Actually, it _doesn't_ work, because canonically, 0101 to 0810 should come
out to J-13 (counting hexes). I thought that perhaps using that formula and
rounding up would be OK, and it probably is for J-3 or less, but I'd really
like one that works and gives canonical answers for _any_ distance. For
Reasons.


On Fri, 27 Mar 2020 19:12:40 -0700, Vareck Bostrom <xxxxxx@gmail.com>
wrote:

>Here's a verification of sorts: https://i.imgur.com/hke5AEm.png
>hexes are drawn with the centers translated per the toMap[] method and then
>range rings independently drawn at 1 parsec radii (with the first at 0.5
>parsec to show that the distance between the centerpoint of the hex and the
>edge of the hex is half a parsec). Between 1,1 and 8,10 you can see it's a
>bit under 10.5 parsec.
>
>On Fri, Mar 27, 2020 at 6:41 PM Vareck Bostrom <xxxxxx@gmail.com> wrote:
>
>> I may have derived this from the travellermap API document or come up with
>> it myself, I don't remember now, but it works.
>>
>> I have a mathematica method toMap[] which will take a vector of the x and
>> y hex number and return a map-space value:
>> toMap[vec_] := Module[{ix, iy, x, y},
>>    ix = vec[[1]] - 0.5;
>>    iy = If[ EvenQ[ vec[[1]] ], vec[[2]] - 0.5, vec[[2]] ];
>>    x = ix Cos[\[Pi] 6^-1];
>>    y = -iy;
>>    {x, y}
>>    ];
>>
>> then just take the regular euclidean distance between them, e.g.,
>> In[972]:= EuclideanDistance[ toMap[{01,01}], toMap[{08,10}] ]
>> Out[972]= 10.4403
>>
>> Asking mathematica for a general solution gives:
>> In[973]:= EuclideanDistance[ toMap[{ax,ay}], toMap[{bx,by}] ]
>> Out[973]= Sqrt[Abs[1/2 Sqrt[3] (-0.5+ax)-1/2 Sqrt[3]
>> (-0.5+bx)]^2+Abs[-ay+by]^2]
>> where ax, ay are the hex coordinates of the first hex and bx, by are the
>> coordinates of the second
>>
>>
>> On Fri, Mar 27, 2020 at 3:33 PM Jeff Zeitlin <
>> xxxxxx@freelancetraveller.com> wrote:
>>
>>> Given a standard Traveller subsector, with coordinates 0101 to 0810,
>>> alternate columns staggered, what's the formula/algorithm to calculate the
>>> jump distance between two hexes?
>>>
>>> ®Traveller is a registered trademark of
>>> Far Future Enterprises, 1977-2020. Use of
>>> the trademark in this notice and in the
>>> referenced materials is not intended to
>>> infringe or devalue the trademark.
>>>
>>> --
>>> Jeff Zeitlin, Editor
>>> Freelance Traveller
>>>     The Electronic Fan-Supported Traveller® Resource
>>> xxxxxx@freelancetraveller.com
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>>>
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>>
>>
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®Traveller is a registered trademark of
Far Future Enterprises, 1977-2020. Use of
the trademark in this notice and in the
referenced materials is not intended to
infringe or devalue the trademark.

--
Jeff Zeitlin, Editor
Freelance Traveller
    The Electronic Fan-Supported Traveller® Resource
xxxxxx@freelancetraveller.com
http://www.freelancetraveller.com

Freelance Traveller extends its thanks to the following
enterprises for hosting services:

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