JAVA实现数学函数图像

基础知识

在java.lang包中有个public final Math类，包含了基本的数字操作，如指数、对数、平方根和三角函数。

【Java的默认包是java.lang，即该包中的所有类不需要导包，不需要再写import，是默认导入的，其它包必须导入。Java就这么定义的，记住就可以了】。

java.lang.Math类中包含E和PI两个静态常量，以及进行科学计算的类(static)方法，可以直接通过类名调用。

public static final Double E = 2.7182818284590452354

public static final Double PI = 3.14159265358979323846

public static long abs(double x)：传回 x 的绝对值。X也可int long float

public static long sin(double x): 传回x径度的正弦函数值

public static long cos(double x)：传回x径度的余弦函数值

public static long tan(double x): 传回x径度的正切函数值

public static long asin(double x)：传回x值的反正弦函数值。

public static long acos(double x)：传回x值的反余弦函数值。

public static long atan(double x)：传回x值的反正切函数值。

public static long atan2(double x, double y)：传回极坐标（polar）的θ值

public static long floor(double x)：传回不大于x的最大整数值

public static long ceil(double x)：传回不小于x的最小整数值。

public static long exp(double x)：传回相当于ex值

public static long log(double x)：传回x的自然对数函数值

public static long max(double x,double y)：传回x、y较大数

public static long min(double x,double y)：传回x、y较小数

public static long pow(double x,double y)：传回x的y次幂值

public static long sqrt(double x): 传回x开平方值

public static long rint(double x):传回最接近x的整数值

public static long round(double x):传回x的四舍五入值

public static long toDegrees(double angrad):传回将angrad径度转换成角度

public static long toRadians(double angdeg): 传回将angdeg角度转换成径度

public static long random():传回随机数值,产生一个0-1之间的随机数(不包括0和1)

关于 Java图形用户界面可参见 https://blog.csdn.net/cnds123/article/details/113251233

下面给出多个示例代码，取自网络。

一、绘制sin函数图像

先看效果图

源码文件DrawSin.java内容如下：

import java.awt.Color;
import java.awt.Graphics;
import javax.swing.JFrame;public class DrawSin extends JFrame {private static int SCALE_X = 40; // X轴缩放倍数private static int SCALE_Y = 100; // Y轴缩放倍数private static int ORIGIN_X = 50; // 原点X private static int ORIGIN_Y = 0; // 原点Y private static int END_ARC = 360 * 2; // 画多长public void paint(Graphics g) {double ox = 0, oy = 0, x = 0, y = 0, arc = 0;super.paint(g);ORIGIN_Y = this.getHeight() / 2;// 画坐标轴g.drawLine(ORIGIN_X, ORIGIN_Y, this.getWidth(), ORIGIN_Y); // 横轴g.drawLine(ORIGIN_X, 0, ORIGIN_X, this.getHeight()); // 纵轴// 每90度画个标尺for (int i = 0; i < END_ARC; i += 90) {arc = Math.PI * i * 2 / 360;x = ORIGIN_X + arc * SCALE_X;g.drawLine((int) x, ORIGIN_Y - 10, (int) x, ORIGIN_Y + 10);}// 画正弦曲线g.setColor(Color.RED);for (int i = 0; i < END_ARC; i += 10) {arc = Math.PI * i * 2 / 360;x = ORIGIN_X + arc * SCALE_X;y = ORIGIN_Y + Math.sin(arc) * SCALE_Y;if (arc > 0) {g.drawLine((int) ox, (int) oy, (int) x, (int) y);}ox = x;oy = y;}}public static void main(String[] args) {DrawSin wnd = new DrawSin();wnd.setSize(600, 500);wnd.setVisible(true);}}

二、画函数图像

先看效果图

源码文件DrawFn.java 内容如下：

import java.awt.Color;
import java.awt.Frame;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.GridLayout;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.awt.event.ItemEvent;
import java.awt.event.ItemListener;
import java.awt.geom.Line2D;
import java.awt.geom.Point2D;
import javax.swing.BorderFactory;
import javax.swing.JButton;
import javax.swing.JComboBox;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.JTextField;
import javax.swing.border.LineBorder; public class DrawFn extends JFrame implements ItemListener{private JTextField txt_c;private JTextField txt_b;private JTextField txt_a;public JComboBox chooseFun;//draw_actionAdapter adapter;public int A;public drawFnPanel panel = new drawFnPanel(); public static void main(String[] args) {DrawFn frame=new DrawFn();frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);frame.setSize(800, 600);frame.setLocationRelativeTo(null);frame.setVisible(true); frame.setBackground(Color.BLACK);}public DrawFn() {super("画函数图像");final JLabel aLabel = new JLabel();aLabel.setForeground(Color.WHITE);aLabel.setText("a=");aLabel.setBounds(650, 10, 21, 18); //设置位置，大小getContentPane().add(aLabel);txt_a = new JTextField();txt_a.setBounds(680, 8, 60, 18);getContentPane().add(txt_a);//final JLabel bLabel = new JLabel();bLabel.setForeground(Color.WHITE);bLabel.setText("b="); bLabel.setBounds(650, 30, 21, 18); getContentPane().add(bLabel); txt_b = new JTextField(); txt_b.setBounds(680, 28, 60, 18); getContentPane().add(txt_b);//final JLabel cLabel = new JLabel(); cLabel.setForeground(Color.WHITE);cLabel.setText("c="); cLabel.setBounds(650, 50, 32, 18);getContentPane().add(cLabel);//this.setContentPane(cLabel); txt_c = new JTextField(); txt_c.setBounds(680, 48, 60, 18); getContentPane().add(txt_c);//this.setContentPane(txt_c);//设置按钮final JButton button = new JButton(); button.addActionListener(new draw_actionAdapter(this));//什么意思？button.setText("绘制"); button.setBounds(680, 80, 60, 18); getContentPane().add(button);//this.setContentPane(button);//定义下拉菜单final JLabel choose = new JLabel(); choose.setForeground(Color.WHITE);choose.setText("请选择函数类型："); choose.setBounds(20, 5, 120, 20);getContentPane().add(choose);JPanel jp1=new JPanel();String []fun={"ax^2+bx+c","ae^bx+c","a*sin(PIx+b)+c","a*b^x+c","a*x^b+c","敬请期待"};chooseFun=new JComboBox(fun);chooseFun.setBounds(20, 30, 120, 20);jp1.add(chooseFun);chooseFun.setMaximumRowCount(3);getContentPane().add(chooseFun);chooseFun.addItemListener(this);getContentPane().add(panel);//this.setContentPane(panel);}public void itemStateChanged(ItemEvent e) {if(e.getStateChange()==e.SELECTED){A=chooseFun.getSelectedIndex();//System.out.println(A);}}public void paintFn(ActionEvent e){panel.paintFn(Integer.parseInt(txt_a.getText()), Integer.parseInt(txt_b.getText()), Integer.parseInt(txt_c.getText()));}class draw_actionAdapter implements ActionListener{ private DrawFn adapter; public draw_actionAdapter(DrawFn adapter){ this.adapter=adapter; } public void actionPerformed(ActionEvent e){//adapter.getA(e);adapter.paintFn(e);adapter.repaint();}} class drawFnPanel extends JPanel{private float fa; private float fb; private float fc;private int UnitLength=100;//可以任意改变该像素值public void paintFn(int a,int b,int c){fa=a;fb=b; fc=c; }public double Fun(double x){//System.out.println("A="+DrawFn.A);if(A==0)return fa*x*x+fb*x+fc;else if(A==1)return fa*Math.pow(Math.E, fb*x)+fc ;//这里可以输入任何函数else if(A==2)return fa*Math.sin(Math.PI*x+fb)+fc;else if(A==3)return fa*Math.pow(fb, x)+fc;else if(A==4)return fa*Math.pow(x,fb)+fc;elsereturn 0;}int width,height;int X,Y;//重载paintComponent函数public void paintComponent(Graphics g){g.setColor(Color.BLACK);width = this.getWidth();//获得宽度height = this.getHeight();//获得高度X=width/2;Y=height/2;//获得原点坐标this.drawAxes(g);this.function(g);}//画坐标轴private void drawAxes(Graphics g){g.setColor(Color.WHITE);g.drawLine(0, Y, width, Y);g.drawLine(X, 0, X, height);g.drawString("0",X + 2,Y +12); //画原点数字for(int i=1;i*UnitLength<width;i++){g.drawLine(X+i*UnitLength,Y-1,X+i*UnitLength,Y-6);//画X轴正向的小竖线g.drawLine(X - i*UnitLength, Y-1, X - i*UnitLength, Y-6);//画X轴负向的小竖线g.drawString(String.valueOf(i), X + i*UnitLength-3, Y + 12);  // x轴正向数字g.drawString(String.valueOf(i*-1), X - i*UnitLength-3, Y + 12);  // x轴负向数字//画Y轴g.drawLine(X+1,Y+i*UnitLength,X+6,Y+i*UnitLength);g.drawLine(X+1,Y-i*UnitLength,X+6,Y-i*UnitLength);g.drawString(String.valueOf(i), X-12, Y - i*UnitLength-3);g.drawString(String.valueOf(i*-1), X-12, Y + i*UnitLength-3);}}//实现任意函数函数图像public void function(Graphics g1){Point2D temp1,temp2;double x,y;//我们看到的坐标值Graphics2D g = (Graphics2D)g1;g.setColor(Color.WHITE);x = -1.0*X/UnitLength;//temp1返回面板的实际坐标值（以像素为单位）y = Fun(x);temp1 = new Point2D.Double(this.alterX(x * UnitLength), this.alterY(y * UnitLength));for(int i = 0 ; i < width; i++){x =x + 1.0/UnitLength;//前进一个像素y = Fun(x);if ( Math.abs(y) < Y){temp2 = new Point2D.Double(this.alterX(x * UnitLength), this.alterY(y * UnitLength));g.draw(new Line2D.Double(temp1, temp2));temp1 = temp2;}}//repaint();}//新坐标对应的原坐标private double alterX(double x){return  x + X;}private double alterY(double y){return -1 *( y - Y);}}
}

三、平面直角坐标系函数图像

源码文件UI.java和MyPanel.java组成

效果图如下：

提示：“输入函数”功能尚未实现！

源码文件UI.java 内容如下

package math;
import java.awt.BorderLayout;
import java.awt.Dimension;
import java.awt.GridLayout;
import java.awt.Toolkit;
import javax.swing.ButtonGroup;
import javax.swing.JButton;
import javax.swing.JComboBox;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.JRadioButton;
import javax.swing.JTextField;
public class UI extends JFrame
{MyPanel mp;JPanel pl = new JPanel();JPanel pl1 = new JPanel(),pl2 = new JPanel(),pl3 = new JPanel(),pl4 = new JPanel();JRadioButton rb1,rb2;ButtonGroup bg = new ButtonGroup();JTextField tf = new JTextField(16);String[] s = {"y = sin(x)", "y = cos(x)", "y = tan(x)","y = pow(x, 2)", "y = pow(x, 3)", "y = log(x)","y = pow(2, x)", "y = sqrt(x)", "r = a(sita)"};JComboBox cb;JButton bn1 = new JButton("变宽"),bn2 = new JButton("变窄"),bn3 = new JButton("拉长"),bn4 = new JButton("压短"),bn = new JButton("绘图"),exit = new JButton("退出"),bn5 = new JButton("左移"),bn6 = new JButton("右移"),bn7 = new JButton("上移"),bn8 = new JButton("下移");public UI(){mp = new MyPanel(this);pl1.setLayout(new GridLayout(1, 2));pl2.setLayout(new GridLayout(1, 2));pl3.setLayout(new GridLayout(1, 2));pl4.setLayout(new GridLayout(1, 2));pl1.add(bn1); bn1.setEnabled(false);pl1.add(bn2); bn2.setEnabled(false);pl2.add(bn3); bn3.setEnabled(false);pl2.add(bn4); bn4.setEnabled(false);pl3.add(bn5); bn5.setEnabled(false);pl3.add(bn6); bn6.setEnabled(false);pl4.add(bn7); bn7.setEnabled(false);pl4.add(bn8); bn8.setEnabled(false);pl.setLayout(new GridLayout(20, 1));rb1 = new JRadioButton("输入函数");rb2 = new JRadioButton("选择已有函数");rb2.setSelected(true);tf.setEnabled(false);bg.add(rb1); bg.add(rb2);rb1.addActionListener(mp);rb2.addActionListener(mp);pl.add(rb1);pl.add(tf);pl.add(rb2);cb = new JComboBox(s);pl.add(cb);pl.add(new JLabel());pl.add(pl1); pl.add(pl2);pl.add(pl3); pl.add(pl4);pl.add(bn);pl.add(exit);bn1.addActionListener(mp);bn2.addActionListener(mp);bn3.addActionListener(mp);bn4.addActionListener(mp);bn5.addActionListener(mp);bn6.addActionListener(mp);bn7.addActionListener(mp);bn8.addActionListener(mp);bn.addActionListener(mp);exit.addActionListener(mp);this.setLayout(new BorderLayout());this.add(mp, BorderLayout.CENTER);this.add(pl, BorderLayout.EAST);this.setTitle("平面直角坐标系函数图像");this.setSize(797, 600 + 37);Dimension dn = Toolkit.getDefaultToolkit().getScreenSize();this.setLocation((dn.width - 797) / 2, (dn.height - 637) / 2);this.setVisible(true);this.setDefaultCloseOperation(3);}public static void main(String[] args){new UI();}
}

源码文件MyPanel.java 内容如下

package math;
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Point;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.awt.event.MouseEvent;
import java.awt.event.MouseMotionListener;
import java.awt.geom.Ellipse2D;
import java.awt.geom.Line2D;
import javax.swing.JOptionPane;
import javax.swing.JPanel;
public class MyPanel extends JPanel implements ActionListener,MouseMotionListener
{UI ui;int flag;double h_times;int w_times;int dx;int dy;String str;Point pt = new Point(0, 0);void init(){flag = -1;h_times = Math.PI / 100;w_times = 100;dx = 300;dy = 300;}public MyPanel(UI ui){this.addMouseMotionListener(this);init();this.ui = ui;}public void paintComponent(Graphics g){super.paintComponent(g);Graphics2D g2 = (Graphics2D)g;drawCoordinate(g2);Line2D line;g2.setColor(Color.BLUE);g2.drawString("(" + (pt.x - 300) + ", " + (300 - pt.y) + ")", pt.x + 20, pt.y + 20);switch(flag){case 0:g2.drawString("y = Asin(Bx + C) + D", 105, 60);for(double i = 0; i < 600; i += 0.01){line = new Line2D.Double(i, dy - Math.sin(getReal_X(i)) * w_times, i + 1, dy - Math.sin(getReal_X(i + 1)) * w_times);g2.draw(line);}break;case 1:g2.drawString("y = Acos(Bx + C) + D", 105, 60);for(double i = 0; i < 600; i += 0.01){line = new Line2D.Double(i, dy - Math.cos(getReal_X(i)) * w_times, i + 1, dy - Math.cos(getReal_X(i + 1)) * w_times);g2.draw(line);}break;case 2:g2.drawString("y = Atan(Bx + C) + D", 105, 60);for(double i = 0; i < 600; i += 0.01){line = new Line2D.Double(i, dy - Math.tan(getReal_X(i)) * w_times, i + 1, dy - Math.tan(getReal_X(i + 1)) * w_times);g2.draw(line);}break;case 3:g2.drawString("y = Apow(Bx + C, 2) + D", 105, 60);for(double i = 0; i < 600; i += 0.01){line = new Line2D.Double(i, dy - Math.pow(getReal_X(i), 2) * w_times, i + 1, dy - Math.pow(getReal_X(i + 1), 2) * w_times);g2.draw(line);}break;case 4:g2.drawString("y = Apow(Bx + C, 3) + D", 105, 60);for(double i = 0; i < 600; i += 0.01){line = new Line2D.Double(i, dy - Math.pow(getReal_X(i), 3) * w_times, i + 1, dy - Math.pow(getReal_X(i + 1), 3) * w_times);g2.draw(line);}break;case 5:g2.drawString("y = Alog(Bx + C) + D", 105, 60);for(double i = 0; i < 600; i += 0.01){line = new Line2D.Double(i, dy - Math.log(getReal_X(i)) * w_times, i + 1, dy - Math.log(getReal_X(i + 1)) * w_times);g2.draw(line);}break;case 6:g2.drawString("y = Apow(2, Bx + C) + D", 105, 60);for(double i = 0; i < 600; i += 0.01){line = new Line2D.Double(i, dy - Math.pow(2, getReal_X(i)) * w_times, i + 1, dy - Math.pow(2, getReal_X(i + 1)) * w_times);g2.draw(line);}break;case 7:g2.drawString("y = Asqrt(Bx + C) + D", 105, 60);for(double i = 0; i < 600; i += 0.01){line = new Line2D.Double(i, dy - Math.sqrt(getReal_X(i)) * w_times, i + 1, dy - Math.sqrt(getReal_X(i + 1)) * w_times);g2.draw(line);}break;case 8:g2.drawString("y = a(sita)", 105, 60);for(double i = 0; i < 600; i += 0.01){line = new Line2D.Double(getReal_X(i) * Math.cos(getReal_X(i)), dy - getReal_X(i) * Math.sin(getReal_X(i)) * w_times, getReal_X(i) * Math.cos(getReal_X(i + 1)), dy - getReal_X(i) * Math.sin(getReal_X(i + 1)) * w_times);g2.draw(line);}break;}if(flag != -1){g2.drawString("A = " + w_times, 105, 90);g2.drawString("B= " + h_times, 105, 120);g2.drawString("C= " + (300 - dx), 105, 150);g2.drawString("D= " + (300 - dy), 105, 180);}}private double getReal_X(double x){return (x - dx) * h_times;}private void drawCoordinate(Graphics2D g2){int len = 20;Line2D line;for(int i = 0; i <= 600 / len; i++){g2.setColor(Color.PINK.darker());if(i == 300 / len)g2.setColor(Color.RED);else;line = new Line2D.Double(0, i * len, 600, i * len);g2.draw(line);line = new Line2D.Double(i * len, 0, i * len, 600);g2.draw(line);}drawPoint(g2, 300, 300);}private void drawPoint(Graphics2D g2, double x, double y){g2.setColor(Color.YELLOW);Ellipse2D circle = new Ellipse2D.Double(x - 2, y - 2, 4, 4);g2.fill(circle);}public void actionPerformed(ActionEvent e){if(e.getSource() == ui.rb1){ui.tf.setEnabled(true);ui.cb.setEnabled(false);flag = -1;}if(e.getSource() == ui.rb2){ui.tf.setEnabled(false);ui.cb.setEnabled(true);}if(e.getSource() == ui.bn1){h_times /= 1.1;}if(e.getSource() == ui.bn2){h_times *= 1.1;}if(e.getSource() == ui.bn3){//   ui.bn4.setEnabled(true);w_times += 10;//   if(w_times >= 300)//   ui.bn3.setEnabled(false);}if(e.getSource() == ui.bn4){//   ui.bn3.setEnabled(true);w_times -= 10;//   if(w_times <= 0)//   ui.bn4.setEnabled(false);}if(e.getSource() == ui.bn5){dx -= 10;}if(e.getSource() == ui.bn6){dx += 10;}if(e.getSource() == ui.bn7){//   ui.bn8.setEnabled(true);dy -= 10;//   if(dy <= 0)//   ui.bn7.setEnabled(false);}if(e.getSource() == ui.bn8){//   ui.bn7.setEnabled(true);dy += 10;//   if(dy >= 600)//   ui.bn8.setEnabled(false);}if(e.getSource() == ui.bn){if(ui.tf.isEnabled() == true){str = ui.tf.getText();if(str == null || str.length() == 0){ui.bn1.setEnabled(false);ui.bn2.setEnabled(false);ui.bn3.setEnabled(false);ui.bn4.setEnabled(false);ui.bn5.setEnabled(false);ui.bn6.setEnabled(false);ui.bn7.setEnabled(false);ui.bn8.setEnabled(false);JOptionPane.showMessageDialog(this, "请输入函数表达式 !");return;}elseJOptionPane.showMessageDialog(this, "本功能尚未实现 !");}else flag = -2;ui.bn1.setEnabled(true);ui.bn2.setEnabled(true);ui.bn3.setEnabled(true);ui.bn4.setEnabled(true);ui.bn5.setEnabled(true);ui.bn6.setEnabled(true);ui.bn7.setEnabled(true);ui.bn8.setEnabled(true);init();if(ui.cb.isEnabled() == true){flag = ui.cb.getSelectedIndex();}}if(e.getSource() == ui.exit)System.exit(0);repaint();}public void mouseDragged(MouseEvent arg0){}public void mouseMoved(MouseEvent e){pt = e.getPoint();repaint();}
}

OK！