计算几何学1-Graham凸壳算法实现

图片:

针对该算法，写了一个随机生成平面点的算法和复现了该算法，代码如下：

#include <iostream>
#include <vector>
#include <time.h>
#include <string>
#include <fstream>
#include <algorithm>
using namespace std;
struct Point
{
	double x;
	double y;
	Point(double a = 0, double b = 0) :x(a), y(b) {};
};

void getrandompoint(int num, vector<Point>&  P, string outfile)
{
	srand(time(0));
	for (int i = 0;i < num; i++)
	{
		double x = rand() / double(RAND_MAX);
		double y = rand() / double(RAND_MAX);
		P.push_back(Point(x, y));
	}
	//保存随机点
	ofstream file(outfile);
	int count = 1;
	for (auto x : P)
	{
		file << count << " ";
		file << x.x << " ";
		file << x.y << " ";
		file << 0 << " ";
		file << 0 << " " << 0 << " " << 1 << " ";//法向量
		for (int i = 0;i < 10;i++) file << 0 << " ";
		file << endl;
		count++;
	}
	file.close();
}

bool comp(const Point& P1, const Point& P2)
{
	return P1.x < P2.x;
}

bool jiancha(const vector<Point>& P)
{
	int size = P.size();
	Point first = P[size - 3];
	Point second = P[size - 2];
	Point third = P[size - 1];
	double v1x = second.x - first.x;
	double v1y = second.y - first.y;
	double v2x = third.x - second.x;
	double v2y = third.y - second.y;
	return v1x * v2y - v2x * v1y < 0;
}

void convex1(vector<Point>& P, string outfile)
{
	vector<Point>upper;
	//根据x坐标对所有点排序
	sort(P.begin(), P.end(), comp);
	upper.push_back(P[0]);
	upper.push_back(P[1]);
	int size = P.size();
	for (int i = 2;i < size;i++)
	{
		upper.push_back(P[i]);
		while (upper.size() >= 3 && !jiancha(upper))
		{
			Point temp = upper.back();
			upper.pop_back();upper.pop_back();
			upper.push_back(temp);
		}
	}
	vector<Point>lower;
	lower.push_back(P[size - 1]);
	lower.push_back(P[size - 2]);
	for (int i = size - 3;i >= 0;i--)
	{
		lower.push_back(P[i]);
		while (lower.size() >= 3 && !jiancha(lower))
		{
			Point temp = lower.back();
			lower.pop_back();lower.pop_back();
			lower.push_back(temp);
		}
	}
	ofstream file(outfile);
	int count = 1;
	for (auto x : upper)
	{
		file << count << " ";
		file << x.x << " ";
		file << x.y << " ";
		file << 0 << " ";
		file << 0 << " " << 0 << " " << 1 << " ";//法向量
		for (int i = 0;i < 10;i++) file << 0 << " ";
		file << endl;
		count++;
	}
	size = lower.size()-1;
	for (int i = 1;i < size;i++)
	{
		file << count << " ";
		file << lower[i].x << " ";
		file << lower[i].y << " ";
		file << 0 << " ";
		file << 0 << " " << 0 << " " << 1 << " ";//法向量
		for (int i = 0;i < 10;i++) file << 0 << " ";
		file << endl;
		count++;
	}
	file.close();
}

int main()
{
	vector<Point>P;
	getrandompoint(100, P, "randomPoint.txt");
	convex1(P, "convex1.txt");
	return 0;
}

因为本人之前写过了一个opengl点云显示的软件，所以将所有结果都保存在txt中供调用，txt中数据的格式有些奇怪，这是本人写的opengl软件读取数据的基本格式，不必在意。

下面给出画出的结果图：