Grid map gaming

Australian Curriculum Yr 4 Achievement Standard. Back to Top Year 5 - Use a grid reference system to describe locations. Describe routes using landmarks and directional language. Australian Curriculum Yr 5 Achievement Standard. Back to Top Year 6 - Locate an ordered pair in any one of the four quadrants on the Cartesian plane.

Australian Curriculum Yr 6 Achievement Standard. Back to Top Year 7 - Represent transformations in the Cartesian plane. Students assign ordered pairs to given points on the Cartesian plane. Australian Curriculum Yr 7 Achievement Standard. Pcie Gen 2. Computer Stylus Pen.

People Also Search. DD Dungeon Maps. Dnd Blank Grid Map. Dnd Farmhouse Map. Dnd TreeMap. Dungeon Temple Maps Dnd. Dnd Town Grid Map. Medieval City Map Dnd. Dnd Lake Map. D D Battle Maps Grid. Printable Dnd Grid Maps. Dnd Grid Paper. Dungeon Dnd Map Grid. Pathfinder Dnd Dungeon Maps. For more about centers, sides, and corners, see my article on grid parts [4] squares, hexagons, and triangles.

Each corner is size units away from the center. In code:. Note that the diagrams on this page use the y axis pointing down angles increase clockwise ; you may have to make some adjustments if your y axis points up angles increase counterclockwise. In math, the "circumradius" is the distance from the center to a corner I call this size ; the "inradius" is the distance from the center to the middle of an edge.

The "maximal diameter" is twice the circumradius; the "minimal diameter" is twice the inradius. Wikipedia [5] has more. Next we want to put several hexagons together.

The size is the distance from the center to any corner. The horizontal distance between adjacent hexagon centers is w. Some games use pixel art for hexagons that does not match an exactly regular polygon. The angles and spacing formulas I describe in this section won't match the sizes of your hexagons. 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.

Now let's assemble hexagons into a grid. With square grids, there's one obvious way to do it. With hexagons, there are multiple approaches. I like cube coordinates for algorithms and axial or doubled for storage. The most common approach is to offset every other column or row. Columns are named col q. Rows are named row r. Another way to look at hexagonal grids is to see that there are three primary axes, unlike the two we have for square grids.

There's an elegant symmetry with these. This is a weird idea but it helps us with hex grid algorithms:. Study how the cube coordinates work on the hex grid. Selecting the hexes will highlight the cube coordinates corresponding to the three axes. The cube coordinates are a reasonable choice for a hex grid coordinate system. The constraint also ensures that there's a canonical coordinate for each hex. It makes many of the algorithms easier to implement. Instead of alternation, the doubled coordinates double either the horizontal or vertical step size.

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.

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. Other possible names: brick or checkerboard. I'm not sure what to call it. If you have any references, please send them to me. In previous versions of this document , I used x z y for hexagonal coordinates and also for cartesian coordinates, and then I also used q r s for hexagonal coordinates.

There are many different valid cube hex coordinate systems. I've shown only one of the many systems. There are also many different valid axial hex coordinate systems, found by using reflections and rotations. There are also cube systems that use q-r, r-s, s-q. One of the interesting properties of that system is that it reveals hexagonal directions.

There are spiral coordinate systems I haven't explored. See this question [9] or this question [10] on stackoverflow, or this paper about machine vision [11] , or this diagram about "generalized balanced ternary" coordinates [12] , or this math paper [13] , or this discussion on reddit [14].

They seem potentially useful for fixed sized hexagonal shaped maps. My recommendation: if you are only going to use non-rotated rectangular maps, consider the doubled or offset system that matches your map orientation. Either choose to store the s coordinate cube , or calculate it when needed as - q - r axial. Therefore you need to be able to convert back and forth.

Axial and Cube coordinates are essentially the same. In the Cube system, we store the third coordinate, s. Converting between the systems like this is probably overkill. If you're using Cube and need Axial, ignore the s coordinate. If you're using Axial and need Cube, calculate the s coordinate in the algorithms that need it.

The conversion is different for each. See a longer explanation on my implementation notes page. If you need Cube coordinates, use Cube q, r, -q-r instead of Hex q, r.

Given a hex, which 6 hexes are neighboring it? As you might expect, the answer is simplest with cube coordinates, still pretty simple with axial coordinates, and slightly trickier with offset coordinates. This results in 6 possible changes. Each corresponds to one of the hexagonal directions. The simplest and fastest approach is to precompute the permutations and put them into a table of Cube dq, dr, ds :.

With the Cube coordinate systems, we can store differences between two coordinates a "vector" , and then add those differences back to a coordinate to get another coordinate. Axial and Doubled coordinates also support this, but the Offset coordinates do not.

Since axial is the same as cube except not storing the third coordinate, the code is the same as the previous section except we won't write out the third coordinate:. As with cube and axial coordinates, we'll build a table of the numbers we need to add to col and row. However offset coordinates can't be safely subtracted and added.

The amount we need to add depends on where in the grid we are. Pick a grid type to see the corresponding code. 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. Also unlike offset coordinates, we can safely subtract and add doubled coordinates, which makes them easier to work with than offset coordinates. Since cube hexagonal coordinates are based on 3d cube coordinates, we can adapt the distance calculation to work on hexagonal grids.

Each hexagon corresponds to a cube in 3d space. Adjacent hexagons are distance 1 apart in the hex grid but distance 2 apart in the cube grid. For every 2 steps in the cube grid, we need only 1 step in the hex grid. 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. The maximum of the three coordinates is the distance. You can also use the max of abs vec. Xiangguo Li's paper Storage and addressing scheme for practical hexagonal image processing. In the axial system, the third coordinate is implicit. We can always convert axial to cube to calculate distance:.