Handling Tables for Rays with Hits Close to Edges

Conventions:

Character       Meaning
------------------------------------------------------
   H		Unambiguous hit - clearly untrimmed

   c		Close to trim (within tolerance) -
		ambiguous hit, may be trimmed

   +		Hit is entering the surface

   -		Hit is leaving the surface
------------------------------------------------------


Hits Per Ray Cases:

Different decisions must be made in different situations;
here we spell out the various cases and how to handle them.
The convention is leftmost H/c character on a line is the
first hit point in the sorted hit list, and points to the
right are ordered in the order they would be encountered
by the ray.



Single Hit: 
	
	Degenerate regardless of ambiguity - reject

General Rules for All Multi-Hit Cases:

	1. First hit point may only be exiting 
	   a surface if it is ambigous - otherwise,
	   return an error.

	2. First hit point which is exiting a surface
	   and ambiguous should be disgarded.
	
	3. Last hit point may only be entering
	   a surface if it is ambiguous - otherwise, 
	   return error

	4. Last hit point which is entering a surface
	   and is ambiguous should be disgarded.

	5. If, after application of rules 2 and 4, a hit
	   list contains only a single hit, return
           an error.

	6. If a list contains a sequence of two unambiguous
	   hits that are both entering or both leaving a
	   surface with no ambiguous cases of opposite
	   parity between them, return error.

	7. If two unambiguous hit points at the beginning
	   of a ray constitute a valid in/out pair, accept
	   the pair and begin again with list of remaining
	   hit points.


	Now we come to the more difficult cases.  If a non-ambiguous 
	hit point is has no matching non-ambiguous hit point in the list, 
	one or more of the ambiguous points must be used to complete the
	pair - the reasoning being that the unambiguous hit is proof 
	positive there should be a solid surface, and thus one of the 
	ambiguous points is intended to be a true hit point. Even more 
	difficult is the situation where TWO cracks are hit - in that 
	case, a miss would be returned if an all-ambiguous hit list were
	ignored.  By the same token, multiple ambiguous hits could complicate
	the situation - a crack may return two hit points and a grazing
	hit on a trim could return a third, but only the two from the crack
	are important for ensuring solidity.  To ensure this is not a problem,
	the following steps must be taken:

	1.  Do a preliminary pass on the hit list looking for pairs of ambiguous hit
	    points with a shared in/out hit status and close 3D space hit
	    coordinates - combine these two ambiguous hit points into a
	    single merged hit point.  May want to "average" the normals
	    of the two hits to get an intermediate normal, since the resulting
	    point will not technically be on either surface. 

	2.  Merged hit points have an elevated status as compared to 
	    ambiguous points - they will be favored over ambiguous hit 
	    points when in/out pair identification is done, but a single
	    unpaired merged point at the end of list processing will be
	    discarded rather than generating an error.  Merged points will
	    still rank below unambiguous hit points - given the choice
	    of paring with an unambiguous hit vs a merged hit, pick the
            unambiguous hit.


For some specific examples of these rules, see following tables:

Double Hit:

	Case			Decision
	(H+)(c-)		Accept ambiguous hit point

Triple Hit:
	
	Case			Decision
	(c+)(c+)(H-)		If points didn't merge, reject the first ambiguous 
				        point, accept the second unless the first shares a 
					surface with the unambiguous point and the second 
					does not.
	(c+)(c-)(H-)		Accept first ambiguous point, reject second
	(c+)(H+)(c-)		Reject first ambiguous point, accept second
	(c+)(H-)(c-)		Accept first ambiguous point, reject second
	(c+)(H+)(H-)		Reject ambiguous point
	(H+)(c+)(c-)		Reject first ambiguous point, accept second
	(H+)(c+)(H-)		Reject ambiguous point
	(H+)(c-)(c-)		If points didn't merge, accept first ambiguous point 
				        and reject the second unless the second shares a 
					surface with the unambiguous point and the first 
					does not.
	(H+)(c-)(H-)		Reject ambiguous point