方法一: 求两条线段所在直线的交点, 再判断交点是否在两条线段上.
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 }
方法二: 判断每一条线段的两个端点是否都在另一条线段的两侧, 是则求出两条线段所在直线的交点, 否则不相交.
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 }; }
方法三: 判断每一条线段的两个端点是否都在另一条线段的两侧, 是则求出两条线段所在直线的交点, 否则不相交.
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 }; }