创建10.000个连接的六边形页面？

Question

我试图创建像蜜蜂梳子那样相互连接的10.000个六边形，我想将所有这些都创建为一个元素，然后将一些东西导入其中，但是为了将六边形连接在一起，我的算法在连接了前6个元素后就卡住了。这是我在Java中的算法。我用Java进行测试。另外，我想使它们的尺寸比连接前更小。

angle= 2*Math.PI/6;
        for (int i=0 ;i<6;i++){

        double v = i*angle-(15);

        pentagon pent = new pentagon(6, 60, a);
        a.x=a.x+(int)Math.round(105*Math.cos(v));
        a.y=a.y+(int)Math.round(105*Math.sin(v));

        pentagonList.add(pent);

这是我的五角形课

import javax.swing.*;
import java.awt.*;
import java.awt.event.*;

/**
 *
 * @author Meko
 */
public class pentagon extends JPanel {

    private int n, r;
    private double angle;
    public int[] x, y;


    Point c;
    int posX, posY;

    public pentagon(int pieces, int radie, Point center) {

        c = center;
        n = pieces;
        r = radie;
        x = new int[n];
        y = new int[n];
        angle = 2 * Math.PI / n;

        posX = c.x + 1024 / 2;
        posY = c.y + 1024 / 2;
    }

    public void drawMe(Graphics g) {

        g.drawString("CENTER", posX, posY);
        //System.out.print(" xO:  "+x0);
        for (int i = 0; i < n; i++) {
            double v = i * angle - (6 * 2 * Math.PI / 360) + 15;
            x[i] = posX + (int) Math.round(r * Math.cos(v));

            //   System.out.print(" x:  "+x[i]);
            y[i] = posY + (int) Math.round(r * Math.sin(v));
            g.drawString("" + i, x[i], y[i]);
        }
        g.drawPolygon(x, y, n);


    }

}

Answer 1

创建矩形网格非常明显-只需倾斜矩形网格（要么全部倾斜并获得平行四边形，然后使用模将其包装，要么倾斜交替的行/列以创建矩形网格）。

创建一个充满六边形的六边形也相当容易

• 在第 n 个等级中，有6条 n 进制的条形
• 相邻六边形的中心的位移是其中一个面的中点到中心的距离的两倍

因此，如果您在两个数组中都有十六进制的x和y坐标，polyX并且polyY，则会得到一个嵌套循环：

    drawHex ( g, cx, cy, 0 );

    for ( int rank = 1; rank < count; ++rank ) {

        for ( int bar = 0; bar < 6; ++bar ) {
            // x and y are twice midpoint of the previous face * the rank away 
            // from centre
            int x = cx + ( polyX [ ( bar + 4 ) % 6 ] + polyX [ ( bar + 5 ) % 6 ] ) * rank;
            int y = cy + ( polyY [ ( bar + 4 ) % 6 ] + polyY [ ( bar + 5 ) % 6 ] ) * rank;

            // move by twice the distance of the midpoint of the next face each time 
            int dx = polyX [ bar ] + polyX [ ( bar + 1 ) % 6 ];
            int dy = polyY [ bar ] + polyY [ ( bar + 1 ) % 6 ];

            for ( int hex = 0; hex < rank; ++hex ) {
                drawHex ( g, x, y, rank );
                x += dx;
                y += dy;
            }
        }
    }

完整示例：

import javax.swing.*;
import java.awt.*;

public class Hexagons
{
    public static void main ( String...args ) throws Exception
    {
        SwingUtilities.invokeAndWait ( new Runnable () {
            @Override
            public void run () {
                new Hexagons().run();
            }
        } );
    }

    Hexagons ()
    {
        final JFrame frame = new JFrame();

        frame.setDefaultCloseOperation ( JFrame.EXIT_ON_CLOSE );

        final JPanel panel = new JPanel () {
            @Override
            public void paintComponent ( Graphics g ) {
                Graphics2D g2D = ( Graphics2D ) g;

                g2D.setRenderingHint ( RenderingHints.KEY_ANTIALIASING,
                RenderingHints.VALUE_ANTIALIAS_ON );

                drawHexes ( g2D, getWidth() / 2, getHeight() / 2 );
            }
        };

        count = 5;

        frame.add ( panel );
        frame.setSize ( 400, 400 );
        frame.setVisible ( true );

    }

    void run () { }

    int count;


    void drawHexes ( Graphics2D g, int cx, int cy )
    {
        int count = Math.min ( 20, Math.min ( cx, cy ) / 34 );

        drawHex ( g, cx, cy, 0 );

        for ( int rank = 1; rank < count; ++rank ) {

            for ( int bar = 0; bar < 6; ++bar ) {
                int x = ( polyX [ ( bar + 4 ) % 6 ] + polyX [ ( bar + 5 ) % 6 ] ) * rank;
                int y = ( polyY [ ( bar + 4 ) % 6 ] + polyY [ ( bar + 5 ) % 6 ] ) * rank;

                int dx = polyX [ bar ] + polyX [ ( bar + 1 ) % 6 ];
                int dy = polyY [ bar ] + polyY [ ( bar + 1 ) % 6 ];

                for ( int hex = 0; hex < rank; ++hex ) {
                    drawHex ( g, cx + x, cy + y, rank );
                    x += dx;
                    y += dy;
                }
            }
        }
    }

    static int polyX[] = { 20, 10, -10, -20, -10,  10 };
    static int polyY[] = {  0, 17,  17,   0, -17, -17 }; 
    static Color fill[] = new Color[20];
    static Color line[] = new Color[20];
    static BasicStroke stroke = new BasicStroke ( 1.5f );

    // make it pretty
    static {
        for ( int rank = 0; rank < 20; ++rank ) {
            double theta0 = rank * 2 * Math.PI / 20;
            double theta1 = theta0 + Math.PI * 2.0/3.0;
            double theta2 = theta1 + Math.PI * 2.0/3.0;

            fill [ rank ] = new Color ( 
                ( int ) ( 128 + 64 * Math.sin ( theta0 ) ),
                ( int ) ( 128 + 64 * Math.sin ( theta1 ) ),
                ( int ) ( 128 + 64 * Math.sin ( theta2 ) ) );
            line [ rank ] = new Color ( 
                ( int ) ( 64+ 32 * Math.sin ( theta0 ) ),
                ( int ) ( 64 + 32 * Math.sin ( theta1 ) ),
                ( int ) ( 64+ 32 * Math.sin ( theta2 ) ) );
        }
    }

    void drawHex ( Graphics2D g, int cx, int cy, int rank ) {
        g.translate ( cx, cy );
        g.setPaint ( fill [ rank ] );
        g.fillPolygon ( polyX, polyY, 6 );
        g.setColor ( line [ rank ] );
        g.setStroke ( stroke );
        g.drawPolygon ( polyX, polyY, 6 );
        g.translate ( -cx, -cy );
    }
}