判断点在多边形内算法的C++实现
#include<iostream>#include <cmath>
#include <vector>
#include <algorithm>
#define EPSILON 0.000001
using namespace std;
//二维double矢量
structVec2d
{
double x, y;
Vec2d()
{
x = 0.0;
y = 0.0;
}
Vec2d(double dx, double dy)
{
x = dx;
y = dy;
}
void Set(double dx, double dy)
{
x = dx;
y = dy;
}
};
//判断点在线段上
bool IsPointOnLine(double px0, double py0, double px1, double py1, double px2, double py2)
{
bool flag = false;
double d1 = (px1 - px0) * (py2 - py0) - (px2 - px0) * (py1 - py0);
if ((abs(d1) < EPSILON) && ((px0 - px1) * (px0 - px2) <= 0) && ((py0 - py1) * (py0 - py2) <= 0))
{
flag = true;
}
return flag;
}
//判断两线段相交
bool IsIntersect(double px1, double py1, double px2, double py2, double px3, double py3, double px4, double py4)
{
bool flag = false;
double d = (px2 - px1) * (py4 - py3) - (py2 - py1) * (px4 - px3);
if (d != 0)
{
double r = ((py1 - py3) * (px4 - px3) - (px1 - px3) * (py4 - py3)) / d;
double s = ((py1 - py3) * (px2 - px1) - (px1 - px3) * (py2 - py1)) / d;
if ((r >= 0) && (r <= 1) && (s >= 0) && (s <= 1))
{
flag = true;
}
}
return flag;
}
//判断点在多边形内
bool Point采用In采用Polygon采用2D(double x, double y, const vector<Vec2d> &POL)
{
bool isInside = false;
int count = 0;
//
double minX = DBL采用MAX;
for (int i = 0; i < POL.size(); i++)
{
minX = std::min(minX, POL.x);
}
//
double px = x;
double py = y;
double linePoint1x = x;
double linePoint1y = y;
double linePoint2x = minX -10; //取最小的X值还小的值作为射线的终点
double linePoint2y = y;
//遍历每一条边
for (int i = 0; i < POL.size() - 1; i++)
{
double cx1 = POL.x;
double cy1 = POL.y;
double cx2 = POL.x;
double cy2 = POL.y;
if (IsPointOnLine(px, py, cx1, cy1, cx2, cy2))
{
return true;
}
if (fabs(cy2 - cy1) < EPSILON) //平行则不相交
{
continue;
}
if (IsPointOnLine(cx1, cy1, linePoint1x, linePoint1y, linePoint2x, linePoint2y))
{
if (cy1 > cy2) //只保证上端点+1
{
count++;
}
}
else if (IsPointOnLine(cx2, cy2, linePoint1x, linePoint1y, linePoint2x, linePoint2y))
{
if (cy2 > cy1) //只保证上端点+1
{
count++;
}
}
else if (IsIntersect(cx1, cy1, cx2, cy2, linePoint1x, linePoint1y, linePoint2x, linePoint2y)) //已经排除平行的情况
{
count++;
}
}
if (count % 2 == 1)
{
isInside = true;
}
return isInside;
}
int main()
{
//定义一个多边形（六边形）
vector<Vec2d> POL;
POL.push采用back(Vec2d(268.28, 784.75));
POL.push采用back(Vec2d(153.98, 600.60));
POL.push采用back(Vec2d(274.63, 336.02));
POL.push采用back(Vec2d(623.88, 401.64));
POL.push采用back(Vec2d(676.80, 634.47));
POL.push采用back(Vec2d(530.75, 822.85));
POL.push采用back(Vec2d(268.28, 784.75)); //将起始点放入尾部，方便遍历每一条边
//
if (Point采用In采用Polygon采用2D(407.98, 579.43, POL))
{
cout << "点（407.98, 579.43）在多边形内" << endl;
}
else
{
cout << "点（407.98, 579.43）在多边形外" << endl;
}
//
if (Point采用In采用Polygon采用2D(678.92, 482.07, POL))
{
cout << "点（678.92, 482.07）在多边形内" << endl;
}
else
{
cout << "点（678.92, 482.07）在多边形外" << endl;
}
return 0;
}
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