[Algorithms] Moving Segment vs Moving Point Intersection (2D)

[metanet s. <met...@ya...>]

hi,
  Hopefully someone can point me towards some good references/theory..  moving-segment tests came up in the context of Carmageddon a while ago  (I think), but searching the archives hasn't turned anything up.
  
  My current "ad-hoc" algorithm is:
  
  given linesegment with endpoints A,B and endpoint velocities vA,vB, and point C with velocity vC:
  1) find the velocity V of C relative to segment A->B**
  2) use this to perform a segment-vs-segment test, using A->B vs C->(C+V)
  
  **for step (1), I find the point on A->B closest to C, and use the  parametric description of this point to blend vA and vB together to  generate a single velocity for the segment (which is subtracted from vC  to get C's velocity from A-B's frame of reference).
  
  Step 1 seems very approximate/hacky, since you can use any combination  of current or future positions, each of which will give you a different  result:
  -point on A->B closest to C
  -point on A->B closest to (C+vC)
  -point on (A+vA)->(B+vB) closest to C
  -point on (A+vA)->(B+vB) closest to (C+vC)
  
  ..there's no obvious "best"/most correct combination, which seems to  indicate that the "real" solution to this problem is probably not so  neat or linear, involving root finding or closest-point-of-approach  calculation.
  
  Anyway, any tips, suggestions or references would be great, I'd really  like to know of any more accurate (or at least less  spontaneously-invented) approached.
  
  I should mention that I only need a boolean result, no time/point of intersection.
  
  thanks,
  raigan
  
		
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