Glyph-space - calling all maths geniuses
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PTeppic
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Jed./Shaz: certainly - but it is written in Ada, so you will probably have to translate it into something else...
One of the benefits (in this case) of Ada is that you can specify the resolution of real numbers (subject to hardware implementation) and in this case I have used 15-digit floating point numbers... i.e. 1E-15 is the smallest number "used" (okay, approximated to in binary). I am not sure how other languages use such numbers, or even if they can be specified!
However, I would LOVE to see some algorithms for polygons.
I can work out the XYZ for 38 points on a sphere - I just need the underlying algorithm to do 3D intersection... I will try to get the code listing today for you nice people.
One of the benefits (in this case) of Ada is that you can specify the resolution of real numbers (subject to hardware implementation) and in this case I have used 15-digit floating point numbers... i.e. 1E-15 is the smallest number "used" (okay, approximated to in binary). I am not sure how other languages use such numbers, or even if they can be specified!
However, I would LOVE to see some algorithms for polygons.
I can work out the XYZ for 38 points on a sphere - I just need the underlying algorithm to do 3D intersection... I will try to get the code listing today for you nice people.
PTeppic
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Well, with no help at all from this forum 
I worked out the algorithm myself, using Ada as a programming language.
(see attached file)
The software WORKS, and it CAN find intersections in space between 38 points around the edge of a sphere. Which means that the addressing system of Stargate could (theoretically at least) actually work!
However (and this is a HUGE "if") - I could only find it working when the specimen sample points I used were very regularly and geometrically spaced [details available as comments in the code!]. If the points are pretty much random, like say the real position of the galaxies used by the show, the intersections just fell apart. What I have not tried is using a lower tolerance over the intersections - we know there is SOME slack, since each detaination planet moves so much in orbit etc.
Theoretically the tolerance could be up to about 1/2 the smallest distance between any identifiable destination...
Warning:For some reason the text file has had all its carriage-returns removed!! Help? I still have the original here of course.
I worked out the algorithm myself, using Ada as a programming language.(see attached file)
The software WORKS, and it CAN find intersections in space between 38 points around the edge of a sphere. Which means that the addressing system of Stargate could (theoretically at least) actually work!
However (and this is a HUGE "if") - I could only find it working when the specimen sample points I used were very regularly and geometrically spaced [details available as comments in the code!]. If the points are pretty much random, like say the real position of the galaxies used by the show, the intersections just fell apart. What I have not tried is using a lower tolerance over the intersections - we know there is SOME slack, since each detaination planet moves so much in orbit etc.
Theoretically the tolerance could be up to about 1/2 the smallest distance between any identifiable destination...
Warning:For some reason the text file has had all its carriage-returns removed!! Help? I still have the original here of course.
ok... i was wondering.... if we take the center or our galexy as 0,0 or a 3d plain.... woild you be able to figure out the position of each galexy or star that is used on the stargate??? cause if you could figure out those X,Y,Z points than you can substute them in for the points. then we could see how many inter sections there are.
i can help with figuring those coridinats out... also where do you download ADA?
i can help with figuring those coridinats out... also where do you download ADA?
PTeppic
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Planets - I assume that you have each galaxial position in terms of polar co-ordinates, in which case they go almost raw into a constant definition. We would also need the radius of the galaxy!!
Ada - we sort of have it at work, and although I don't write the stuff for a living, I have to read and analyse such code, and therefore examples such as this one are useful to "keep my hand in" as it were.
Ada - Try some of the big shareware places - I think there is a Gnu version. BUT the problem with my listing is that it uses a specific MATHS_LIB package - which although standard-ish would probably have to be adapted for any DL'ed version. TEXT_IO should be standard (according to the language definition anyway!).
Ada - we sort of have it at work, and although I don't write the stuff for a living, I have to read and analyse such code, and therefore examples such as this one are useful to "keep my hand in" as it were.
Ada - Try some of the big shareware places - I think there is a Gnu version. BUT the problem with my listing is that it uses a specific MATHS_LIB package - which although standard-ish would probably have to be adapted for any DL'ed version. TEXT_IO should be standard (according to the language definition anyway!).
PTeppic
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Just thinking aloud again:
a) my model used a sphere of radius 1000 units.
b) the galaxy is radius 50,000 light years, so my model represents 50 light years per unit.
Now, the accuracy of the model was 14 decimal places (in theory), and a light year is 5.88E12 miles, SO, after all of that, the model is actually too accurate for a glyph address system we have elsewhere deduced needs at least 180 million miles of tolerance!
Which means if we undo the tolerance that much, almost any combination of the glyph symbols will count as intersecting!
a) my model used a sphere of radius 1000 units.
b) the galaxy is radius 50,000 light years, so my model represents 50 light years per unit.
Now, the accuracy of the model was 14 decimal places (in theory), and a light year is 5.88E12 miles, SO, after all of that, the model is actually too accurate for a glyph address system we have elsewhere deduced needs at least 180 million miles of tolerance!
Which means if we undo the tolerance that much, almost any combination of the glyph symbols will count as intersecting!
PTeppic
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I would imagine, in fact, that it will be the pattern of the glyph constellations around the galaxy that will determine the tolerance... :eek7:
My model is too accurate, since it is approximately accurate to within three miles (even on a stellar scale). To reduce the accuracy of tolerance means that the "near misses" will get the chance to "hit" as a result of orbits and rotations and so on....
But, conversely and more importantly, each reduction in tolerance gives rise to the possibility of a planet orbiting into a SECOND glyph address intersection. One thing I have not done yet is to calculate the closest distance between any two intersections. It is THIS distance that would perhaps be the limiting factor - or not as my thoughts below show.
a) Of course, any race powerful enough to design the gates could also install some sort of call-barring to prevent the over-lapping theoretical addresses from being used which may not be a problem if there is physically no planet there anyway, apart from the one which is moving between the two intersections
b) It theoretically allows two DIFFERENT addresses to be used for accessing the SAME planet [to any SG-1 writers reading this: I hereby give full permission to use this idea in any show/fan-fic]
c) This loose tolerance explains why there are so many valid address combinations
d) And (as a next step) it explains why it is so easy to calculate a NEW (valid) address as a result of stellar drift (i.e. the thing the dialling computer is doing based on the old stellar positions from the Abydos cartouche room)
e) It also allows almost any planet to get a gate if it didn't have one before (e.g. Tollana) though there will be SOME limitations.
In fact, thinking back to previous threads, the limiting factor on tolerance in the gate system will be the size of the largest orbit of a "valid" and intended planet within the stargate system. The ancients designed the system to work for different planets, which rotate about their suns at differing distances. This means they have a net movement about the galaxy of approximately twice the radius of orbit. So, any tolerance in intersection would have to be able to allow for that. But, if the intersection point were actually at the sun, the tolerance would only need to be, say, 105% of the orbit etc. But you get the idea... it is this orbit which determines the tolerance.
A step further: from experience of the those visited and also Sam's explanation to her father that the gate system appears designed for human-like beings (despite there not being a gate on Earth - though we only assume Ra brought it!) we can extrapolate from physics that to get a breathable atmosphere requires a fairly tightly specified planet in terms of gravity, radius, and *position with the star system*. Temperature and atmosphere would all be affected by relative positions, so even in other planets, the solar radius to the planet would be relatively similar to Earth, for a given type/size of sun. [This is where my knowledge breaks down a bit]
My model is too accurate
, since it is approximately accurate to within three miles (even on a stellar scale). To reduce the accuracy of tolerance means that the "near misses" will get the chance to "hit" as a result of orbits and rotations and so on....But, conversely and more importantly, each reduction in tolerance gives rise to the possibility of a planet orbiting into a SECOND glyph address intersection. One thing I have not done yet is to calculate the closest distance between any two intersections. It is THIS distance that would perhaps be the limiting factor - or not as my thoughts below show.
a) Of course, any race powerful enough to design the gates could also install some sort of call-barring
to prevent the over-lapping theoretical addresses from being used which may not be a problem if there is physically no planet there anyway, apart from the one which is moving between the two intersectionsb) It theoretically allows two DIFFERENT addresses to be used for accessing the SAME planet [to any SG-1 writers reading this: I hereby give full permission to use this idea in any show/fan-fic]
c) This loose tolerance explains why there are so many valid address combinations
d) And (as a next step) it explains why it is so easy to calculate a NEW (valid) address as a result of stellar drift (i.e. the thing the dialling computer is doing based on the old stellar positions from the Abydos cartouche room)
e) It also allows almost any planet to get a gate if it didn't have one before (e.g. Tollana) though there will be SOME limitations.
In fact, thinking back to previous threads, the limiting factor on tolerance in the gate system will be the size of the largest orbit of a "valid" and intended planet within the stargate system. The ancients designed the system to work for different planets, which rotate about their suns at differing distances. This means they have a net movement about the galaxy of approximately twice the radius of orbit. So, any tolerance in intersection would have to be able to allow for that. But, if the intersection point were actually at the sun, the tolerance would only need to be, say, 105% of the orbit etc. But you get the idea... it is this orbit which determines the tolerance.
A step further: from experience of the those visited and also Sam's explanation to her father that the gate system appears designed for human-like beings (despite there not being a gate on Earth - though we only assume Ra brought it!
) we can extrapolate from physics that to get a breathable atmosphere requires a fairly tightly specified planet in terms of gravity, radius, and *position with the star system*. Temperature and atmosphere would all be affected by relative positions, so even in other planets, the solar radius to the planet would be relatively similar to Earth, for a given type/size of sun. [This is where my knowledge breaks down a bit]ya those are some really good points.... what i'm going to do one my March break is i will work out the positions of the 38 galexies on a 3D cartesian plane so that we can extrapolate from that as to the possiblities of the of the nubers of gates... ok???
PTeppic
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The algorithm for doing that is in the software (as supplied)... or you could use your own method
[The only slight variation from the equations you might expect are that instead of 0-90N/S, due N is 0 degrees, and then down to 180 at due S.]
[The only slight variation from the equations you might expect are that instead of 0-90N/S, due N is 0 degrees, and then down to 180 at due S.]
PTeppic
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Oh no!
I have discovered some sort of problem with my algorithm... I *think* the theory is correct, it is just the implementation.
However, I was looking at some of the output, and (for example) the last two "intersections" should not go anywhere near meeting!
I have discovered some sort of problem with my algorithm... I *think* the theory is correct, it is just the implementation.
However, I was looking at some of the output, and (for example) the last two "intersections" should not go anywhere near meeting!
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