            repaint();
            }
            
            public void paintComponent(Graphics g){
            super.paintComponent(g);
            
        //Find the length
            length = Math.min(getWidth(),getHeight());
            for (int i = 0; i < order; i++)
                length/=2;
            
        //Reset
            a = length/2; b=length/2;
            Upper(g,order);
            }
            
        //Display upper
            private void Upper(Graphics g, int order){
                if (order >0){
                    Left(g, order-1);
                    lineNewPosition(g,0,length);
                    Upper(g,order-1);
                    lineNewPosition(g,0,-length);
                    right(g, order-1);
                
                }
            }
        
        //Display left
            private void Left(Graphics g, int order){
                if (order>0){
                    Upper(g,order-1);
                    lineNewPosition(g,length,0);
                    Left(g,order-1);
                    lineNewPosition(g,0,length);
                    Left(g,order-1);
                    lineNewPosition(g,-length,0);
                    Down(g,order-1);
                
                }
            }
            
        //Display right 
             private void right(Graphics g, int order){
                if (order>0){
                    Down(g,order-1);
                    lineNewPosition(g,-length,0);
                    right(g,order-1);
                    lineNewPosition(g,0,-length);
                    right(g,order-1);
                    lineNewPosition(g,length,0);
                    Upper(g,order-1);
                
                }
            }
        
        //Display down 
             private void Down(Graphics g, int order){
                if (order>0){
                    right(g,order-1);
                    lineNewPosition(g,0,-length);
                    Down(g,order-1);
                    lineNewPosition(g,-length,0);
                    Down(g,order-1);
                    lineNewPosition(g,0,length);
                    Left(g,order-1);
                
                }
            }     
        //Draw a line
             public void lineNewPosition(Graphics g, int deltaX, int deltaY){
             g.drawLine(a, b, a + deltaX, b + deltaY);
             a+=deltaX;
             b+=deltaY;
            }
        }
        
        public static void main(String[] args) {
        JApplet applet = new HilbertCurves();
        applet.init();
        applet.start();
        JFrame frame = new JFrame();
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.setTitle("Visualising Hilbert Curves");
        frame.getContentPane().add(applet,BorderLayout.CENTER);
        frame.setSize(512,512);
        frame.setVisible(true);
        }
    }

In my opinion there is something wrong when defining the drawing functions, but at this point it seems I cannot figure out the solution. Here is the output I get (it is different from my goal):

Answer 1

Your drawing code seems a lot longer than necessary.

With a state that consists of a current position and direction, and these primitive operations:

• turn(x) will turn left x*90 degrees (negative numbers turn right)
• step() will draw a line and move forward one step

You can make a Hilbert curve like this:

// draw a hilbert curve.  Resulting total movement will be forward,
// and the current direction is left unchanged
// order: order of curve to draw
// side: -1 to draw on the left, 1 to draw on the right

hilbert(order, side):
    if (order > 0):
        turn(side)
        hilbert(order-1,-side)
        step()
        turn(-side)
        hilbert(order-1,side)
        step()
        hilbert(order-1,side)
        turn(-side)
        step()
        hilbert(order-1,-side)
        turn(side)