Is That a Sparse Matrix? Extraordinary!

Okay, I get it now: you're proposing that there are two "vector spaces", one scaled-up for the really big objects and another scaled-down for the really small ones.

The small-scale space always occludes the large, so that no object in "small space" could ever be represented accurately as being on the opposite side of or obscured by an object in "large space".

You'll never notice that small objects can never be behind large ones because the large objects are much larger than 400 km, so that an object behind a large object would always be beyond the 400 km clip range (never mind the ~100 km visual range).

Space stations, which never clip, must exist in both systems, but the mode switch occurs at 400 klicks where the player can't see it.

That certainly seems possible.

The way I would do it (ha ha) would be to write -- or buy -- a math library that handled really, really big integers, then fix the decimal point issues in the display algorithm (so that the display algorithm represents a distance of, say, 1600 units as "1.6 meters").

Every significant digit costs log10 / log2, or around 3 1/3 bits. It seems to me the minimum practical number of bits required to give you the I-War vector space's level of precision and magnitude is 48 bits, a 3-byte integer, but I suspect 64-bit integers are easier to deal with. (There are probably software libraries available that do 64-bit integer math.)

Ironically as long as you never touch the FPU you can make numbers arbitrarily significant (large and/or precise) quite easily. I would use all integer-based math routines. There are ways to do even trig functions and the like purely with integer math, although I suspect some of the table-based solutions wouldn't scale well to 64-bit coordinates.

Something else that's been bothering me: I think my understanding of "sparse matrix" is flawed ... a 3D vector space isn't a "matrix". The points within the vector space cannot contain "values" per se; rather objects have a particular address composed of coordinates. Just as cells in spreadsheets don't typically fly around, points in flight sim space don't have little formulas or values in them, even if there happens to be a space ship flying through them. Err, as Jafs would say, "Oops! Heh heh, I guess that's one less pod for me to pick up."

Just as cells in spreadsheets don't typically fly around, points in flight sim space don't have little formulas or values in them, even if there happens to be a space ship flying through them.

The objects (sims) have little formulas and values in them.

like position (as a vector), velocity (as a vector) and angular velocity (as a vector)

My understanding of the whole thing is like Einstein said: Everything is relative. Including size.




Have Gun, Will Travel

Right, the objects have the focus, not the addresses, which makes me think it isn't properly labelled a "matrix".

A given coordinate does not possess any discrete properties, except by virtue of objects occupying space which incidentally includes that coordinate. Of course one could argue that this constitutes an extreme example of a "sparse matrix", but I don't buy that.

If I ask, "What is the value of cell 45 x 1098 x 12" and you answer, "Just a moment, let me check my object database to see if there are any objects occupying that coordinate," that's not a matrix. That's a vector space with objects flying through it.

Hmm, I wonder if cellular automata could be treated as objects in vector-space instead of as values in a matrix? Or whether matrices of cellular automata could be used to simulate things like "living ships" or nanotechnology acting on vector-space objects? Or what kind of slow-ass framerate you'd end up with?

Whoa -- if life itself is but a quantum cellular automaton, and if movie CG effects take place in 3D vector space, that would mean the movie "The Matrix" is really a vector-space, while life itself is really a matrix! (They should put me in a shrine on a mountaintop for coming up with this stuff ...)

They probably already have, but it's in a parallel reality, or rather the adjacent matrix of the hyper vector space that defines all possible matrices.

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Hot4Darmat

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