5e grid movement

Find out what’s new in the latest patch. There are also more direct formulas for distances; see the rot.js manual[13] for a formula in the "Odd shift" section. The horizontal distance between adjacent hexagon centers is w. The vertical distance between adjacent hexagon centers is h * 3/4. Characters generally don’t walk during combat—they hustle or run. @Zeus Clarified it - avoid an OA is what I meant. See Overland Movement, below, for movement measured in miles per hour. Wraparound depends on the map shape, not the tile shape. However all the hex coordinate systems lead to wasted space when using a triangular or hexagonal map. Recent Changes; Random page; Community; Videos; Images; Discuss. A character can hustle without a problem on the local scale. See page 252 of the DMG for more information. The cube coordinates are a reasonable choice for a hex grid coordinate system. Start with the simplest algorithm, but expect that it may not compute exactly the answer you want for your project. Implementation note: I use a&1 (bitwise and[8]) instead of a%2 (modulo[9]) to detect whether something is even (0) or odd (1), because it works with negative numbers too. So the easiest way to avoid an OA is to not move at all. In code it's a nested loop: This loop will work but it's somewhat inefficient. This is simple with cube coordinates if we stick with rotations of 1/6th of a circle. The scale, add, and neighbor operations also work on axial and doubled coordinates, so the same algorithm can be used. There are many different valid cube hex coordinate systems. Related: Sander Evers has a nice explanation of how to combine small hexagons into a grid of large hexagons[34] and also a coordinate system to represent small hexagons within a larger one[35]. After 6 * radius steps it ends up back where it started. Do you have suggestions for things to change or add? Instead of alternation, the doubled coordinates double either the horizontal or vertical step size. Regular hexagons have all the sides the same length. One side features a stone floor good for dungeon and city encounters alike, while the other features terrain useable for a wide range of rural and wilderness encounters. Inside the back cover, you'll find a blank reusable section for notes and maps. I'm not sure what to call it. There are times when this algorithm slightly goes outside the marked hexagons. Here's the algorithm: For non-cube coordinates, the simplest thing to do is to convert to cube coordinates, use the rounding algorithm, then convert back: The same would work if you have oddr, evenr, oddq, or evenq instead of axial. Putting these together to draw a line from A to B: Given a hex center and a range N, which hexes are within N steps from it? Opt-in alpha test for a new Stacks editor, Visual design changes to the review queues. One of the most common questions is, how do I take a pixel location (such as a mouse click) and convert it into a hex grid coordinate? These are shown as white arrows in the diagram. For example, a speed of 30 feet translates into a speed of 6 squares. To learn more, see our tips on writing great answers. in: OGL, SRD, Creature. This makes distances simple. an online demo of directional field of view, convert pixel coordinates back to hex coordinates, invert the pointy-top hex-to-pixel matrix, visualization showing why the rounding algorithm works, nice explanation of how to combine small hexagons into a grid of large hexagons, coordinate system to represent small hexagons within a larger one, Charles Fu's posting to rec.games.programmer, DevMag has a nice visual overview of hex math, James McNeill has a nice visual explanation of grid transformations, Convert cube hex coordinates to pixel coordinates, pros and cons of “pointy topped” and “flat topped” hexagons, correspondence between hexagons and cubes, Generalized Balanced Ternary for hex coordinates, Each direction on the cube grid corresponds to a, Each direction on the hex grid is a combination of, Convert each sample point (float) back into a hex (int). A 180° rotation flips the signs but the coordinates have rotated back to where they originally were. A character can walk without a problem on the local scale. This allows the in-between values for the hexes that are halfway in between: I haven't found much information about this system — tri-bit.com called it interlaced[5], rot.js calls it double width[6], and this paper[7] calls it rectangular. I have an guide to implementing your own hex grid library, including sample code in C++, Java, C#, Javascript, Haxe, and Python. In this diagram, the limit is set to moves. The conversion is different for each. Columns are named col (q). This measures a diagonal move as 1 unit. For example, the “difference of differences” described here[12] 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. Why does catting a symlinked file and redirecting the output to the original file make the latter file empty? Each ring is 6 * k hexes. A movement triggers the Boom effect that occurs AFTER the attack hits. Maybe any part of the other hex from any part of the starting point? Determine which type of offset system you use; *-r are pointy top; *-q are flat top. If there are obstacles, the simplest thing to do is a distance-limited flood fill (breadth first search). Optional Rule: You can choose to bias a starting position. There's an elegant symmetry with these. 2. With cube coordinates, we swap the coordinates that aren't the axis we're reflecting over. This guide will cover various ways to make hexagonal grids, the relationships between different approaches, and common formulas and algorithms. Most of the time, movement in these games is done simply by moving a set number of tiles in the grid. One of the common complaints about the axial coordinate system is that it leads to wasted space when using a rectangular map; that's one reason to favor an offset coordinate system. Is there a good way of dealing with both movement and tactical combat in Shadowrun? However offset coordinates can't be safely added and subtracted. The simplest way to do this is to draw a line to every hex that's in range. In a cube grid, Manhattan distances are abs(dx) + abs(dy) + abs(dz). Green Flame Blade 5e… Diagonals. Is it correct to say "My teacher yesterday was in Beijing."? I chose corner 4 to start with because it lines up the way my direction numbers work but you may need a different starting corner. [10] (DOI[11]) gives a formula for Euclidean distance, which can be adapted to axial coordinates: sqrt(dq² + dr² + dq*dr). Although I recommend axial/cube coordinates, if you are sticking to offset coordinates, consider the doubled variant. The rest of the article, describing algorithms on hex grids, will work even if your hexagons are stretched or shrunk a bit, and I explain on the implementation page how to handle stretching. In order to be out of standard 5' reach. I haven't come up with an easy fix for this. ENHANCE RPG Grid Mat - Tabletop DND Map (24x36 inch) Role Playing Dry Erase DND Mat Complete Gaming Set for Masters and Starters, Erasable Parchment Battle Grid Game Mat with Travel Pouch, Marker Kit. Unlike offset coordinates, the neighbors for doubled coordinates do not depend on which column/row we're on. However on a grid, the center points of two medium creatures must be 10' apart in order to be outside of that range, so maybe that's what you're talking about? Your position in the grid is more of a representation of your location, rather than your exact position. There is an optional rule in ... \$ that 3.5e uses, any position that is “at least as up as it is over” should be eligible to drag the target to a square 10 feet above its position (potentially as well as 5 feet over). 5e Community. Study how the cube coordinates work on the hex grid. As before, you can convert these into axial by dropping one of the three coordinates, or convert to offset/doubled by precalculating the results. This sturdy double-sided, grid-lined play surface is ideal for when your Dungeons & Dragons campaign gets tactical. For offset coordinates, we need to offset either the column or row number (it will no longer be an integer). Here's the code: That's three lines of code to convert a pixel location into an axial hex coordinate. We pick all the hexes that satisfy all six inequalities. However, although x + y + z = 0, after rounding we do not have a guarantee that rx + ry + rz = 0. "But Amit!" Evenly sample the line at N+1 points, and figure out which hexes those samples are in. Sometimes we don't have obvious algorithms for hex grids, but we do have algorithms for cube grids. This results in 6 possible changes. It makes many of the algorithms easier to implement. As with axial coordinates, we'll convert offset coordinates to cube coordinates, then use cube distance. This is particularly easy if you translate your speed into squares by dividing the speed by 5. This was a matrix multiply: To invert the hex-to-pixel process into a pixel-to-hex process we  invert the pointy-top hex-to-pixel matrix[30] into a pixel-to-hex matrix: This calculation will give us fractional axial coordinates (floats) for q and r. The hex_round() function will convert the fractional axial coordinates into integer axial hex 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). Use MathJax to format equations. * rectangular maps require an adapter, shown in the map storage section. Using the above lookup tables is the easiest way to to calculate neighbors. Sometimes you'll want. I'm keeping a list on Trello[67]. Given a hex, which 6 hexes are neighboring it? you say, "I don't want to store 3 numbers for coordinates. Make a lookup table storing, for each hex just off the map, the corresponding cube on the other side. If you're using graph-based pathfinding such as A* or Dijkstra's algorithm or Floyd-Warshall, pathfinding on hex grids isn't different from pathfinding on square grids. There are a few more algorithms in hex-algorithms.js. The implementation guide has code in C++, Javascript, C#, Python, Java, Typescript, and more. Specifically, what do you mean by escaping an OA? Each line is an inequality (a half-plane[19]). Square Grids have four options for measuring: 1. For one hex region we set xmin = H.x - N and xmax = H.x + N and likewise for y and z. In code: To fill a hexagon, gather the polygon vertices at hex_corner(…, 0) through hex_corner(…, 5). The sqrt(3) comes from sin(60°). Since a hex region is expressed as ranges over x, y, z, we can separately intersect each of the x, y, z ranges then use the nested loop to generate a list of hexes in the intersection. Rolling for Movement in Theatre of the Mind. If so, how do you track that on the map? You can shortcut some of these steps by defining rotation directly on axial coordinates, but hex vectors don't work for offset coordinates and I don't know a shortcut for offset coordinates. I'm going to solve it algebraically: First, we rewrite constraint -N ≤ dx ≤ +N into a more general form, xmin ≤ x ≤ To find out whether a given hex is on a ring of a given radius, calculate the distance from that hex to the center and see if it's radius. Community Forums; API Announcements; Specific Use Questions & Macros; Character Sheets & Compendium; API; Roll20 Marketplace & Creative Content; Looking for Group ; Bug Reports & Technical Issues; Suggestions & Ideas; Pathfinder/3.5E movement formula 1473095126 DarKDinDoN Permalink Quote. The only thing stopping you from straddling a grid line is a strict DM. A standard Mini might have a 25mm sq base which perfectly fits a 5' representation on this grid. If you have any references, please send them to me. 1.1.1 Moving between Attacks; 1.1.2 Using Different Speeds; 1.2 Difficult Terrain; 1.3 Being Prone. In the diagram, each range is a pair of lines. As you might expect, the answer is simplest with cube coordinates, still pretty simple with axial coordinates, and slightly trickier with offset coordinates. There are more things I want to do for this guide. Generally, a character can run for a minute or two before having to rest for a minute Axial discards the third coordinate. The pixel coordinate is q_basis * q + r_basis * r. For example, the hex at (1,1) is the sum of 1 q vector and 1 r vector. Some games use pixel art for hexagons that does not match an exactly regular polygon. Geometrically, each region is a cube in 3D space, and we're going to intersect two cubes in 3D space to form a cuboid[20] in 3D space, then project back to the x + y + z = 0 plane to get hexes. The typical orientations for hex grids are vertical columns (flat topped) and horizontal rows (pointy topped). These maps, most commonly used for in-person games, can be combined with terrain pieces or … See stackoverflow[33] for another approach. Hexagons have 6 sides and 6 corners. Ergo they are not simultaneous. There are six “wedges”, each an equilateral triangle with 60° angles inside. Look at (1,1) on the grid map above and see how col and row change as you move in each of the six directions. Buying a house with my new partner as Tenants in common. 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’re no longer forced to do all your moving at the beginning or end of your turn. Xiangguo Li's paper Storage and addressing scheme for practical hexagonal image processing. Break it up into 5 ft increments and use them when you need to. To draw a hexagon outline, use those vertices, and then draw a line back to hex_corner(…, 0). what would have happened if apollo/gemin/mercury splashdown hit a ship? In the cube coordinate system, each hexagon is a cube in 3d space. In a square grid, Manhattan distances are abs(dx) + abs(dy). I've chosen q for "column" = x and r as "row" = z. Movement in grid-based games. This simplifies the counting of squares at the expense of realism. Under the Variant: Playing on a grid (PHB, 192) it states, emphasis mine: Rather than moving foot by foot, move square by square on the grid. How to make D&D maps. We might also want to calculate the 6 “diagonal” hexes. However, in most statically typed languages, you'll need a separate class/struct type for float coordinates, and cube_round will have type FloatCube → Cube. Thanks for contributing an answer to Role-playing Games Stack Exchange! Use tactical movement for combat. The algorithm is called. Another approach is to convert the offset coordinates into cube/axial coordinates, then use the cube/axial to pixel conversion. 99. Characters may become proficient with the ship’s helm, in the same way as with artisan’s tools, in order to add their proficiency bonuses to checks to pilot a ship via the helm. The same pattern works for intersecting three or more regions, and can generalize to other shapes[21] (triangles, trapezoids, rhombuses, non-regular hexagons). The sum will 1 + 6 * sum(1…radius). Under the grid system, you move in 5 foot segments, but under Theatre of the Mind, you can move in 1 foot increments. This video is an a look at Movement in Dungeons and Dragons 5th Edition. Therefore you need to be able to convert back and forth. So we reset the component with the largest change back to what the constraint rx + ry + rz = 0 requires. @Zeus I'm wondering if the linked example is confusing the question. Alternatively, you could write cube_round to take three floats as inputs instead of defining a new type just for this function. You can also use the max of abs(dx-dy), abs(dy-dz), The angles and spacing formulas I describe in this section won't match the sizes of your hexagons. A creature provokes an opportunity attack when they move out of an enemy’s reach. For example, if the y-change abs(ry-y) is larger than abs(rx-x) and abs(rz-z), then we reset ry = -rx-rz. Ergo the Boom effect cannot crit. Take the table of Cube(dx, dy, dz) and convert into a table of Hex(dq, dr): With offset coordinates, the change depends on where in the grid we are. One issue that still confounds me is the diagonal measurement of AoEs that is consistent with the simplified diagonal grid movement rule of 5e. Converting a floating point value to an integer value is called rounding so I call this algorithm cube_round. The compact 5E character sheet inside the front cover is coated with a 1.5mil polypropylene laminate that works with wet- or dry-erase markers. Sometimes we'll end up with a floating-point cube coordinate (x, y, z), and we'll want to know which hex it should be in. Visiting the hexes this way can also be used to calculate movement range. A character can walk without a problem on the local scale. To get a list of all such hexes, take radius steps away from the center, then follow the rotated vectors in a path around the ring. Each side is shared by 2 hexagons. Some DMs might require 5' increments, but its not a rule. What would allow gasoline to last for years? Of all the values of z we loop over, only one of them actually satisfies the x + y + z = 0 constraint on cubes. When you go off the map, you subtract the mirror center closest to you until you are back on the main map. The game organizes the chaos of combat into a cycle of rounds and turns. In the horizontal (pointy top hex) layout it increases the column by 2 each hex; in the vertical (flat top hex) layout it increases the row by 2 each hex. The size is the distance from the center to any corner. N, H2.x - N) and xmax = Given a location and a distance, what is visible from that location, not blocked by obstacles? It only takes a minute to sign up. How do spaceships compensate for the Doppler shift in their communication frequency? I will be DMing my first D&D 5e game in a few weeks and have been carefully studying the rules and the Roll20 VTT system to prepare. Moving one space in hex coordinates involves changing one of the 3 cube coordinates by +1 and changing another one by -1 (the sum must remain 0). This is the oldest reference I can find for axial grids: Luczak, E. and Rosenfeld, A., There's a paper that calls cube coordinates, [1]: http://www-cs-students.stanford.edu/~amitp/gameprog.html#hex, [2]: http://www-cs-students.stanford.edu/~amitp/Articles/Hexagon2.html, [3]: http://www-cs-students.stanford.edu/~amitp/Articles/HexLOS.html, [4]: http://www-cs-students.stanford.edu/~amitp/game-programming/grids/, [5]: http://web.archive.org/web/20090205120106/http://sc.tri-bit.com/Hex_Grids, [6]: http://ondras.github.io/rot.js/manual/#hex/indexing, [7]: https://www.researchgate.net/publication/235779843_Storage_and_addressing_scheme_for_practical_hexagonal_image_processing?_sg=flKEA6rk1KmOpC4LBjQJN_-NBuiR1KJtJt-XeYRXnd0z_MNUrB2gjb2FKV3iBoKg988P2xHCpQ, [8]: https://en.wikipedia.org/wiki/Bitwise_operation#AND, [9]: https://en.wikipedia.org/wiki/Modulo_operation, [10]: https://www.researchgate.net/publication/235779843_Storage_and_addressing_scheme_for_practical_hexagonal_image_processing?_sg=flKEA6rk1KmOpC4LBjQJN_-NBuiR1KJtJt-XeYRXnd0z_MNUrB2gjb2FKV3iBoKg988P2xHCpQ, [11]: https://doi.org/10.1117/1.JEI.22.1.010502, [12]: http://3dmdesign.com/development/hexmap-coordinates-the-easy-way, [13]: http://ondras.github.io/rot.js/manual/#hex/indexing, [14]: http://ondras.github.io/rot.js/manual/#hex/indexing, [15]: https://en.wikipedia.org/wiki/Digital_differential_analyzer_(graphics_algorithm), [16]: http://zvold.blogspot.com/2010/02/line-of-sight-on-hexagonal-grid.html, [17]: http://stackoverflow.com/questions/3233522/elegant-clean-special-case-straight-line-grid-traversal-algorithm, [18]: https://doi.org/10.1111/1467-8659.1210027, [19]: http://devmag.org.za/2013/08/31/geometry-with-hex-coordinates/, [20]: https://en.wikipedia.org/wiki/Cuboid, [21]: http://devmag.org.za/2013/08/31/geometry-with-hex-coordinates/, [22]: http://gamedev.stackexchange.com/questions/15237/how-do-i-rotate-a-structure-of-hexagonal-tiles-on-a-hexagonal-grid/, [23]: https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF, [24]: http://www-cs-students.stanford.edu/~amitp/Articles/HexLOS.html, [26]: https://s3.amazonaws.com/jbochi/layout.html, [27]: http://www.adammil.net/blog/v125_Roguelike_Vision_Algorithms.html, [28]: http://www.roguebasin.com/index.php?title=Pre-Computed_Visibility_Tries, [29]: http://www.roguebasin.com/index.php?title=Field_of_Vision, [30]: http://www.wolframalpha.com/input/?i=inv+%7B%7Bsqrt%283%29%2C+sqrt%283%29%2F2%7D%2C+%7B0%2C+3%2F2%7D%7D, [31]: http://www.wolframalpha.com/input/?i=inv+%7B%7B3%2F2%2C+0%7D%2C+%7Bsqrt%283%29%2F2%2C+sqrt%283%29%7D%7D, [32]: https://bl.ocks.org/patricksurry/0603b407fa0a0071b59366219c67abca, [33]: http://gamedev.stackexchange.com/a/137603/2472, [34]: https://observablehq.com/@sanderevers/hexagon-tiling-of-an-hexagonal-grid, [35]: https://observablehq.com/@sanderevers/hexmod-representation, [36]: https://www.redblobgames.com/pathfinding/a-star/introduction.html, [37]: http://www-cs-students.stanford.edu/~amitp/Articles/HexLOS.html, [38]: http://www-cs-students.stanford.edu/~amitp/Articles/Hexagon2.html, [39]: http://devmag.org.za/2013/08/31/geometry-with-hex-coordinates/, [40]: http://www.gamelogic.co.za/downloads/HexMath2.pdf, [41]: http://gamelogic.co.za/grids/documentation-contents/quick-start-tutorial/gamelogics-hex-grids-for-unity-and-amit-patels-guide-for-hex-grids/, [42]: http://www-cs-students.stanford.edu/~amitp/game-programming/grids/, [43]: http://playtechs.blogspot.com/2007/04/hex-grids.html, [44]: http://web.archive.org/web/20090205120106/http://sc.tri-bit.com/Hex_Grids, [45]: http://ondras.github.io/rot.js/manual/#hex/indexing, [46]: http://stackoverflow.com/questions/2049196/generating-triangular-hexagonal-coordinates-xyz, [47]: http://keekerdc.com/2011/03/hexagon-grids-coordinate-systems-and-distance-calculations/, [48]: http://stackoverflow.com/questions/2459402/hexagonal-grid-coordinates-to-pixel-coordinates, [49]: http://gamedev.stackexchange.com/questions/51264/get-ring-of-tiles-in-hexagon-grid, [50]: http://www.battleanalysis.com/battlefield.html, [51]: http://gamedev.stackexchange.com/questions/49718/vertical-vs-horizontal-hex-grids-pros-and-cons, [52]: http://arges-systems.com/blog/2011/01/10/hex-grid-line-of-sight-revisited/, [53]: http://hexnet.org/content/permutohedron, [54]: http://incompetech.com/graphpaper/hexagonal/, [55]: http://old.reddit.com/r/gamedev/comments/19wmvn/a_data_structure_for_a_game_board_with_hexagonal/c8s9qbe, [56]: https://www.springer.com/us/book/9781852339142, [57]: https://doi.org/10.1007/1-84628-203-9, [58]: http://hexgridutilities.codeplex.com/documentation, [59]: https://doi.org/10.1109/TC.1976.1674642, [61]: https://doi.org/10.1109/PROC.1979.11356, [64]: http://old.reddit.com/r/gamedev/comments/1dz1tr/, [65]: https://news.ycombinator.com/item?id=5809724, [66]: http://www.metafilter.com/128649/Hexagonal-Grids, [67]: https://trello.com/card/hexagonal-grids-2-0/4f1dbfdc0fc2508c1b238d7d/52. This diagram is the same as the previous one, except I don't show y: There are many choices of cube coordinate system, and many choices of axial coordinate system. The center is 1 hex. Characteristic class that cannot be represented by disjoint tori. Write and erase your hit points, spell slots, ability modifiers over and over as you level up and your hero's story grows. There are 3 possible coordinates to change by +1, and 2 remaining that could be changed by -1. Were SVMs developed as a method of efficiently training neural networks? Asking for help, clarification, or responding to other answers. Let's convert 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. The cases are likely edge cases when this will matter, but it is something to consider and understand when answering questions here regarding movement as well as at your tables. When measuring distance, the first diagonal counts as 1 square, the second counts as 2 squares, the third counts as 1, the fourth as 2, and so on. If there is, does it create any cases that may be a concern? With square grids, there's one obvious way to do it. To reflect over a line that's not at 0, pick a reference point on that line. To find all hexes within N steps, we need max(abs(x), abs(y), abs(z)) ≤ N. This means we need all three to be true: abs(x) ≤ N and abs(y) ≤ N and abs(z) ≤ N. Removing absolute value, we get -N ≤ x ≤ +N and -N ≤ y ≤ +N and -N ≤ z ≤ +N. Count by the shortest route. The GM can summarize the adventurers’ movement without calculating exact distances or travel times: “You travel through the forest and find the dungeon entrance late in the evening of the third day.” Even in a dungeon, particularly a large dungeon or a cave network, the GM can summarize movement between encounters: “After killing the guardian at the entrance to the ancient dwarven stronghold, you consult … Adjacent hexagons are distance 1 apart in the hex grid but distance 2 apart in the cube grid. Battlemaps are usually overlaid by a standard 5-foot by 5-foot grid to make player movement and scaling consistent. For hex to pixel, it's useful to review the size and spacing diagram at the top of the page. In the axial system, the third coordinate is implicit. This guarantees that rx + ry + rz = 0. min(H1.x + N, H2.x + N), and likewise for y and z. This can also be viewed as a matrix multiply, where the basis vectors are the columns of the matrix: The matrix approach will come in handy later when we want to convert pixel coordinates back to hex coordinates. Why do guitarists specialize on particular techniques? I wrote this guide to the most elegant approaches that lead to the simplest code, starting from the guides by Charles Fu[2] and Clark Verbrugge[3]. This comes up in line drawing and pixel to hex. I'll assume all the hexagons we're working with here are regular. In a dungeon environment, the adventurers' movement happens on a scale of minutes. In the diagram, try exiting the center map, and watch one of the mirrors enter the map on the opposite side. Also if your grid spaces are large enough, and your token small enough, it could be easy to represent 1' squares within the 5' square. Click or drag to toggle walls. 1.1 Breaking Up Your Move. In my projects, I name the axes q, r, s so that I have the constraint q + r + s = 0, and then I can calculate s = -q - r when I need the third coordinate for algorithms that work better with cube coordinates. If I am hiding and moving silently at the same time, what is my total movement penalty? Each corresponds to one of the hexagonal directions. Where was Malkitzedek of Jerusalem at the time of the Akedah? With hexagons, there are multiple approaches. I'll show how to do this for axial or cube coordinates. How and when are the raw materials used in the Fabricate spell converted into the item(s)? I've been collecting hex grid resources[1] for over 25 years. For each of the six mirror centers M, and each of the locations on the map L, store mirror_table[cube_add(M, L)] = L. Then any time you calculate a hex that's in the mirror table, replace it by the unmirrored version.

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