【算法】一些牛逼轰轰的算法记录

1.判断点是否在三角形内

衍生：快速计算三角形面积

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#include <iostream>
#include <string>
#include <math.h>
#define S_FLOAT 0.00000001

using namespace std;
//点类型
typedef struct Point
{
	float x;
	float y;
	Point() {}
	Point(float x,float y)
	{
		this->x = x;
		this->y = y;
	}
};
//计算三角形面积
float GetTriangleSquar(const Point a, const Point b, const Point c)
{
	Point AB, BC;
	AB.x = b.x - a.x;
	AB.y = b.y - a.y;
	BC.x = c.x - b.x;
	BC.y = c.y - b.y;
	return fabs(AB.x*BC.y - AB.y*BC.x) / 2;
}
//判断点是否在三角形内
string IsInTriang(Point a, Point b, Point c, Point d)
{
	float Sabc, Sabd, Sacd, Sbcd;
	Sabc = GetTriangleSquar(a, b, c);
	Sabd = GetTriangleSquar(a, b, d);
	Sacd = GetTriangleSquar(a, c, d);
	Sbcd = GetTriangleSquar(b, c, d);
	float Sums = Sabd + Sacd + Sbcd;
	cout << "Sabd:" << Sabd << endl << "Sacd:" << Sacd << endl << "Sbcd:" << Sbcd << endl;
	cout<< "Sabc:"<<Sabc<<endl<<"Sums:"<<Sums << endl;
	if ((-S_FLOAT < (Sabc - Sums) && (Sabc - Sums) < S_FLOAT))
		return "Yes";
	else return "No";
}
//测试函数
void Test()
{
	Point a(2, 2), b(0, 0), c(4, 0), d(2, 1);
	cout << IsInTriang(a, b, c, d) << endl;
}
int main()
{
	Test();
	system("pause");
	return 0;
}

2.PNPoly算法-判断点是否在多边形内

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bool PointInPolygon(Point point, Polygon polygon) {
  vector<Point> points = polygon.getPoints();
  int i, j, nvert = points.size();
  bool c = false;

  for(i = 0, j = nvert - 1; i < nvert; j = i++) {
    if( ( (points[i].y >= point.y ) != (points[j].y >= point.y) ) &&
        (point.x <= (points[j].x - points[i].x) * (point.y - points[i].y) / (points[j].y - points[i].y) + points[i].x)
      )
      c = !c;
  }

  return c;
}