OpenGL线段求交，有图有真相

最新推荐文章于 2025-09-05 20:12:42 发布

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该博客介绍如何使用OpenGL进行线段交点检测，通过示例代码展示了线段相交、平行及无交点但直线相交的情况，并提供了完整的实例下载链接。

OpenGL 线段求交，有图有真相

点此下载完整实例：

http://rorger.download.youkuaiyun.com/

#include "windows.h" #include "glut.h" #include "math.h" #define pi 3.14159265358 class Point2{ public: float x, y ; void set(float x, float y){this->x=x ;this->y=y;} void set(Point2&p){x=p.x;y=p.y;} }; typedef Point2 Vector2; //用四个点表示两条线段，如果线段没有焦点（直线有相交），返回0 ，如果有，则返回1. //如果相交，那么焦点的值会存入InterPt.如果父直线不相交，则返回-1 int segIntersect(Point2 A,Point2 B,Point2 C,Point2 D,Point2 &InterPtr) ; int SystemOfLinearEquationOfTwo(Vector2 b,Vector2 c,Vector2 d,float& t,float& u); int SystemOfLinearEquationOfTwo(float bx,float by, float cx,float cy,float dx,float dy,float& t,float& u); void test(Point2 A,Point2 B,Point2 C,Point2 D,Point2& InterPtr); int segIntersect(Point2 A,Point2 B,Point2 C,Point2 D,Point2 &InterPtr) { float t,u ; int result ; Vector2 b; b.set(B.x-A.x,B.y-A.y) ; Vector2 c ; c.set(C.x-A.x,C.y-A.y) ; Vector2 d; d.set(D.x-C.x,D.y-C.y) ; result=SystemOfLinearEquationOfTwo(b,c,d,t,u); switch(result) { case 1: //both t or u are ok,here we use t InterPtr.x=A.x+t*b.x; InterPtr.y=A.y+t*b.y; break; case -1: break; case 0: //we also calculate the intersect point InterPtr.x=A.x+t*b.x; InterPtr.y=A.y+t*b.y; break; default: break; } return result; } //看来我要编写一个二元一次方程组的求解函数啊 //形式如：6t=5/2+7/2u // -7/2t=-3/2+5/2u //我想在计算机中不必考虑那种相加和相乘的方法,因为这样还需要寻找最小公倍数 //可以这样求u时，另两个等式左边的t的系数都化为1，那么等式1右边和等式2右边相等，很容易求出u //求t时，同理吧 //parameter ax,ay represents VectorA(ax,ay), and so on. int SystemOfLinearEquationOfTwo(float bx,float by, float cx,float cy,float dx,float dy,float& t,float& u) { Vector2 b ; b.set(bx,by) ; Vector2 c ; c.set(cx,cy) ; Vector2 d; d.set(dx,dy) ; return SystemOfLinearEquationOfTwo(b,c,d,t,u); } //求解二元一次方程组 int SystemOfLinearEquationOfTwo(Vector2 b,Vector2 c,Vector2 d,float& t,float& u) { //判断向量a和d是否平行,先归一化向量 Vector2 unia ; Vector2 unid; unia.x=b.x/(sqrt(b.x*b.x+b.y*b.y)); //分母比不为0，因为如果为0就是0向量了，而这在实际情况没有意义 unia.y=b.y/(sqrt(b.x*b.x+b.y*b.y)); unid.x=d.x/(sqrt(d.x*d.x+d.y*d.y)); unid.y=d.y/(sqrt(d.x*d.x+d.y*d.y)); if (unia.x == unid.x && unia.y==unid.y) { return -1 ; //没有交点，线段平行,有无数的解 } //计算u //a.x==0和a.y==0不会同时出现 if(b.x==0)// 无需判断if(a.x==0 && d.x!=0)，因为如果a.x,d.x都为0，必然是平行的情况 { u=-c.x/d.x ; } else if (b.y==0)// && d.y!=0) { u=-c.y/d.y; } else if (b.x !=0 && b.y != 0) { //方程组1两边同时除以a.x //方程组2两边同时除以a.y //另方程组相等即:c.x/a.x+d.x/a.x *u = c.y/a.y+d.y*u /a.y; u=(c.y/b.y-c.x/b.x)/(d.x/b.x-d.y/b.y) ; } //计算t //d.x==0 && d.y==0是不会同时出现的，因为(0,0)向量在这里没有意义 if (d.x==0)// && a.x!=0) { t=c.x/b.x; } else if (d.y ==0 )//&& a.y!=0) { t=c.y/b.y; } else if(d.x !=0 && d.y != 0) { //计算t //方程组1两边同时除以d.x //方程组两边同时除以d.y // 同上得:a.x/d.x*t-c.x/d.x=a.y/d.y*t-c.y/d.y t=(c.x/d.x-c.y/d.y)/(b.x/d.x-b.y/d.y) ; } //如果线段有交点，那么t和u必然介于0和1之间 if(0<=t&&t<=1 && 0<=u&&u<=1) { return 1;//线段有交点 } else if (t<0 || t>1 || u<0 || u>1) { return 0;//线段没有交点，但是线段所在的直线有交点 } return -9999 ; } void myDisplay(void) // plot the sinc function, using world coordinates { Point2 A,B,C,D; Point2 InterPtr; //test1,线段有交点 pass A.set(1,4); B.set(7,1/2.0); C.set(7/2.0,5/2.0); D.set(7,5); test(A,B,C,D,InterPtr); // t=1/109,u=46/109 //test2,线段平行 pass //A.set(0,7); //B.set(7,0); //C.set(8,-1); //D.set(10,-3); //test(A,B,C,D,InterPtr); //test3,线段无交点，但所在直线有交点 pass /*A.set(0,2); B.set(5,0); C.set(0,5); D.set(3,3);*/ //test(A,B,C,D,InterPtr);// t=9/4, t=15/4 //test4,平行的情况，同时a.x=0,,d.x=0的情况 pass /*A.set(0,2); B.set(0,4); C.set(1,2); D.set(1,4); test(A,B,C,D,InterPtr); */ } void test(Point2 A,Point2 B,Point2 C,Point2 D,Point2& InterPtr) { int result ; result=segIntersect(A,B,C,D,InterPtr); switch(result) { case -1: glColor3f(0.0,1.0,0.0); glBegin(GL_LINES); glVertex2f(A.x,A.y); glVertex2f(B.x,B.y); glVertex2f(C.x,C.y); glVertex2f(D.x,D.y); glEnd(); glFlush(); break; case 0: glColor3f(0.0,1.0,0.0); glBegin(GL_LINES); glVertex2f(A.x,A.y); glVertex2f(B.x,B.y); glVertex2f(C.x,C.y); glVertex2f(D.x,D.y); glEnd(); glColor3f(0.0,0.0,1.0); glBegin(GL_POINTS); glVertex2f(InterPtr.x,InterPtr.y); glEnd(); glEnable(GL_LINE_STIPPLE); glLineStipple (1, 0x000F); glColor3f(0.0,1.0,0.0); glBegin(GL_LINES); glVertex2f(A.x,A.y); glVertex2f(InterPtr.x,InterPtr.y); glVertex2f(C.x,C.y); glVertex2f(InterPtr.x,InterPtr.y); glEnd(); glDisable(GL_LINE_STIPPLE); glFlush(); break; case 1: glColor3f(0.0,1.0,0.0); glBegin(GL_LINES); glVertex2f(A.x,A.y); glVertex2f(B.x,B.y); glVertex2f(C.x,C.y); glVertex2f(D.x,D.y); glEnd(); glColor3f(1.0,0.0,0.0); glBegin(GL_POINTS); glVertex2f(InterPtr.x,InterPtr.y); glEnd(); glFlush(); break; default: break; } }