Intersection between two vectors

Question

Is there efficient way to find intersection between two vectors? Ray is infinite so one way is to turn one vector to ray, find intersection between that ray and other vector. Then if there is intersection, find distance between intersection and first vector. If it is 0 then there is intersection between two vectors, if i don't miss something. But is there better way in three.js?

Answer 1

That is more a math question than a three.js one, as you mentioned you could use existing methods on the Ray object and work your way out from there, but I doubt this would be optimal as you are concerned about performance.

The right approach is probably to determine the shortest distance between two segments and if this distance is zero then they intersect. You can find a similar discussion on that thread: The Algorithm to Find the Point of Intersection of Two 3D Line Segment

And here I found a C algorithm that does exactly that, it should translate to Javascript without much efforts:

typedef struct {
  double x,y,z;
} XYZ;

/*
 Calculate the line segment PaPb that is the shortest route between
 two lines P1P2 and P3P4. Calculate also the values of mua and mub where
 Pa = P1 + mua (P2 - P1)
 Pb = P3 + mub (P4 - P3)
 Return FALSE if no solution exists.
 */
int LineLineIntersect(
  XYZ p1,XYZ p2,XYZ p3,XYZ p4,XYZ *pa,XYZ *pb,
double *mua, double *mub)
{
  XYZ p13,p43,p21;
  double d1343,d4321,d1321,d4343,d2121;
  double numer,denom;

  p13.x = p1.x - p3.x;
  p13.y = p1.y - p3.y;
  p13.z = p1.z - p3.z;
  p43.x = p4.x - p3.x;
  p43.y = p4.y - p3.y;
  p43.z = p4.z - p3.z;
  if (ABS(p43.x) < EPS && ABS(p43.y) < EPS && ABS(p43.z) < EPS)
    return(FALSE);
  p21.x = p2.x - p1.x;
  p21.y = p2.y - p1.y;
  p21.z = p2.z - p1.z;
  if (ABS(p21.x) < EPS && ABS(p21.y) < EPS && ABS(p21.z) < EPS)
    return(FALSE);

  d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z;
  d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z;
  d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z;
  d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z;
  d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z;

  denom = d2121 * d4343 - d4321 * d4321;
  if (ABS(denom) < EPS)
    return(FALSE);
  numer = d1343 * d4321 - d1321 * d4343;

*mua = numer / denom;
*mub = (d1343 + d4321 * (*mua)) / d4343;

    pa->x = p1.x + *mua * p21.x;
    pa->y = p1.y + *mua * p21.y;
    pa->z = p1.z + *mua * p21.z;
    pb->x = p3.x + *mub * p43.x;
    pb->y = p3.y + *mub * p43.y;
    pb->z = p3.z + *mub * p43.z;

  return(TRUE);
}