判断两条线段是否相交（三种算法）

算法1：

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///----------alg 1------------

struct Point

{

double x, y;

};

bool between(double a, double X0, double X1)

{

double temp1= a-X0;

double temp2= a-X1;

if ( ( temp1<1e-8 && temp2>-1e-8 ) || ( temp2<1e-6 && temp1>-1e-8 ) )

{

return true;

}

else

{

return false;

}

}

// 判断两条直线段是否有交点，有则计算交点的坐标

// p1,p2是直线一的端点坐标

// p3,p4是直线二的端点坐标

bool detectIntersect(Point p1, Point p2, Point p3, Point p4)

{

double line_x,line_y; //交点

if ( (fabs(p1.x-p2.x)<1e-6) && (fabs(p3.x-p4.x)<1e-6) )

{

return false;

}

else if ( (fabs(p1.x-p2.x)<1e-6) ) //如果直线段p1p2垂直与y轴

{

if (between(p1.x,p3.x,p4.x))

{

double k = (p4.y-p3.y)/(p4.x-p3.x);

line_x = p1.x;

line_y = k*(line_x-p3.x)+p3.y;

if (between(line_y,p1.y,p2.y))

{

return true;

}

else

{

return false;

}

}

else

{

return false;

}

}

else if ( (fabs(p3.x-p4.x)<1e-6) ) //如果直线段p3p4垂直与y轴

{

if (between(p3.x,p1.x,p2.x))

{

double k = (p2.y-p1.y)/(p2.x-p1.x);

line_x = p3.x;

line_y = k*(line_x-p2.x)+p2.y;

if (between(line_y,p3.y,p4.y))

{

return true;

}

else

{

return false;

}

}

else

{

return false;

}

}

else

{

double k1 = (p2.y-p1.y)/(p2.x-p1.x);

double k2 = (p4.y-p3.y)/(p4.x-p3.x);

if (fabs(k1-k2)<1e-6)

{

return false;

}

else

{

line_x = ((p3.y - p1.y) - (k2*p3.x - k1*p1.x)) / (k1-k2);

line_y = k1*(line_x-p1.x)+p1.y;

}

if (between(line_x,p1.x,p2.x)&&between(line_x,p3.x,p4.x))

{

return true;

}

else

{

return false;

}

}

}

///------------alg 1------------

算法2：

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///------------alg 2------------

//叉积

double mult(Point a, Point b, Point c)

{

return (a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y);

}

//aa, bb为一条线段两端点 cc, dd为另一条线段的两端点 相交返回true, 不相交返回false

bool intersect(Point aa, Point bb, Point cc, Point dd)

{

if ( max(aa.x, bb.x)<min(cc.x, dd.x) )

{

return false;

}

if ( max(aa.y, bb.y)<min(cc.y, dd.y) )

{

return false;

}

if ( max(cc.x, dd.x)<min(aa.x, bb.x) )

{

return false;

}

if ( max(cc.y, dd.y)<min(aa.y, bb.y) )

{

return false;

}

if ( mult(cc, bb, aa)*mult(bb, dd, aa)<0 )

{

return false;

}

if ( mult(aa, dd, cc)*mult(dd, bb, cc)<0 )

{

return false;

}

return true;

}

///------------alg 2------------

算法3：http://dec3.jlu.edu.cn/webcourse/t000096/graphics/chapter5/01_1.

html

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///------------alg 3------------

double determinant(double v1, double v2, double v3, double v4) // 行列式

{

return (v1*v4-v2*v3);

}

bool intersect3(Point aa, Point bb, Point cc, Point dd)

{

double delta = determinant(bb.x-aa.x, cc.x-dd.x, bb.y-aa.y, cc.y-dd.y);

if ( delta<=(1e-6) && delta>=-(1e-6) ) // delta=0，表示两线段重合或平行

{

return false;

}

double namenda = determinant(cc.x-aa.x, cc.x-dd.x, cc.y-aa.y, cc.y-dd.y) / delta;

if ( namenda>1 || namenda<0 )

{

return false;

}

double miu = determinant(bb.x-aa.x, cc.x-aa.x, bb.y-aa.y, cc.y-aa.y) / delta;

if ( miu>1 || miu<0 )

{

return false;

}

return true;

}

///------------alg 3------------

main函数测试：

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int main()

{

Point p1, p2, p3, p4;

p1.x = 1;

p1.y = 4;

p2.x = 3;

p2.y = 0;

p3.x = 0;

p3.y = 1;

p4.x = 4;

p4.y = 3;

int i=0, j=0;

bool flag = false;

flag = intersect3(p1, p2, p3, p4);

// alg 2

time_t seconds1 = time (NULL);

for ( ; i!=20000; ++i )

{

for ( j=0; j!=60000; ++j )

{

flag = detectIntersect(p1, p2, p3, p4);

}

}

time_t seconds2 = time (NULL);

cout << "Time used in alg 1:" << seconds2-seconds1 << " seconds." << endl;

// alg 2

time_t seconds3 = time (NULL);

i=0;

j=0;

for ( ; i!=20000; ++i )

{

for ( j=0; j!=60000; ++j )

{

flag = intersect(p1, p2, p3, p4);

}

}

time_t seconds4 = time (NULL);

cout << "Time used in alg 2:" << seconds4-seconds3 << " seconds." << endl;

// alg 3

time_t seconds5 = time (NULL);

i=0;

j=0;

for ( ; i!=20000; ++i )

{

for ( j=0; j!=60000; ++j )

{

flag = intersect3(p1, p2, p3, p4);

}

}

time_t seconds6 = time (NULL);

cout << "Time used in alg 3:" << seconds6-seconds5 << " seconds." << endl;

return 0;

}

VS2008编译器环境下测试结果：

Debug模式下：

alg 1: 315 seconds;

alg 2: 832 seconds;

alg 3: 195 seconds;

Release模式下：

alg 1: 157 seconds;

alg 2: 169 seconds;

alg 3: 122 seconds;

结论： 使用算法3，时间复杂度最低。