Discussion with Dad, part 2: Detecting boundaries and out-of-bounds moves

I also spoke in a more high-level sense with my dad about an important issue that I need to solve programmatically via Flash and Actionscript: the program's "awareness" of boundaries.  Here are some methods that I or we came up with:  (Note that I may not have yet researched the feasibility of each.)

• Store a 2D array of booleans.  Each cell corresponds to a grid point (i.e. potential position) and the boolean simply states whether the point is inside (true) or outside (false) the track boundaries.  This takes initial overhead to create but makes detection of out-of-bounds moves a simple array-access call.  I could create such arrays manually for tracks I draw that will be provided as pre-made tracks; the bigger issue is how to compute this array for user-drawn tracks.  My dad's solution to that is to allow users to draw the track only as a series of connected straight line segments; as each segment is created, the its slope (change in x / change in y, in grid-points) can be used to set the booleans for nearby grid points.  [This corresponds to the left-hand part of the scanned diagram below.]
• Check each player move for bounds-crossing.  An idea I had already had is for each time a player selects their next move, a line will be "drawn" (programmatically and hopefully invisibly) from the previous position to the new one.  Then, check if this line intersects with (crosses) a track boundary.  I'm not exactly sure how such an intersection check would be accomplished in Actionscript, though I tried to look around a bit for some methods (see the resource links post)...  [This corresponds to the right-hand side of the diagram below.]
• Use the intrinsic ability of Flash to "know" which area is inside and outside a shape.  This is not as crazy as it sounds.  My dad explained that such data must be stored somehow; the simplest justifying example is that enclosing bounds (i.e. a shape) can be filled with a color.  Since I had no clue how I might access this stored data, I realized maybe I could take the color-filling ability at face value: maybe I can just fill the space outside the outer boundary and inside the inner boundary with a color, and check pixel colors to see if a particular move is in bounds or not.  Again, I figure this can be accomplished with Actionscript; the solution could range from not-so-elegant to rather-hackerish.  Anyway, I'll have to look into it.  [This only corresponds to diagrams in my head, so far.]