编程之美4.4 判断点是否在三角形内

推荐  http://blog.youkuaiyun.com/zhanglei0107/article/details/8453405

http://blog.youkuaiyun.com/erorr/article/details/5900852

#include <iostream>
using namespace std;
struct Point{
	Point(int a,int b){
		x = a;
		y = b;
	}
	int x;
	int y;
};
bool check(Point p1,Point p2,Point p3){
	int sum = (p2.x-p1.x)*(p3.y-p1.y)-(p2.y-p1.y)*(p3.x-p1.x);
	if(sum>0)
		return true;
	return false;
}
void calc(Point p1,Point p2,Point p3,Point p){
	if(check(p1,p2,p)==true&&check(p2,p3,p)==true&&check(p3,p1,p)==true){
		cout<<"good"<<endl;
		return;
	}
	if(check(p1,p2,p)==false&&check(p2,p3,p)==false&&check(p3,p1,p)==false){
		cout<<"good"<<endl;
		return;
	}
	cout<<"failed"<<endl;
}
int main(){
	Point p1(1,2);
	Point p2(0,0);
	Point p3(2,0);
	//Point p(1,1);
	Point p(1,3);
	calc(p1,p2,p3,p);
	return 0;
}

不包括点在边线上的情况，判断点是否在三角形内，仍然用面积法进行判断

边线上的情形用向量平行的判定条件设向量AB(x1,y1),向量AD(x2,y2)若x1y2-x2y1==0则这两向量平行，表面D要么在边线上要么在三角形外

均属于不在三角形内的情形

其余的判定为点D与三边围成的面积之和是否等于三角形ABC的面积

三角形的面积用海伦公式计算

#include<iostream>
#include<cmath>
using namespace std;

struct point{
	point(double i,double j):x(i),y(j){}
	double x,y;
};
void computeEdgeLen(point A,point B,
	point C,double& a,double &b,double &c){
		a=sqrt(pow(B.x-A.x,2)+pow(B.y-A.y,2));
		b=sqrt(pow(C.x-B.x,2)+pow(C.y-B.y,2));
		c=sqrt(pow(A.x-C.x,2)+pow(A.y-C.y,2));
}

double Area(point A,point B,point C)
{
	double a,b,c=0;
	computeEdgeLen(A,B,C,a,b,c);
	double p=(a+b+c)/2;
//海伦公式
	return sqrt(p*(p-a)*(p-b)*(p-c));

}
bool isParallel(point A,point B,point C){
	if((B.x-A.x)*(C.y-A.y)-(B.y-A.y)*(C.x-A.x)==0)
		return true;
	else
		return false;

}
bool isTriangle(point A,point B,point C,point D)
{
	if(isParallel(A,B,D)||
		isParallel(B,C,D)||isParallel(C,A,D))
		return false;
	return (Area(A,B,D)+Area(B,C,D)+Area(C,A,D)<=Area(A,B,C));

}
int main(){
	point A(0,2);
	point B(0,0);
	point C(1,0);
	point D(0.1,0);
	if(isTriangle(A,B,C,D))
		cout<<"true"<<endl;
	else
		cout<<"false"<<endl;
	system("pause");
	return 0;


}