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:
whered = Σ(s * s * ((rx ? 3 : 0) ^ (ry ? 1 : 0)))
s
is the quadrant size,rx
andry
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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