Algorithm to generate a hexagonal grid with coordinate system
I am trying to roll up 19 lines of code into a single for loop, but I am feeling a bit stumped. The reason I ask, is because I want the grid to be other sizes instead of 5.
In Main::drawHexGridAdvanced(), I am trying to deduce the similarities between each line as opposed to Main::drawHexGridBasic() where I am hard-coding values.
I am not sure how to determine the start of the x for each column in each row, because the pattern for n == 5 is 0, -1 -2 -2 -2 after that each consecutive column is just incremented except when the loop reaches the halfway point...
Information and Understanding
`n` must be odd
n | columns-per row sequence
--+-------------------------
3 | 2 3 2
5 | 3 4 5 4 3
7 | 4 5 6 7 6 5 4
9 | 5 6 7 8 9 8 7 6 5
int[] columns(int n) {
int[] columns = new int[n];
int h = (int) java.lang.Math.floor(n / 2);
for (int i = 0; i < n; i++) {
columns[i] = n - java.lang.Math.abs(i - h);
}
return columns;
}
// Prints [5, 6, 7, 8, 9, 8, 7, 6, 5]
System.out.println(java.util.Arrays.toString(columns(n)));
Python looks so much more elegant:
def hex(n):
for x in [(n-abs(x-int(n/2))) for x in range(n)]:
for y in range(n-x):
print(' '),
for y in range(x):
print(' * '),
print('')
hex(5)
# * * *
# * * * *
# * * * * *
# * * * *
# * * *
Here is my expected output:
Main.java
package Foo.Bar.Hexagon;
import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.Font;
import java.awt.FontMetrics;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Stroke;
import javax.swing.JFrame;
import javax.swing.JPanel;
public class Main extends JPanel {
private static final long serialVersionUID = 1L;
private final int WIDTH = 1200;
private final int HEIGHT = 800;
private final int W2 = WIDTH / 2;
private final int H2 = HEIGHT / 2;
private Font font = new Font("Arial", Font.BOLD, 24);
FontMetrics metrics;
public Main() {
setPreferredSize(new Dimension(WIDTH, HEIGHT));
}
@Override
public void paintComponent(Graphics g) {
Graphics2D g2d = (Graphics2D) g;
g2d.setStroke(new BasicStroke(4.0f, BasicStroke.CAP_SQUARE, BasicStroke.JOIN_MITER));
g2d.setFont(font);
metrics = g.getFontMetrics();
drawCircle(g2d, W2, H2, 660, true, true, 0x4488FF, 0);
drawHexGridAdvanced(g2d, 5, 60);
}
private void drawHexGridAdvanced(Graphics g, int n, int r) {
double ang30 = Math.toRadians(30);
double xOff = Math.cos(ang30) * r;
double yOff = Math.sin(ang30) * r;
int h = n / 2;
int cols = 0;
int row = 0;
int col = 0;
cols = 3;
row = 0; col = 0;
drawHex(g, +0, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 - yOff * (n - cols) * 3), r);
row = 0; col = 1;
drawHex(g, +1, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 - yOff * (n - cols) * 3), r);
row = 0; col = 2;
drawHex(g, +2, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 - yOff * (n - cols) * 3), r);
cols = 4;
row = 1; col = 0;
drawHex(g, -1, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 - yOff * (n - cols) * 3), r);
row = 1; col = 1;
drawHex(g, +0, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 - yOff * (n - cols) * 3), r);
row = 1; col = 2;
drawHex(g, +1, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 - yOff * (n - cols) * 3), r);
row = 1; col = 3;
drawHex(g, +2, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 - yOff * (n - cols) * 3), r);
cols = 5;
row = 2; col = 0;
drawHex(g, -2, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
row = 2; col = 1;
drawHex(g, -1, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
row = 2; col = 2;
drawHex(g, +0, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
row = 2; col = 3;
drawHex(g, +1, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
row = 2; col = 4;
drawHex(g, +2, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
cols = 4;
row = 3; col = 0;
drawHex(g, -2, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
row = 3; col = 1;
drawHex(g, -1, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
row = 3; col = 2;
drawHex(g, +0, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
row = 3; col = 3;
drawHex(g, +1, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
cols = 3;
row = 4; col = 0;
drawHex(g, -2, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
row = 4; col = 1;
drawHex(g, -1, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
row = 4; col = 2;
drawHex(g, +0, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
}
private void drawHexGridBasic(Graphics g, int n, int r) {
double ang30 = Math.toRadians(30);
double xOff = Math.cos(ang30) * r;
double yOff = Math.sin(ang30) * r;
int h = n / 2;
drawHex(g, +0, -2, W2 - (int) (xOff * 2), H2 - (int) (yOff * 6), r);
drawHex(g, +1, -2, W2 - (int) (xOff * 0), H2 - (int) (yOff * 6), r);
drawHex(g, +2, -2, W2 + (int) (xOff * 2), H2 - (int) (yOff * 6), r);
drawHex(g, -1, -1, W2 - (int) (xOff * 3), H2 - (int) (yOff * 3), r);
drawHex(g, +0, -1, W2 - (int) (xOff * 1), H2 - (int) (yOff * 3), r);
drawHex(g, +1, -1, W2 + (int) (xOff * 1), H2 - (int) (yOff * 3), r);
drawHex(g, +2, -1, W2 + (int) (xOff * 3), H2 - (int) (yOff * 3), r);
drawHex(g, -2, +0, W2 - (int) (xOff * 4), H2 - (int) (yOff * 0), r);
drawHex(g, -1, +0, W2 - (int) (xOff * 2), H2 - (int) (yOff * 0), r);
drawHex(g, +0, +0, W2 - (int) (xOff * 0), H2 - (int) (yOff * 0), r);
drawHex(g, +1, +0, W2 + (int) (xOff * 2), H2 - (int) (yOff * 0), r);
drawHex(g, +2, +0, W2 + (int) (xOff * 4), H2 - (int) (yOff * 0), r);
drawHex(g, -2, +1, W2 - (int) (xOff * 3), H2 + (int) (yOff * 3), r);
drawHex(g, -1, +1, W2 - (int) (xOff * 1), H2 + (int) (yOff * 3), r);
drawHex(g, +0, +1, W2 + (int) (xOff * 1), H2 + (int) (yOff * 3), r);
drawHex(g, +1, +1, W2 + (int) (xOff * 3), H2 + (int) (yOff * 3), r);
drawHex(g, -2, +2, W2 - (int) (xOff * 2), H2 + (int) (yOff * 6), r);
drawHex(g, -1, +2, W2 - (int) (xOff * 0), H2 + (int) (yOff * 6), r);
drawHex(g, +0, +2, W2 + (int) (xOff * 2), H2 + (int) (yOff * 6), r);
}
private void drawHex(Graphics g, int posX, int posY, int x, int y, int r) {
Hexagon hex = new Hexagon(x, y, r);
String text = String.format("%s : %s", coord(posX), coord(posY));
int w = metrics.stringWidth(text);
int h = metrics.getHeight();
g.setColor(new Color(0x008844));
g.fillPolygon(hex);
g.setColor(new Color(0xFFDD88));
g.drawPolygon(hex);
g.setColor(new Color(0xFFFFFF));
g.drawString(text, x - w/2, y + h/2);
}
private String coord(int value) {
return (value > 0 ? "+" : "") + Integer.toString(value);
}
public void drawCircle(Graphics2D g, int x, int y, int diameter,
boolean centered, boolean filled, int colorValue, int lineThickness) {
drawOval(g, x, y, diameter, diameter, centered, filled, colorValue, lineThickness);
}
public void drawOval(Graphics2D g, int x, int y, int width, int height,
boolean centered, boolean filled, int colorValue, int lineThickness) {
// Store before changing.
Stroke tmpS = g.getStroke();
Color tmpC = g.getColor();
g.setColor(new Color(colorValue));
g.setStroke(new BasicStroke(lineThickness, BasicStroke.CAP_ROUND,
BasicStroke.JOIN_ROUND));
int x2 = centered ? x - (width / 2) : x;
int y2 = centered ? y - (height / 2) : y;
if (filled)
g.fillOval(x2, y2, width, height);
else
g.drawOval(x2, y2, width, height);
// Set values to previous when done.
g.setColor(tmpC);
g.setStroke(tmpS);
}
public static void main(String[] args) {
JFrame f = new JFrame();
Main p = new Main();
f.setContentPane(p);
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
}
}
Haxagon.java
package Foo.Bar.Hexagon;
import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.Graphics2D;
import java.awt.Point;
import java.awt.Polygon;
import java.awt.Stroke;
public class Hexagon extends Polygon {
private static final long serialVersionUID = 1L;
public static final int SIDES = 6;
private Point[] points = new Point[SIDES];
private Point center = new Point(0, 0);
private int radius;
private int rotation = 90;
public Hexagon(Point center, int radius) {
npoints = SIDES;
xpoints = new int[SIDES];
ypoints = new int[SIDES];
this.center = center;
this.radius = radius;
updatePoints();
}
public Hexagon(int x, int y, int radius) {
this(new Point(x, y), radius);
}
public int getRadius() {
return radius;
}
public void setRadius(int radius) {
this.radius = radius;
updatePoints();
}
public int getRotation() {
return rotation;
}
public void setRotation(int rotation) {
this.rotation = rotation;
updatePoints();
}
public void setCenter(Point center) {
this.center = center;
updatePoints();
}
public void setCenter(int x, int y) {
setCenter(new Point(x, y));
}
private double findAngle(double fraction) {
return fraction * Math.PI * 2 + Math.toRadians((rotation + 180) % 360);
}
private Point findPoint(double angle) {
int x = (int) (center.x + Math.cos(angle) * radius);
int y = (int) (center.y + Math.sin(angle) * radius);
return new Point(x, y);
}
protected void updatePoints() {
for (int p = 0; p < SIDES; p++) {
double angle = findAngle((double) p / SIDES);
Point point = findPoint(angle);
xpoints[p] = point.x;
ypoints[p] = point.y;
points[p] = point;
System.out.printf("%d. (%d, %d)\n", p, point.x, point.y);
}
}
public void drawPolygon(Graphics2D g, int x, int y, int lineThickness, int colorValue, boolean filled) {
// Store before changing.
Stroke tmpS = g.getStroke();
Color tmpC = g.getColor();
g.setColor(new Color(colorValue));
g.setStroke(new BasicStroke(lineThickness, BasicStroke.CAP_SQUARE, BasicStroke.JOIN_MITER));
if (filled)
g.fillPolygon(xpoints, ypoints, npoints);
else
g.drawPolygon(xpoints, ypoints, npoints);
// Set values to previous when done.
g.setColor(tmpC);
g.setStroke(tmpS);
}
}
I have figured it out, thanks for the feedback Tanmay.
I noticed that the y-offset was incorrect for n - cols and should be row - half instead.
Below is the most comprehensive and compact code I could obtain. Although it is preferred to enter an odd integer for the size, you could enter a positive value. I also added a padding to the offset.
This if-conditional still troubles me: int xLbl = row < half ? col - row : col - half;
private void drawHexGridLoop(Graphics g, Point origin, int size, int radius, int padding) {
double ang30 = Math.toRadians(30);
double xOff = Math.cos(ang30) * (radius + padding);
double yOff = Math.sin(ang30) * (radius + padding);
int half = size / 2;
for (int row = 0; row < size; row++) {
int cols = size - java.lang.Math.abs(row - half);
for (int col = 0; col < cols; col++) {
int xLbl = row < half ? col - row : col - half;
int yLbl = row - half;
int x = (int) (origin.x + xOff * (col * 2 + 1 - cols));
int y = (int) (origin.y + yOff * (row - half) * 3);
drawHex(g, xLbl, yLbl, x, y, radius);
}
}
}
Main.java
import java.awt.*;
import javax.swing.*;
public class Main extends JPanel {
private static final long serialVersionUID = 1L;
private final int WIDTH = 1200;
private final int HEIGHT = 800;
private Font font = new Font("Arial", Font.BOLD, 18);
FontMetrics metrics;
public Main() {
setPreferredSize(new Dimension(WIDTH, HEIGHT));
}
@Override
public void paintComponent(Graphics g) {
Graphics2D g2d = (Graphics2D) g;
Point origin = new Point(WIDTH / 2, HEIGHT / 2);
g2d.setStroke(new BasicStroke(4.0f, BasicStroke.CAP_SQUARE, BasicStroke.JOIN_MITER));
g2d.setFont(font);
metrics = g.getFontMetrics();
drawCircle(g2d, origin, 380, true, true, 0x4488FF, 0);
drawHexGridLoop(g2d, origin, 7, 50, 8);
}
private void drawHexGridLoop(Graphics g, Point origin, int size, int radius, int padding) {
double ang30 = Math.toRadians(30);
double xOff = Math.cos(ang30) * (radius + padding);
double yOff = Math.sin(ang30) * (radius + padding);
int half = size / 2;
for (int row = 0; row < size; row++) {
int cols = size - java.lang.Math.abs(row - half);
for (int col = 0; col < cols; col++) {
int xLbl = row < half ? col - row : col - half;
int yLbl = row - half;
int x = (int) (origin.x + xOff * (col * 2 + 1 - cols));
int y = (int) (origin.y + yOff * (row - half) * 3);
drawHex(g, xLbl, yLbl, x, y, radius);
}
}
}
private void drawHex(Graphics g, int posX, int posY, int x, int y, int r) {
Graphics2D g2d = (Graphics2D) g;
Hexagon hex = new Hexagon(x, y, r);
String text = String.format("%s : %s", coord(posX), coord(posY));
int w = metrics.stringWidth(text);
int h = metrics.getHeight();
hex.draw(g2d, x, y, 0, 0x008844, true);
hex.draw(g2d, x, y, 4, 0xFFDD88, false);
g.setColor(new Color(0xFFFFFF));
g.drawString(text, x - w/2, y + h/2);
}
private String coord(int value) {
return (value > 0 ? "+" : "") + Integer.toString(value);
}
public void drawCircle(Graphics2D g, Point origin, int radius,
boolean centered, boolean filled, int colorValue, int lineThickness) {
// Store before changing.
Stroke tmpS = g.getStroke();
Color tmpC = g.getColor();
g.setColor(new Color(colorValue));
g.setStroke(new BasicStroke(lineThickness, BasicStroke.CAP_ROUND,
BasicStroke.JOIN_ROUND));
int diameter = radius * 2;
int x2 = centered ? origin.x - radius : origin.x;
int y2 = centered ? origin.y - radius : origin.y;
if (filled)
g.fillOval(x2, y2, diameter, diameter);
else
g.drawOval(x2, y2, diameter, diameter);
// Set values to previous when done.
g.setColor(tmpC);
g.setStroke(tmpS);
}
public static void main(String[] args) {
JFrame f = new JFrame();
Main p = new Main();
f.setContentPane(p);
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
}
}
Hexagon.java
import java.awt.*;
public class Hexagon extends Polygon {
private static final long serialVersionUID = 1L;
public static final int SIDES = 6;
private Point[] points = new Point[SIDES];
private Point center = new Point(0, 0);
private int radius;
private int rotation = 90;
public Hexagon(Point center, int radius) {
npoints = SIDES;
xpoints = new int[SIDES];
ypoints = new int[SIDES];
this.center = center;
this.radius = radius;
updatePoints();
}
public Hexagon(int x, int y, int radius) {
this(new Point(x, y), radius);
}
public int getRadius() {
return radius;
}
public void setRadius(int radius) {
this.radius = radius;
updatePoints();
}
public int getRotation() {
return rotation;
}
public void setRotation(int rotation) {
this.rotation = rotation;
updatePoints();
}
public void setCenter(Point center) {
this.center = center;
updatePoints();
}
public void setCenter(int x, int y) {
setCenter(new Point(x, y));
}
private double findAngle(double fraction) {
return fraction * Math.PI * 2 + Math.toRadians((rotation + 180) % 360);
}
private Point findPoint(double angle) {
int x = (int) (center.x + Math.cos(angle) * radius);
int y = (int) (center.y + Math.sin(angle) * radius);
return new Point(x, y);
}
protected void updatePoints() {
for (int p = 0; p < SIDES; p++) {
double angle = findAngle((double) p / SIDES);
Point point = findPoint(angle);
xpoints[p] = point.x;
ypoints[p] = point.y;
points[p] = point;
}
}
public void draw(Graphics2D g, int x, int y, int lineThickness, int colorValue, boolean filled) {
// Store before changing.
Stroke tmpS = g.getStroke();
Color tmpC = g.getColor();
g.setColor(new Color(colorValue));
g.setStroke(new BasicStroke(lineThickness, BasicStroke.CAP_SQUARE, BasicStroke.JOIN_MITER));
if (filled)
g.fillPolygon(xpoints, ypoints, npoints);
else
g.drawPolygon(xpoints, ypoints, npoints);
// Set values to previous when done.
g.setColor(tmpC);
g.setStroke(tmpS);
}
}
Even more compact code is possible, but this gives output without repetition and without if branching.
for (row = 0; row < h; row ++) {
cols = h + row + 1;
for (col = 0; col < cols; col++) {
drawHex(g, col - row, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 - yOff * (n - cols) * 3), r);
}
}
for (row = h; row < n; row++) {
cols = n - row + h;
for (col = 0; col < cols; col++) {
drawHex(g, -h + col, -h + row, (int) (W2 + xOff * (-cols + (col * 2 + 1))), (int) (H2 + yOff * (n - cols) * 3), r);
}
}
Hope this helps.