判定一个点是否在三角形内

判定一个点是否在三角形内

如何判定一个点P是否存在于指定的三角形ABC内，这肯定是一个简单的问题，本文仅用一个图形界面程序展示了该问题，有兴趣的朋友可以看看。(2008.07.24最后更新)

在此处使用一种常见且简便的方法：如果三角形PAB，PAC和PBC的面积之和与三角形ABC的面积相等，即可判定点P在三角形ABC内(包括在三条边上)。
可知，该方法的关键在于如何计算三角形的面积。幸运地是，当知道三角形顶点(A，B和C)的坐标((Ax, Ay)，(Bx, By)和(Cx, Cy))之后，即可计算出其面积：

S = |(Ax * By + Bx * Cy + Cx * Zy - Ay * Bx - By * Cx - Cy * Ax) / 2|

关键的代码如下，

// 由给定的三个顶点的坐标，计算三角形面积。
// Point(java.awt.Point)代表点的坐标。
private static double triangleArea(Point pos1, Point pos2, Point pos3) {
     double result = Math.abs((pos1.x * pos2.y + pos2.x * pos3.y + pos3.x * pos1.y
             - pos2.x * pos1.y - pos3.x * pos2.y - pos1.x * pos3.y) / 2.0D );
     return result;
}

// 判断点pos是否在指定的三角形内。
private static boolean inTriangle(Point pos, Point posA, Point posB,
        Point posC) {
     double triangleArea = triangleArea(posA, posB, posC);
     double area = triangleArea(pos, posA, posB);
    area += triangleArea(pos, posA, posC);
    area += triangleArea(pos, posB, posC);
     double epsilon = 0.0001 ;   // 由于浮点数的计算存在着误差，故指定一个足够小的数，用于判定两个面积是否(近似)相等。
     if (Math.abs(triangleArea - area) < epsilon) {
         return true ;
    }
     return false ;
}

执行该应用程序，用鼠标在其中点击三次，即可绘制一个三角形，如下组图所示：
判定一个点是否在三角形内

然后仅需移动鼠标，就会出现一个空心圆圈。如果圆圈的中心在三角内(包含在三条边上)，则圆圈显示为红色；否则，显示为蓝色。如下组图所示：
判定一个点是否在三角形内

完整代码如下：

public class CanvasPanel extends JPanel {

     private static final long serialVersionUID = - 6665936180725885346L ;

     private Point firstPoint = null ;

     private Point secondPoint = null ;

     private Point thirdPoint = null ;

     public CanvasPanel() {
        setBackground(Color.WHITE);
        addMouseListener(mouseAdapter);
        addMouseMotionListener(mouseAdapter);
    }

     public void paintComponent(Graphics g) {
         super .paintComponent(g);
        drawTriangel(g);
    }

     private void drawTriangel(Graphics g) {
         if (firstPoint != null && secondPoint != null ) {
            g.drawLine(firstPoint.x, firstPoint.y, secondPoint.x, secondPoint.y);
             if (thirdPoint != null ) {
                g.drawLine(firstPoint.x, firstPoint.y, thirdPoint.x, thirdPoint.y);
                g.drawLine(secondPoint.x, secondPoint.y, thirdPoint.x, thirdPoint.y);
            }
        }
    }

     private static boolean inTriangle(Point pos, Point posA, Point posB,
            Point posC) {
         double triangeArea = triangleArea(posA, posB, posC);
         double area = triangleArea(pos, posA, posB);
        area += triangleArea(pos, posA, posC);
        area += triangleArea(pos, posB, posC);
         double epsilon = 0.0001 ;
         if (Math.abs(triangeArea - area) < epsilon) {
             return true ;
        }
         return false ;
    }

     private static double triangleArea(Point pos1, Point pos2, Point pos3) {
         double result = Math.abs((pos1.x * pos2.y + pos2.x * pos3.y + pos3.x * pos1.y
                            - pos2.x * pos1.y - pos3.x * pos2.y - pos1.x * pos3.y) / 2.0D );
         return result;
    }

     private MouseInputAdapter mouseAdapter = new MouseInputAdapter() {

         public void mouseReleased(MouseEvent e) {
            Point pos = e.getPoint();
             if (firstPoint == null ) {
                firstPoint = pos;
            } else if (secondPoint == null ) {
                secondPoint = pos;
                Graphics g = CanvasPanel. this .getGraphics();
                CanvasPanel. this .paintComponent(g);
                g.drawLine(firstPoint.x, firstPoint.y, secondPoint.x, secondPoint.y);
            } else if (thirdPoint == null ) {
                thirdPoint = pos;
                Graphics g = CanvasPanel. this .getGraphics();
                CanvasPanel. this .paintComponent(g);
                g.drawLine(firstPoint.x, firstPoint.y, secondPoint.x, secondPoint.y);
                g.drawLine(firstPoint.x, firstPoint.y, thirdPoint.x, thirdPoint.y);
                g.drawLine(secondPoint.x, secondPoint.y, thirdPoint.x, thirdPoint.y);
            }
        }

         public void mouseMoved(MouseEvent e) {
            Point pos = e.getPoint();
            Graphics2D g2 = (Graphics2D) CanvasPanel. this .getGraphics();
            CanvasPanel. this .paintComponent(g2);
             if (firstPoint != null && secondPoint == null ) {
                g2.drawLine(firstPoint.x, firstPoint.y, pos.x, pos.y);
            } else if (firstPoint != null && secondPoint != null && thirdPoint == null ) {
                g2.drawLine(firstPoint.x, firstPoint.y, pos.x, pos.y);
                g2.drawLine(secondPoint.x, secondPoint.y, pos.x, pos.y);
            } else if (firstPoint != null && secondPoint != null && thirdPoint != null ) {
                 if (inTriangle(pos, firstPoint, secondPoint, thirdPoint)) {
                    g2.setColor(Color.RED);
                } else {
                    g2.setColor(Color.BLUE);
                }
                 int radius = 4 ;
                g2.drawOval(pos.x - radius, pos.y - radius, radius * 2 , radius * 2 );
            }
        }
    };
}

public class Triangle extends JFrame {

     private static final long serialVersionUID = 1L ;

     private CanvasPanel mainPanel = null ;

     public Triangle() {
        setTitle( " Triangle " );
        setSize( new Dimension( 300 , 200 ));
        setResizable( false );

        init();

        Container container = getContentPane();
        container.add(mainPanel);

        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        setVisible( true );
    }

     private void init() {
        mainPanel = new CanvasPanel();
    }

     public static void main(String[] args) {
         new Triangle();
    }
}

还可参见一篇英文文章： http://www.blackpawn.com/texts/pointinpoly/default.html 好文章 ;-)

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判定一个点是否在三角形内

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