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 9:8 mystery

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icy001
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PostSubject: 9:8 mystery   Sat May 12, 2012 10:56 pm

The following image shows yellow squares where a player can reach from south on any altar.



Look at the top-left corner, where there are holes at 9:8 and 10:9, respectively. You probably know about these, but I (as well as you probably) have no idea how Jagex could program their "reachability" algorithm to have these holes o.O. Any ideas?

(You can also find similar holes in the southwest corner.)

These holes seem to be compensated by "extra" reachable squares which are diagonal from the holes. However, that is completely illogical. What sort of reasonable mathematical algorithm could do this?
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San

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PostSubject: Re: 9:8 mystery   Sat May 12, 2012 11:16 pm

This is something that has puzzled me consistently for as long as I can remember. I think I came up with a theory for it... I'm not sure if I put it in document form. I'll have a check tomorrow, when I'm less tired.
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Timo
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PostSubject: Re: 9:8 mystery   Sun May 13, 2012 12:09 pm

No idea!

The holes become bigger when you're next to the pillar:


Those are "compensated" with awkward reach on the other side of the 1:1 diagonal as well.
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San

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PostSubject: Re: 9:8 mystery   Sun May 13, 2012 4:31 pm

alright! after trawling my computer I am pleased to report that I found sod all. That's disappointing. Looks like this puzzle has continued to elude me.

Nonetheless! I'll have a look into it tomorrow since I have a few (more pressing) matters to contend with at the moment.

I've got a few thoughts - though they are pretty much obvious - that are consistent at least with Timo's diagram.

gaps occur at n:m where 1 < n/m < 2
compensated squares mirror perfect diagonal
consistent with mirror principle
test against bend theory




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icy001
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PostSubject: Re: 9:8 mystery   Fri Jun 22, 2012 2:33 am

Eureka! After much work during 6 overs over 2 days, I have come up with a complete theory of GOP angles!

This will take me a while to write and revise, so expect a lot of edits. Check here often!
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icy001
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PostSubject: Re: 9:8 mystery   Sat Jun 23, 2012 2:55 am

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Aimee
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PostSubject: Re: 9:8 mystery   Sun Jun 24, 2012 10:53 am

Wonderful Icy, this explains a lot to me! Really happy with this!

One thing:
Icy001 wrote:
Note that the starting and ending points of the line with respect to the starting square is dependent on the slope of the line. This is the crucial discovery that I made and immediately explains the 8:9 mystery. For those who don't know what the 8:9 mystery is, place the player at (0, -2) and an orb at (8, -7). Notice that, contrary to common logic, the orb turns out to not be reachable. The line of sight shows why.

(8, -7) is perfectly reachable from (0, -2). I think you intended to place the orb at (-8, 7), which is not reachable from center South.


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Aimee
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PostSubject: Re: 9:8 mystery   Sun Jun 24, 2012 1:50 pm

Also, the lower rocks on earth altar should somehow be taken into account. They behave more like the little pillars around the altar; orbs cannot go trough it, but you can attract orbs over it. The sheet is now inaccurate for the earth altar, because according to the line of sight, some angles are not possible, due to the fact that the lower rocks are viewed as barriers, although those angles are possible to perform.



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Timo
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PostSubject: Re: 9:8 mystery   Sun Jun 24, 2012 5:02 pm

Also, is it possible add a click (or right-click) area over some tiles to draw a menu down that contains the option of normal selecting and redirection to a page containing videos of angles about that spawnpoint?
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icy001
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PostSubject: Re: 9:8 mystery   Sun Jun 24, 2012 5:35 pm

Okay Aimee, I have fixed both of your issues, and also added many new capabilities.
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Zelda

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PostSubject: Re: 9:8 mystery   Mon Jun 25, 2012 11:08 am

Wow, this angle map is really impressive, Icy!
It must have taken you ages to make it, and I have no idea how you managed to crack the theory of GOP angles in the first place (once again, impressive).

I tested the first version on Saturday, and it was working great and all, however, after you added all the new features to it yesterday it became GODLIKE. I have to admit that I love the detailed altar maps above everything else though, the work you've done with the mapping is superb!

Anyways, I'm sure this angle map will serve as an amazing knowledge base to everyone who loves GOP, and there's no doubt that it will be used frequently by many dedicated GOPers (they better find it, haha)!

Thanks for making this, Icy!


PS: I would also like to thank Timo for his earlier submissions to the altar mapping project, although I think Icy's maps will more than suffice from now on. The spawn locations might be useful though.

PPS: Hi.
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Timo
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PostSubject: Re: 9:8 mystery   Mon Jun 25, 2012 5:04 pm

Zelda wrote:

Thanks! But... They're completely obsolete by now. X) It's like I invented the wheel and he makes a spacecraft. All credit due where it should be, thanks! =P

The spawn maps, though, should be integrated with a button to Icy's map, hm?

P.P.S.: Hei
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