找到共线之间的重叠

Question

给定两条共线线段AB和CD,如何找到它们是否重叠？如何找到重叠的起点和终点？

以下是我正在使用的方法.我首先确保A <B和C <D.

if(pa < pc){
  if(pc < pb){
    if(pd < pb){
      //  overlap exists; CD falls entirely within AB
    }
    else {
      //  overlap exists; CB is the overlapping segment
    }
  }
  else {
    //  no overlap exists; AB lies before CD
  }
}
else {
  if(pa < pd){
    if(pb < pd){
      //  overlap exists; AB lies entirely within CD
    }
    else {
      //  overlap exists; AD is the overlapping segment
    }
  }
  else {
    //  no overlap exists; CD lies before AB
  }
}

现在,有没有更简单的解决方案呢？

更新:还有另一种方法...比较两个段的长度之和与最外点之间的距离.如果后者较小,则存在重叠.

Answer 1

确保A <B,C <D:

if (pb - pc >= 0 and pd - pa >=0 ) { // overlap
    OverlapInterval = [ max(pa, pc), min(pb, pd) ] // it could be a point [x, x]
} // else: not overlap