[OpenGL] 绘制并且判断凹凸多边形、自相交多边形。

#include <iostream>
#include <ctime>
#include <GL/glut.h>
#include <math.h>
#include <vector>

using namespace std;

struct Pos
{
	int x;
	int y;
};

struct Edge
{
	int x1, x2;
	int y1, y2;
	int vx;
	int vy;
	int a, b, c;
};

struct Poly
{
	// 点集
	int xx[100];
	int yy[100];

	// 边集
	Edge Edges[100];

	int plotNums = 0; //点数量
	int edgeNums = 0; //边数量

	// 记录凹点
	int conv = 0;
};

Poly poly;

// 求交点坐标
Pos CrossPos(int p1,int p2){
	Pos res;
	int A1 = poly.Edges[p1].a;
	int B1 = poly.Edges[p1].b;
	int A2 = poly.Edges[p2].a;
	int B2 = poly.Edges[p2].b;
	int C1 = poly.Edges[p1].c;
	int C2 = poly.Edges[p2].c;

	int m = A1 * B2 - A2 * B1;
	if (m == 0)
		cout <<"第"<<p1<<"边和第"<<p2<<"边"<< "无交点" << endl;
	else
	{
		res.x = (C2*B1 - C1 * B2) / m;
		res.y = (C1*A2 - C2 * A1) / m;
	}
	return res;

}

// 判断点是否在线段内
bool JudgeInLine(Pos pos,Edge edge)
{
	int maxX = edge.x1 >= edge.x2 ? edge.x1 : edge.x2;
	int minX = edge.x1 <= edge.x2 ? edge.x1 : edge.x2;
	int maxY = edge.y1 >= edge.y2 ? edge.y1 : edge.y2;
	int minY = edge.y1 <= edge.y2 ? edge.y1 : edge.y2;
	if (pos.x<=maxX && pos.x>=minX && pos.y<=maxY && pos.y>=minY)
	{
		return true;
	}
	return false;
}

// 求叉积 返回正负值
int CrossProduct(int n)
{
	n = n % poly.edgeNums;
	int np = (n + 1) % poly.edgeNums;
	return (poly.Edges[n].vx*poly.Edges[np].vy - poly.Edges[np].vx*poly.Edges[n].vy) >= 0 ? 1 : -1;
}

// 切割凹多边形
void ChangePoly() {
	int convP = poly.conv; //凹点的下一个点
	Pos interPos;

	for (int i = 0; i < poly.edgeNums; i++)
	{
		if (i<convP-1 || i>convP+1)
		{
			interPos = CrossPos(convP, i);
		}
	}

	glClearColor(0.0, 0.0, 0.0, 0.0);
	glClear(GL_COLOR_BUFFER_BIT);
	glBegin(GL_POLYGON);
	glColor3f(1.0f, 0.0f, 0.0f);
	for (int i = 0; i <= convP; i++)
	{
		glVertex2f(poly.xx[i], poly.yy[i]);
	}
	glVertex2f(interPos.x, interPos.y);
	glEnd();

	glBegin(GL_POLYGON);
	glColor3f(0.0f, 1.0f, 1.0f);
	glVertex2f(interPos.x, interPos.y);
	for (int i=convP+1;i<poly.plotNums;i++)
	{
		glVertex2f(poly.xx[i], poly.yy[i]);
	}
	glEnd();

	glFlush();
}

// 判断是什么多边形
bool Judge()
{
	/*输出边信息*/
	for (int i = 0; i < poly.edgeNums; i++)
	{
		cout << "Vx：" << poly.Edges[i].vx << "  " << "Vy：" << poly.Edges[i].vy << "  " << "A：" << poly.Edges[i].a<< "  " << "B：" << poly.Edges[i].b << "  " << "C：" << poly.Edges[i].c <<endl;
	}

	/*判断自交*/
	Pos interPos;
	if (poly.edgeNums > 3)
		for (int i = 0; i < poly.edgeNums; i++)
		{
			interPos = CrossPos(i, (i + 2) % poly.edgeNums);
			if (JudgeInLine(interPos, poly.Edges[i]) && JudgeInLine(interPos, poly.Edges[(i + 2) % poly.edgeNums]))
			{
				cout << "该多边形为自相交多边形" << endl;
				return false;
			}
		}

	/*判断凹凸*/
	// 判断向量叉积 是否为同一正负
	int judge;
	if (CrossProduct(0) >= 0)
		judge = 1;
	else
		judge = -1;
	//判断每一个角，两边向量乘积是否同符号
	for (int i = 1; i <= poly.edgeNums; i++)
	{
		if (judge*CrossProduct(i) < 0)
		{
			poly.conv = i;
			ChangePoly();
			cout << "该多边形为凹多边形" << endl;
			return false;
		}
	}
	cout << "该多边形为凸多边形" << endl;
	return true;
}

void init(void)
{
	glClearColor(0.0, 0.0, 0.0, 0.0);

	glMatrixMode(GL_PROJECTION);//设置投影矩阵
	gluOrtho2D(0.0, 400.0, 0.0, 300.0);//二维视景区域

	glColor3f(1.0, 0.0, 0.0);
	glPointSize(3.0);//点的大小
}

void plotpoint(GLint x, GLint y)
{
	glBegin(GL_POINTS);
	glVertex2i(x, y);
	glEnd();
}

void displayFcn(void)
{
	glClearColor(0.0, 0.0, 0.0, 0.0);
	glClear(GL_COLOR_BUFFER_BIT);
	for (int i = 0; i < poly.plotNums; i++)
	{
		plotpoint(poly.xx[i], poly.yy[i]);
	}
	glBegin(GL_POLYGON);
	for (int i = 0; i < poly.edgeNums; i++)
	{
		glVertex2f(poly.xx[i], poly.yy[i]);
	}
	glEnd();

	glFlush();
}

void mouse(GLint button, GLint action, GLint x, GLint y)
{
	if (button == GLUT_LEFT_BUTTON && action == GLUT_DOWN)
	{
		poly.xx[poly.plotNums] = x;
		poly.yy[poly.plotNums] = 300 - y;
		cout << "x：" << x << "  " << "y：" << 300 - y << endl;
		poly.plotNums++;
		glutPostRedisplay();//重绘窗口
	}
	if (button == GLUT_RIGHT_BUTTON && action == GLUT_DOWN)
	{
		poly.edgeNums = poly.plotNums;
		if (poly.plotNums > 2)
		{
			for (int i = 1; i <= poly.plotNums; i++)
			{
				poly.Edges[i - 1].x1 = poly.xx[i - 1];
				poly.Edges[i - 1].y1 = poly.yy[i - 1];
				poly.Edges[i - 1].x2 = poly.xx[i%poly.plotNums];
				poly.Edges[i - 1].y2 = poly.yy[i%poly.plotNums];
				poly.Edges[i - 1].vx = poly.Edges[i - 1].x2 - poly.Edges[i - 1].x1;
				poly.Edges[i - 1].vy = poly.Edges[i - 1].y2 - poly.Edges[i - 1].y1;
				poly.Edges[i - 1].a = poly.Edges[i - 1].vy;
				poly.Edges[i - 1].b = -poly.Edges[i - 1].vx;
				poly.Edges[i - 1].c = poly.Edges[i - 1].x2 * poly.Edges[i - 1].y1 - poly.Edges[i - 1].x1 * poly.Edges[i - 1].y2;
			}
			if (Judge())
				glutPostRedisplay();//重绘窗口
		}
	}
}

int main(int argc, char** argv)
{
	glutInit(&argc, argv);
	glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
	glutInitWindowPosition(50, 100);
	glutInitWindowSize(400, 300);
	glutCreateWindow("mouse");

	init();
	glutDisplayFunc(displayFcn);

	glutMouseFunc(mouse);

	glutMainLoop();

}