koobas.hobune.stream
Finding shortest line segment between two rays / Closest Point of Approach
Assuming I have two rays (or, alternately, two position vectors and 2 corresponding speed vectors), what is the fastest / most resource-efficient (i.e. no for loops etc.) way to find the shortest possible line segment connecting the two rays, OR the Closest Point of Approach (for the 2+2 vectors)? Thanks in advance!
Nobody answered, and I figured on my own. Sample solution in case somebody else is interested:
public static float ClosestTimeOfApproach(Vector3 pos1, Vector3 vel1, Vector3 pos2, Vector3 vel2)
{
//float t = 0;
var dv = vel1 - vel2;
var dv2 = Vector3.Dot(dv, dv);
if (dv2 < 0.0000001f) // the tracks are almost parallel
{
return 0.0f; // any time is ok. Use time 0.
}
var w0 = pos1 - pos2;
return (-Vector3.Dot(w0, dv)/dv2);
}
public static float ClosestDistOfApproach(Vector3 pos1, Vector3 vel1, Vector3 pos2, Vector3 vel2, out Vector3 p1, out Vector3 p2)
{
var t = ClosestTimeOfApproach(pos1,vel1,pos2,vel2);
p1 = pos1 + (t * vel1);
p2 = pos2 + (t*vel2);
return Vector3.Distance(p1, p2); // distance at CPA
}
public static Vector3 ClosestPointOfApproach(Vector3 pos1, Vector3 vel1, Vector3 pos2, Vector3 vel2)
{
var t = ClosestTimeOfApproach(pos1, vel1, pos2, vel2);
if (t<0) // don't detect approach points in the past, only in the future;
{
return (pos1);
}
return (pos1 + (t * vel1));
}
@molokh, mark your own answer as accepted (click the "check" button below the voting thumbs). This will help others to find this great solution - and may render you some up votes too!
actually I get the resaults wrong:
Vector3 P1;
Vector3 P2;
ClosestDistOfApproach(new Vector3(1, 0, 0), new Vector3(0,1,1), new Vector3(-1,0,0), new Vector3(0,1,-1),out P1,out P2);
Debug.Log(P1 + " : " + P2); //(1.0, 0.0, 0.0) : (-1.0, 0.0, 0.0)
actually closest points are:
0,0,0 AND 0,1,0
ok found this video:
http://www.youtube.com/watch?v=HC5YikQxwZA
explains very good.
by asking and searching around I found a solution
Yea, it took me about an hour to figure out this guy's solution wasn't correct - and I was so happy I didn't have to write one myself - which took less than to get my textbook out, search for the page and transcribe the code (before I read the comments and saw your link and then beat myself up over it).
I guess I'll chalk it up to my mentality to thinking my code's always the problem and marked solutions on Unity Answers are always checked and correct.
I took the line-to-line collision code in Christer Ericson's RealTime Collision Detection book, turned into into ray collision by unclamping the ends, and it pretty much looked exactly like that wiki's code.
Found this post that helped me when I couldn't get this solution to work. https://answers.unity.com/questions/759630/point-of-intersection-between-two-rays.html
The answer links to these resources (the function ClosestPointsOnTwoLines helped me out the most with my problem): http://wiki.unity3d.com/index.php/3d_Math_functions?_ga=2.104569024.1350420062.1572253629-1502904723.1553610781
Hope it helps :)
