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。
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);
- }
-
- }
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;
- else
- return 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
- {
- 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;
- }else
- JOptionPane.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!