How to resolve the algorithm Hilbert curve step by step in the Java programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Hilbert curve step by step in the Java programming language

Table of Contents

Problem Statement

Produce a graphical or ASCII-art representation of a Hilbert curve of at least order 3.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Hilbert curve step by step in the Java programming language

Overview:

The code implements the Hilbert curve, a space-filling curve that traverses a 2D space in a continuous and non-intersecting manner.

Key Concepts:

  • Hilbert curve: A mathematical curve that fills a 2D space without crossing itself.
  • Space-filling curve: A curve that covers every point in a given space without leaving any gaps or overlaps.

Classes:

  • Point: Represents a point in the 2D plane.
  • HilbertCurve: Contains methods for generating and drawing the Hilbert curve.

Methods:

Point class:

  • rot(int n, boolean rx, boolean ry): Rotates/flips the point around a given quadrant.
  • calcD(int n): Calculates the Hilbert index (distance) of the point.

HilbertCurve class:

  • fromD(int n, int d): Generates a point from a given Hilbert index.
  • getPointsForCurve(int n): Generates a list of points along the Hilbert curve of order n.
  • drawCurve(List<Point> points, int n): Draws the Hilbert curve in ASCII art, separating lines by 3 characters to account for vertical lines.

main function:

  • Generates Hilbert curves of orders 1 to 5 and prints them to the console.

Implementation Details:

  • The calcD method uses the Hilbert index formula:
    d = Σ(s * s * ((rx ? 3 : 0) ^ (ry ? 1 : 0)))
    
    where s is the quadrant size, rx and ry indicate if the point is in the X or Y direction, respectively.
  • The rot method effectively rotates/flips the point around specific quadrants based on the input parameters.
  • The fromD method uses the inverse of the Hilbert index formula to reconstruct a point from an index.
  • The drawCurve method draws the curve as a string of characters representing lines and spaces.
  • The main function demonstrates the curve by varying the order, generating points, and drawing the ASCII art representation.

Usage:

This code can be used to explore the properties of the Hilbert curve, including its space-filling nature and fractal-like patterns. It can also be applied in various fields such as image compression and spatial indexing.

Source code in the java programming language

// Translation from https://en.wikipedia.org/wiki/Hilbert_curve

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class HilbertCurve {
    public static class Point {
        public int x;
        public int y;
        
        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }
        
        public String toString() {
            return "(" + x + ", " + y + ")";
        }
        
        //rotate/flip a quadrant appropriately
        public void rot(int n, boolean rx, boolean ry) {
            if (!ry) {
                if (rx) {
                    x = (n - 1) - x;
                    y = (n - 1) - y;
                }
        
                //Swap x and y
                int t  = x;
                x = y;
                y = t;
            }
            
            return;
        }
        
        public int calcD(int n) {
            boolean rx, ry;
            int d = 0;
            for (int s = n >>> 1; s > 0; s >>>= 1) {
                rx = ((x & s) != 0);
                ry = ((y & s) != 0);
                d += s * s * ((rx ? 3 : 0) ^ (ry ? 1 : 0));
                rot(s, rx, ry);
            }
            
            return d;
        }
        
    }

    public static Point fromD(int n, int d) {
        Point p = new Point(0, 0);
        boolean rx, ry;
        int t = d;
        for (int s = 1; s < n; s <<= 1) {
            rx = ((t & 2) != 0);
            ry = (((t ^ (rx ? 1 : 0)) & 1) != 0);
            p.rot(s, rx, ry);
            p.x += (rx ? s : 0);
            p.y += (ry ? s : 0);
            t >>>= 2;
        }
        return p;
    }
    
    public static List<Point> getPointsForCurve(int n) {
        List<Point> points = new ArrayList<Point>();
        for (int d = 0; d < (n * n); d++) {
            Point p = fromD(n, d);
            points.add(p);
        }
        
        return points;
    }
    
    public static List<String> drawCurve(List<Point> points, int n) {
        char[][] canvas = new char[n][n * 3 - 2];
        for (char[] line : canvas) {
            Arrays.fill(line, ' ');
        }
        for (int i = 1; i < points.size(); i++) {
             Point lastPoint = points.get(i - 1);
            Point curPoint = points.get(i);
            int deltaX = curPoint.x - lastPoint.x;
            int deltaY = curPoint.y - lastPoint.y;
            if (deltaX == 0) {
                if (deltaY == 0) {
                    // A mistake has been made
                    throw new IllegalStateException("Duplicate point, deltaX=" + deltaX + ", deltaY=" + deltaY);
                }
                // Vertical line
                int row = Math.max(curPoint.y, lastPoint.y);
                int col = curPoint.x * 3;
                canvas[row][col] = '|';
            }
            else {
                if (deltaY != 0) {
                    // A mistake has been made
                    throw new IllegalStateException("Diagonal line, deltaX=" + deltaX + ", deltaY=" + deltaY);
                }
                // Horizontal line
                int row = curPoint.y;
                int col = Math.min(curPoint.x, lastPoint.x) * 3 + 1;
                canvas[row][col] = '_';
                canvas[row][col + 1] = '_';
            }
            
        }
        List<String> lines = new ArrayList<String>();
        for (char[] row : canvas) {
            String line = new String(row);
            lines.add(line);
        }
        
        return lines;
    }
    
    public static void main(String... args) {
        for (int order = 1; order <= 5; order++) {
            int n = (1 << order);
            List<Point> points = getPointsForCurve(n);
            System.out.println("Hilbert curve, order=" + order);
            List<String> lines = drawCurve(points, n);
            for (String line : lines) {
                System.out.println(line);
            }
            System.out.println();
        }
        return;
    }
}


  

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