判断一个点是否在三角形内部

- 日理万妓 2022-05-28 07:06 195阅读 0赞

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//判断一个点是否在三角形内部
    public class IsIntriangle{
    	 
    	 //(1)面积法求解
    	public static boolean isInside1(double x1, double y1, double x2, double y2,
    			double x3, double y3, double x, double y) {
    		double area1 = getArea(x1, y1, x2, y2, x, y);
    		double area2 = getArea(x1, y1, x3, y3, x, y);
    		double area3 = getArea(x2, y2, x3, y3, x, y);
    		double allArea = getArea(x1, y1, x2, y2, x3, y3);
    		return (area1 + area2 + area3) <=allArea;
    	}
        //海伦公式求三角形的面积
    	public static double getArea(double x1, double y1, double x2, double y2,
    			double x3, double y3) {
    		double side1Len = getSideLength(x1, y1, x2, y2);
    		double side2Len = getSideLength(x1, y1, x3, y3);
    		double side3Len = getSideLength(x2, y2, x3, y3);
    		double p = (side1Len + side2Len + side3Len) / 2;
    		return Math.sqrt((p - side1Len) * (p - side2Len) * (p - side3Len) * p);
    	}
         //获得一条边的长度
    	public static double getSideLength(double x1, double y1, double x2,double y2) {
    		double a = Math.abs(x1 - x2);
    		double b = Math.abs(y1 - y2);
    		return Math.sqrt(a * a + b * b);
    	}
    
    	//(2)向量法求解
    
    	//求交叉值
    	public static double crossProduct(double x1,double y1,double x2,double y2)
    	{
             return x1*y2-x2*y1;
    	}
    
    	public static boolean isInside2(double x1,double y1,double x2,double y2,
    		                     double x3,double y3,double x,double y)
    	{
    		//如果三角形的点不是逆时针输入，改变一下顺序
    		if(crossProduct(x3-x1,y3-y1,x2-x1,y2-y1)>=0)
    		{
    			 double tmpx=x2;
    			 double tmpy=y2;
    			 x2=x3;
    			 y2=y3;
    			 x3=tmpx;
    			 y3=tmpy;
    		}
    		 //在这条边的右边
    		if(crossProduct(x2-x1,y2-y1,x-x1,y-y1)<0)
    		{
    			 return false;
    		}
    		//在这条边的右边
    		if(crossProduct(x3-x2,y3-y2,x-x2,y-y2)<0)
    		{
    			return false;
    		}
    		//在这条边的右边
    		if(crossProduct(x1-x3,y1-y3,x-x3,y-y3)<0)
    		{
    			return false;
    		}
    		return true;
    	}
    
    	 public static void main(String[]args)
    	 {
            double x1 = -5;
    		double y1 = 0;
    		double x2 = 0;
    		double y2 = 8;
    		double x3 = 5;
    		double y3 = 0;
    		double x = 0;
    		double y = 6;
    		System.out.println(isInside1(x1, y1, x2, y2, x3, y3, x, y));
    		System.out.println(isInside2(x1, y1, x2, y2, x3, y3, x, y));
    
    	 }
    }

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[Center]: /images/20220528/c461ce2469aa424785bc931453387ffe.png
[Center 1]: /images/20220528/5a0876a297ed44daa34e37c22933fc51.png