Java——謝爾賓斯地毯，三角形

目錄：

1.地毯理解及代碼

2.三角形理解及代碼

3.地毯+三角形+畫圖板表示

下圖就是我在Java畫圖板上畫出的一個謝爾賓斯地毯

1.地毯理解及代碼

製做謝爾賓斯地毯咱們須要用到——迭代

理解：

咱們能夠看出2圖是由若干個1圖這樣的基本圖形組成的

一樣無論迭代多少次都是由基本圖形組成

因此咱們的任務就是畫出1圖這樣的基本圖形，剩下的就交給迭代去完成

算法

public void draw(Graphics g,int n,int x,int y,int width,int height) {
        
        /**
        *x:左上角x座標，y:左上角y座標
        *width:寬，height：高
        *n：迭代層次
        */
        g.fillRect(x+width/3,y+height/3,width/3,height/3);
        
        if(n==0)//遞歸結束條件
            return;
        n--;
        
        //八個維度
        draw(g,n,x, y, width/3, height/3);    //1
        draw(g,n,x+width/3, y, width/3, height/3);//2
        draw(g,n,x+2*(width/3), y, width/3, height/3);//3
                 
        draw(g,n,x, y+height/3, width/3, height/3);//4
        draw(g,n,x+2*(width/3), y+height/3, width/3, height/3);//5
                 
        draw(g,n,x, y+2*(height/3), width/3, height/3);//6
        draw(g,n,x+width/3, y+2*(height/3), width/3, height/3);//7
        draw(g,n,x+2*(width/3), y+2*(height/3), width/3, height/3);//8
    }

2.三角形理解及代碼

理解：
原理和地毯同樣，都要用到迭代

這是最基礎的謝爾賓斯三角形

最外面的大三角形的三個座標是咱們本身取的

咱們只要知道六個頂點，畫出六條直線，剩下的就能夠交給遞歸了

假設最外層三角形的座標分別爲（x1,y1）(x2,y2)，(x3,y3)

那麼三個中點的座標就是

1. ( (x1+x2)/2, (y1+y2)/2 ）
2. ( (x1+x3)/2, (y1+y3)/2 )
3. ( (x3+x2)/2, (y3+y2)/2 )

public void drawtri(Graphics g,int n,int x1,int y1,int x2,int y2,int x3,int y3 ){
        
        g.drawLine(x1,y1,x2,y2);
        g.drawLine(x3,y3,x2,y2);
        g.drawLine(x1,y1,x3,y3);
        g.drawLine((x1+x2)/2,(y1+y2)/2,(x1+x3)/2,(y1+y3)/2);
        g.drawLine((x1+x2)/2,(y1+y2)/2,(x2+x3)/2,(y2+y3)/2);
        g.drawLine((x3+x2)/2,(y3+y2)/2,(x1+x3)/2,(y1+y3)/2);
        
        if(n==0)
            return;
        n--;
        drawtri(g,n,x1,y1,(x1+x2)/2,(y1+y2)/2,(x1+x3)/2,(y1+y3)/2);
        drawtri(g,n,(x1+x2)/2,(y1+y2)/2,x2,y2,(x3+x2)/2,(y3+y2)/2);
        drawtri(g,n,(x1+x3)/2,(y1+y3)/2,(x2+x3)/2,(y2+y3)/2,x3,y3);
    }

3.地毯+三角形+畫圖板表示

咱們在畫圖板上加上兩個按鈕，達到點擊按鈕

以鼠標點擊與落下的線段做爲地毯的對角線去繪製地毯

以咱們在畫圖板上點擊的三個點去繪製三角形

畫圖板類：

import javax.swing.JFrame;               //窗體
import javax.swing.JButton;              //按鈕

import java.awt.FlowLayout;              //流式佈局器
import java.awt.Graphics;                //畫筆


public class DrawPad {
    public static void main(String args[]){
        DrawPad dp = new DrawPad();//建立畫圖板對象
        dp.showUI();
        
        
    }
    
    public void showUI(){
        JFrame jf = new JFrame();
        
        DrawPadListener dl = new DrawPadListener();
        String[] brnstrs = {"地毯","三角形"};
        for (int i = 0; i < brnstrs.length; i++) {
            JButton btn = new JButton(brnstrs[i]);
            btn.setName(brnstrs[i]);
            btn.addActionListener(dl);//按鈕添加監聽器
            jf.add(btn);//將按鈕添加到窗體上
        }

        FlowLayout fl = new FlowLayout();
        //流式佈局器，使得添加到窗體上的組件從上到下，從左到右排列
        //JFrame默認是
        
        jf.setTitle("可視化");                  //名稱
        jf.setSize(800,600);               //尺寸
        jf.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);    //關閉進程
        jf.setLayout(fl);            //設置流式佈局
        jf.setResizable(false);      //不能夠改變窗體大小
        jf.setLocationRelativeTo(null);//居中顯示
        jf.addMouseListener(dl);
        jf.setVisible(true);             //設置窗體可視
    
        
        Graphics g = jf.getGraphics();    //取畫筆    
        dl.g = g;
    }
}

監聽器類：

package 分形;

import java.awt.Color;               //顏色
import java.awt.Graphics;            //畫筆
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;//動做監聽器
import java.awt.event.MouseEvent;
import java.awt.event.MouseListener; //鼠標監聽器

import java.util.Random;

public class DrawPadListener implements MouseListener, ActionListener{
    
    String btnstr;
    Graphics g;
    
    int x1,x2,y1,y2,x3,y3,x4,y4,x5,y5;
    int count = 0;
    int n = 1;
    Random r = new Random();
    public void actionPerformed(ActionEvent e){
        btnstr = e.getActionCommand();
        System.out.println("actionPerformed方法被調用，btnstr爲："+btnstr);            
    }
    
    public void mouseClicked(MouseEvent e){
        System.out.println("點擊");        
    }

   
    public void mousePressed(MouseEvent e){
        System.out.println("按下");
        x1=e.getX();
        y1=e.getY();
        double a,b,c,d;
        
        if(btnstr.equals("三角形")){
            if(count == 0){
                x3 = e.getX();
                y3 = e.getY(); 
                count++;
            }else if(count==1){
                x4 = e.getX();
                y4 = e.getY(); 
                count++;
            }else if(count==2){
                x5 = e.getX();
                y5 = e.getY(); 
                drawtri(g,n,x3,y3,x4,y4,x5,y5);
                count = 0;
            }                        
        }        
    }

    public void mouseReleased(MouseEvent e){
        System.out.println("釋放");
        
        x2=e.getX();
        y2=e.getY();//釋放點的座標

        if(btnstr.equals("地毯"))
            drawcpt(g,n,x1,y1,x2-x1,y2-y1);
    }

    public void mouseEntered(MouseEvent e){
        System.out.println("進入");
    }
    
    public void mouseExited(MouseEvent e){
        System.out.println("退出");
    }
      
    //謝爾賓斯地毯
    public void drawcpt(Graphics g,int n,int x,int y,int width,int height) {                
        g.fillRect(x+width/3,y+height/3,width/3,height/3);
  
        if(n==0)//遞歸結束條件
            return;
        n--;
        drawcpt(g,n,x, y, width/3, height/3);
        drawcpt(g,n,x+width/3, y, width/3, height/3);
        drawcpt(g,n,x+2*(width/3), y, width/3, height/3);
                 
        drawcpt(g,n,x, y+height/3, width/3, height/3);
        drawcpt(g,n,x+2*(width/3), y+height/3, width/3, height/3);
                 
        drawcpt(g,n,x, y+2*(height/3), width/3, height/3);
        drawcpt(g,n,x+width/3, y+2*(height/3), width/3, height/3);
        drawcpt(g,n,x+2*(width/3), y+2*(height/3), width/3, height/3);
    }
    
    //謝爾賓斯三角形
    public void drawtri(Graphics g,int n,int x1,int y1,int x2,int y2,int x3,int y3 ){
        
        g.drawLine(x1,y1,x2,y2);
        g.drawLine(x3,y3,x2,y2);
        g.drawLine(x1,y1,x3,y3);
        g.drawLine((x1+x2)/2,(y1+y2)/2,(x1+x3)/2,(y1+y3)/2);
        g.drawLine((x1+x2)/2,(y1+y2)/2,(x2+x3)/2,(y2+y3)/2);
        g.drawLine((x3+x2)/2,(y3+y2)/2,(x1+x3)/2,(y1+y3)/2);
        
        if(n==0)
            return;
        n--;
        drawtri(g,n,x1,y1,(x1+x2)/2,(y1+y2)/2,(x1+x3)/2,(y1+y3)/2);
        drawtri(g,n,(x1+x2)/2,(y1+y2)/2,x2,y2,(x3+x2)/2,(y3+y2)/2);
        drawtri(g,n,(x1+x3)/2,(y1+y3)/2,(x2+x3)/2,(y2+y3)/2,x3,y3);
    }
}