```
function segmentsIntr(a, b, c, d){

/** 1 解线性方程组, 求线段交点. **/
// 如果分母为0 则平行或共线, 不相交
var denominator = (b.y - a.y)*(d.x - c.x) - (a.x - b.x)*(c.y - d.y);
if (denominator==0) {
return false;
}

// 线段所在直线的交点坐标 (x , y)
var x = ( (b.x - a.x) * (d.x - c.x) * (c.y - a.y)
+ (b.y - a.y) * (d.x - c.x) * a.x
- (d.y - c.y) * (b.x - a.x) * c.x ) / denominator ;
var y = -( (b.y - a.y) * (d.y - c.y) * (c.x - a.x)
+ (b.x - a.x) * (d.y - c.y) * a.y
- (d.x - c.x) * (b.y - a.y) * c.y ) / denominator;

/** 2 判断交点是否在两条线段上 **/
if (
// 交点在线段1上
(x - a.x) * (x - b.x) <= 0 && (y - a.y) * (y - b.y) <= 0
// 且交点也在线段2上
&& (x - c.x) * (x - d.x) <= 0 && (y - c.y) * (y - d.y) <= 0
){

// 返回交点p
return {
x : x,
y : y
}
}
//否则不相交
return false

}

```

```
function segmentsIntr(a, b, c, d){

//线段ab的法线N1
var nx1 = (b.y - a.y), ny1 = (a.x - b.x);

//线段cd的法线N2
var nx2 = (d.y - c.y), ny2 = (c.x - d.x);

//两条法线做叉乘, 如果结果为0, 说明线段ab和线段cd平行或共线,不相交
var denominator = nx1*ny2 - ny1*nx2;
if (denominator==0) {
return false;
}

//在法线N2上的投影
var distC_N2=nx2 * c.x + ny2 * c.y;
var distA_N2=nx2 * a.x + ny2 * a.y-distC_N2;
var distB_N2=nx2 * b.x + ny2 * b.y-distC_N2;

// 点a投影和点b投影在点c投影同侧 (对点在线段上的情况,本例当作不相交处理);
if ( distA_N2*distB_N2>=0 ) {
return false;
}

//
//判断点c点d 和线段ab的关系, 原理同上
//
//在法线N1上的投影
var distA_N1=nx1 * a.x + ny1 * a.y;
var distC_N1=nx1 * c.x + ny1 * c.y-distA_N1;
var distD_N1=nx1 * d.x + ny1 * d.y-distA_N1;
if ( distC_N1*distD_N1>=0 ) {
return false;
}

//计算交点坐标
var fraction= distA_N2 / denominator;
var dx= fraction * ny1,
dy= -fraction * nx1;
return { x: a.x + dx , y: a.y + dy };
}

```

```
function segmentsIntr(a, b, c, d){

// 三角形abc 面积的2倍
var area_abc = (a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x);

// 三角形abd 面积的2倍
var area_abd = (a.x - d.x) * (b.y - d.y) - (a.y - d.y) * (b.x - d.x);

// 面积符号相同则两点在线段同侧,不相交 (对点在线段上的情况,本例当作不相交处理);
if ( area_abc*area_abd>=0 ) {
return false;
}

// 三角形cda 面积的2倍
var area_cda = (c.x - a.x) * (d.y - a.y) - (c.y - a.y) * (d.x - a.x);
// 三角形cdb 面积的2倍
// 注意: 这里有一个小优化.不需要再用公式计算面积,而是通过已知的三个面积加减得出.
var area_cdb = area_cda + area_abc - area_abd ;
if ( area_cda * area_cdb >= 0 ) {
return false;
}

//计算交点坐标
var t = area_cda / ( area_abd- area_abc );
var dx= t*(b.x - a.x),
dy= t*(b.y - a.y);
return { x: a.x + dx , y: a.y + dy };

}

```