threeinone.java

插值演示

package mypack;
import java.awt.*;
import java.awt.event.*;
public class ThreeInOne
{
	public static void main(String args[])
	{
		Three t=new Three();
		t.display();
	}
}
class _paint extends Panel implements ActionListener
{
	public int p_count=0,flag=0;
	int point[][]=new int[100][2];
	double h[],ath[],c[],b[],d[],s2[],s1;
	double a[];
	
	int tempx,tempy;
	public _paint()
	{
		p_count=0;
		this.addMouseListener(new IsMouseClicked());
	}
	///////////////////////////
	public void p_random()
	{
		Graphics g = getGraphics();
		g.setColor(Color.black);
		int i,set=0,j,flag=0;
		//p_count=10;
		for(i=0;i<6;i++)
		{
			set=0;
			while(set==0)
			{
				System.out.println("1_");
				tempx=(int)(Math.random()*1000);
				if(tempx>=50&&tempx<=690)
				{
						point[p_count][0]=tempx-401;
						set=1;
				}
			}
			set=0;
			while(set==0)
			{
				System.out.println("2_");
				tempy=(int)(Math.random()*1000);
				if(tempy>=200&&tempy<=300)
				{
					point[p_count][1]=-tempy+281;
					set=1;
				}
			}
			System.out.println("3_");
			p_count++;
			g.fillOval(tempx,tempy,5,5);
		}
	}
	//////////////////////////////
	public void paint(Graphics g)
	{
		g.setColor(Color.black);
		Font fntName=new Font("Serif",0,40);
    	g.setFont(fntName);
 
    	g.drawString("y",378,50);
    	g.drawString("↑",381,50);
    	g.drawRect(400,50,1,450);
    	
    	g.drawRect(40,280,700,1);
    	g.drawString("→",720,295);
    	g.drawString("x",730,305);
    	
    	g.setFont(new Font("Serif",2,25));
    	g.drawString("0",400,300);
	}
	/////////////////////////////////////
	public void drawLagrange()
    {
    	Graphics g = getGraphics();
    	Color color=Color.red;
    	g.setColor(color);
    	if(p_count>1)
    	{    
    		for(int x=point[0][0];x<=point[p_count-1][0];x++)
    		{
    			double t=1,s=0;
    			for(int k=0;k<p_count;k++)
    			{
    				t=1; 
    				for(int i=0;i<p_count;i++)
    				{
    					if(i!=k&&point[k][0]!=point[i][0])
    					{
    						t*=(double)(x-point[i][0])/(point[k][0]-point[i][0]);
    					}
    				}
    				s+=t*point[k][1];
    			}
    			g.fillOval(x+401,281-(int)s,3,3);
    		}
    	}	
    }
    ///////////////////////////////////////
    public void setAarray()
    {
    	a=new double[p_count];
    	int n=p_count-1;
    	for(int ext=0;ext<=n;ext++)
    	{
    		double s=0;
    		double p;
    		for(int k=0;k<=ext;k++)
    		{
    			p=point[k][1];
    			for(int i=0;i<=ext;i++)
    			{
    				if(i!=k)
    				{
    					p/=(double)(point[k][0]-point[i][0]);
    				}
    			}
    			s+=p;
    		}
    		a[ext]=s;
    	}
    }
    public void drawNewton()
    {
    	int m=0;
    	Graphics g = getGraphics();
    	Color color=Color.blue;
    	g.setColor(color);
    	if(p_count>=1)
    	{   m=0;
    		for(int x=point[0][0];x<=point[p_count-1][0];x++)
    		{
    			
    			double p=a[p_count-1];
    			for(int i=p_count-2;i>=0;i--)
    			{
    				if(x!=point[i][0])
    				p=p*(x-point[i][0])+a[i];
    			}
    			if(x==point[m][0]&&m<p_count)
    			{
    				g.fillOval(x+401,281-point[m][1],3,3);
    				m++;
    				//System.out.println("oo");
    			}
    			else
    				g.fillOval(x+401,281-(int)p,3,3);
    		}
    	}
    }
    ///////////////
    public void setParameters()  //prepare for the threeSpline
    {
    	//distribute space for the arrays
    	h=new double[p_count];
    	ath=new double[p_count];
    	c=new double[p_count];
    	d=new double[p_count];
    	b=new double[p_count];
    	s2=new double[p_count];
        
    	int k,n=p_count-1;
    	for(k=0;k<=n-1;k++)  //step 2
    	{
    		h[k]=point[k+1][0]-point[k][0];
    	}
    	ath[1]=2*(h[0]+h[1]);   //step 3
    	for(k=2;k<=n-1;k++)  //step 4
    	{
    		ath[k]=2*(h[k-1]+h[k])-h[k-1]*h[k-1]/ath[k-1];
    	}
    	for(k=1;k<=n;k++)    //step 5
    	{
    		c[k]=(point[k][1]-point[k-1][1])/h[k-1];
    	}
    	for(k=1;k<=n-1;k++)  //step 6
    	{
    		d[k]=6*(c[k+1]-c[k]);
    	}
    	b[1]=d[1];              //step 7
    	for(k=2;k<=n-1;k++)  //step 8
    	{
    		b[k]=d[k]-b[k-1]*h[k-1]/ath[k-1];
    	}
    	s2[n-1]=b[n-1]/ath[n-1]; //step 9
    	for(k=n-2;k>0;k--)   //step 10
    	{
    		s2[k]=(b[k]-h[k]*s2[k+1])/ath[k];
    	}
    	s2[0]=0;s2[n]=0;    //step 11
    }
    public void drawThreeSpline()
    {
    	int k,n=p_count-1; //loop veriable
    	double s;    //final result
    	
    	Graphics g = getGraphics();
    	Color color=Color.yellow;
    	g.setColor(color);
    	if(p_count>1)
    	{    
    		for(int x=point[0][0];x<=point[p_count-1][0];x++)
    		{
    			for(k=0;k<n;k++)   //step 12.2
    			{
    				if(x<=point[k+1][0])
    				break;
    			}
    			if(k>=p_count)
    			{
    				System.out.println("Error Exit!!!");
    				return ;
    			}
    			s1=c[k+1]-s2[k+1]*h[k]/6-s2[k]*h[k]/3; //step 12.4
    			s=point[k][1]+s1*(x-point[k][0])+s2[k]*(x-point[k][0])*(x-point[k][0])/2+(s2[k+1]-s2[k])*(x-point[k][0])*(x-point[k][0])*(x-point[k][0])/(6*h[k]);  //step 12.5
    			g.fillOval(x+401,281-(int)s,3,3);
    		}//for every point x
    	}
    }
    ////////////////////////////////
    public void clear()
    {
    	p_count=0;
    	Graphics g = getGraphics();
    	Color color=Color.white;
    	update(g);
    }
    /////////////////
    public void sequence()    
    {
    	int j;
    	int tempX,tempY;
    	for(int i=0;i<p_count-1;i++)
    	{
    		for(j=0;j<(p_count-1)-i;j++)
    		if(point[j][0]>point[j+1][0])
    		{
    			tempX=point[j][0];tempY=point[j][1];point[j][0]=point[j+1][0];point[j][1]=point[j+1][1];
    			point[j+1][0]=tempX;point[j+1][1]=tempY;
    		}
    	}
	}
	//////////////////////////
	public void actionPerformed(ActionEvent e)
	{}
	public class IsMouseClicked extends MouseAdapter 
    {
    	public void mouseClicked(MouseEvent e)
		{
			Graphics g = getGraphics();
			point[p_count][0] = e.getX()-401;
			point[p_count][1] = -e.getY()+281;
			g.fillOval((int)e.getX(),(int)e.getY(),5,5);
			p_count++;
		}
    } 
	
}
class Three extends WindowAdapter implements ActionListener
{
	Frame f;
	Panel p1,p2,p3;
	Button b1,b2,b3,b4,b5;
	_paint p;
	public void display()
	{
		f=new Frame("数值算法");
		f.setSize(800,600);        //设置框架的大小
		f.setResizable(false);     //框架不能改变大小
		f.setBackground(Color.gray);
		f.setLayout(new BorderLayout());
		p1=new Panel();
		p=new _paint();
		p.setBackground(Color.white);
		b1=new Button("随机产生点");
		b2=new Button("拉格朗日插值");
		b2.setBackground(Color.red);
		b3=new Button("  牛顿插值  ");
		b3.setBackground(Color.blue);
		b4=new Button("三次样条插值");
		b4.setBackground(Color.yellow);
		b5=new Button("  清空  ");
		
		f.add(p1,BorderLayout.SOUTH);
		f.add(p,BorderLayout.CENTER);
		f.addWindowListener(this);
		p1.add(b1);
		p1.add(b2);
		p1.add(b3);
		p1.add(b4);
		p1.add(b5);
		b1.addActionListener(this);
		b2.addActionListener(this);
		b3.addActionListener(this);
		b4.addActionListener(this);
		b5.addActionListener(this);
		f.setVisible(true);
	}
	public void actionPerformed(ActionEvent e)
	{
		if(e.getSource()==b1)
		{
			p.p_random();
		}
		if(e.getSource()==b2)
		{
			if(p.p_count>1)
			{
				p.sequence();
				p.drawLagrange();
			}
		}
		if(e.getSource()==b3)
		{
			if(p.p_count>1)
			{
				p.sequence();
				p.setAarray();
				p.drawNewton();
			}
		}
		if(e.getSource()==b4)
		{
			if(p.p_count>1)
			{
				p.sequence();
				p.setParameters();
				p.drawThreeSpline();
			}
		}
		if(e.getSource()==b5)
		{
			p.clear();
      	}
		
	}
	public void windowClosing(WindowEvent e)
	{
		System.exit(0);
	}
}