//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));
}
}
