Biegral Blog

       本题最好不要用直线方程或线段夹角来判断，因为这涉及到分类与讨论，下面的算法是相对比较好的算法，代码如下：

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

typedef struct point
{
	float x;
	float y;
}Point;

float side(Point A, Point B)
{
	float xLen = A.x - B.x;
	float yLen = A.y - B.y;
	return sqrt(xLen * xLen + yLen * yLen);
}

float area(Point A, Point B, Point C)
{
	float a = side(B, C);
	float b = side(A, C);
	float c = side(A, B);
	float p = (a + b + c)/ 2;
	
	//海伦公式
	float s = sqrt(p * (p - a) * (p - b) * ( p - c));
	return s;
}

bool isEqual(float x, float y)
{
	if(fabs(x - y) < 0.0001)
		return true;

	return false;
}

int main()
{
	Point A, B, C, P;
    //可以对A进行整体赋值，下面采用的是分步赋值
	
	A.x = 0;
	A.y = 0;  // A(0, 0)
	B.x = 2;
	B.y = 0;  // B(2, 0)
	C.x = 1;
	C.y = 1;  // C(1, 1)

	P.x = 0.5;
	P.y = 0.6; // P(0.5, 0.6)

	float s  = area(A, B, C);
	float s1 = area(P, B, C);
	float s2 = area(P, A, C);
	float s3 = area(P, A, B);

	if(isEqual(s1 + s2 + s3, s) && !isEqual(s1, 0) && !isEqual(s2, 0) && !isEqual(s3, 0))
		cout << "Point P lies in the triangle ABC" << endl;
	else
		cout << "Point P does not lie in the triangle ABC" << endl;

	return 0;
}