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UGG Classic Tall II Boots
pick a grid type
Pick a grid type:

Using the above lookup tables is the easiest way to to calculate neighbors. It’s also possible to derive these numbers , for those of you who are curious.

Unlike offset coordinates, the neighbors for doubled coordinates do not depend on which column/row we’re on. They’re the same everywhere, like axial and cube coordinates. Also unlike offset coordinates, we can safely add and subtract doubled coordinates, which makes them easier to work with than offset coordinates.

Moving to a “diagonal” space in hex coordinates changes one of the 3 cube coordinates by ±2 and the other two by ∓1 (the sum must remain 0).

As before, you can convert these into axial by dropping one of the three coordinates, or convert to offset/doubled by precalculating the results.

In the cube coordinate system, each hexagon is a cube in 3d space. Adjacent hexagons are distance 1 apart in the hex grid but distance 2 apart in the cube grid. This makes distances simple. In a square grid, Manhattan distances are . In a cube grid, Manhattan distances are . The distance on a hex grid is half that:

An equivalent way to write this is by noting that one of the three coordinates must be the sum of the other two, then picking that one as the distance. You may prefer the “divide by two” form above, or the “max” form here, but they give the same result:

The maximum of the three coordinates is the distance. You can also use the max of to figure out which of the 6 “wedges” a hex is in; see diagrams here .

Xiangguo Li’s paper Storage and addressing scheme for practical hexagonal image processing. () gives a formula for Euclidean distance, which can be adapted to axial coordinates: sqrt(dq² + dr² + dq*dr) .

In the axial system, the third coordinate is implicit. Let’s Dolce amp; Gabbana Lace slippers XqNUumV
axial to cube to calculate distance:

If your compiler inlines axial_to_cube and cube_distance , it will generate this code:

There are lots of different ways to write hex distance in axial coordinates, but no matter which way you write it, axial hex distance is derived from the Mahattan distance on cubes . For example, the “difference of differences” described results from writing a.q + a.r - b.q - b.r as a.q - b.q + a.r - b.r , and using “max” form instead of the “divide by two” form of cube_distance . They’re all equivalent once you see the connection to cube coordinates.

As with axial coordinates, we’ll convert offset coordinates to cube coordinates, then use cube distance.

We’ll use the same pattern for many of the algorithms: convert hex to cube, run the cube version of the algorithm, and convert any cube results back to hex coordinates (whether axial or offset). There are also more direct formulas for distances; see the rot.js manual for a formula in the “Odd shift” section.

An interesting conflict!

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YES! Sally Hogshead, I just might be in love with you. What a great message. It just gives me more hutzpah and confidence. And…I always leave my clothes’ tags on for at least a week. The skirt looked great. You can take the tag off now. xoxo Kristin


Thank you so much Marie! Perfect timing for me as I navigate my way through B-school and figuring out my personal brand.

Took the test and the results were right on and amazing! I am Subtle Touch with my primary triggers being Mystique and Passion. As a physician acupuncturist who is passionate about nutrition a huge part of my job is to be intuitive and observant of people as soon as I walk into the room so that they have the best opportunity to heal receive the correct treatment. I’m excited to dive more into my archetype so I can continue to “fascinate” others to lead healthy lives.


Hugs to all!


I loved this episode Marie! Sally is fascinating, as are you, and it’s just cool to see two women who are rocking their own personalities shine.

My combo is the Avant Guarde: Prestige and Rebellion, and I think I need to balance the two a bit better. Sometimes I’m all prestige no rebellion, and things come out flat… other times I’m all rebellion, and that might scare people off.

Like for my upcoming event in NYC, Off The Charts – it feels rebellious to me but I’m not sure if that’s what others feel about it or not. Same with my videos, sometimes they feel too prestigious and not rebellious enough. I’d love to hear people’s thoughts on that. 🙂


Nathalie! Off the Charts is totally rebellious and I so wish I could come and sync my Rockstar to your Avant Guard-ism!

There’s a photo of you flexing your muscles which you use in your training video on websites (I’m one of your Tutees). It’s the one where you can see a tattoo on your arm (a hash sign #). That totally brings together Prestige (make a kick-ass website) with Rebellion (and use your gut!) to me.

Rock on lady!


Nathalie, I don’t know if Off the Charts is rebellious, but it is certainly very brave! I’m hugely impressed and look forward to seeing you there. And as Sally says, if some people are scared off, then that’s a good thing.

I do know that I tend to play it too safe because I’ve always been the “good girl,” yet when I allow myself to be silly — even raunchy! — that’s when I really shine and everyone has more fun. 🙂


Nathalie, your videos are AMAZING: clear, practical, down to earth, accessible, easy to follow and a life saver for non naturally techy persons like myself. They are rebellious in being kind to non natural born techies 🙂

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