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In an upcoming campaign I'm planning, I would like a combat encounter to take place on a small sphere, with gravity pointing in towards the center. I'd like a sphere about 50' in diameter - something large enough to allow plenty of movement on its surface, but small enough so that players can typically run around it in a few turns.

My problem is setting up the map. My first thought is to purchase a to-scale foam craft sphere, and provide miniatures with small pins so that they stick into the "board." The problem with this, tho, is that I would either need to draw on a geodesic grid by hand or go grid-less, which my group has not done before.

My second thought is to simply use a flat map with "wrapping" edges, so that it acts somewhat sphere-like. The problems with this are that it distorts the distances greatly, and, more importantly, doesn't show the affect that the curvature of the sphere has on line-of-sight. I could get around this by imposing a circular limit to line-of-sight, but I feel it loses much of the effect.

Has anyone attempted to run grid-based combat on a non-flat surface like this? What tools and rules made the combat go smoothly without ignoring important aspects of the unique terrain?

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Mike Krahulik did this some time ago. He detailed the crafting process and talked about the encounter experience itself‌​. –  BESW Oct 7 '13 at 18:54
    
@BESW That's a great read and I'll consider some of those ideas more, but unfortunately he says his grid "got sort of wonky in some places but that is why [he] made separate ares of grid zones on each planet" - which means no prolonged combat and no running around the sphere. –  dlras2 Oct 7 '13 at 19:03
    
@dlras2 in context "...separate areas of grid zones on each planet" does not appear to forego combat or running around the sphere. I more likely suspect that it actually facilitated movement and combat in the battle grid and scale without resorting to weird grid constraints at the poles. IMHO, hand wave "jumps" to other grid sections. The scale in the images by Mike Krahulik appears to remain intact. –  javafueled Oct 7 '13 at 19:19
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buy a soccer ball, add velcro –  zzzzBov Oct 7 '13 at 22:57
    
@okeefe, done. –  zzzzBov Oct 8 '13 at 0:05

6 Answers 6

The line-of-sight benefits are not actually very much, if any. If you've every played wargames with model-based LOS, you're familiar with the excruciating process of eyeballing, using bits of string, and finally arguing over whether being able to draw LOS to a teeny bit of the tip of a sword sticking up above terrain counts as having LOS or not.

Using real LOS, you lose much of the time saved by using a grid. Either go gridless on a sphere and measure everything in real inches, or use a flat, imprecise abstraction with extra LOS limits and movement rules to roughly emulate a spherical surface. Besides which, there's no good tiling of squares onto a sphere that doesn't introduce aberrations in how they connect to each other. To get regularity you have to use a different tile shape, at which point you'd have to make up new rules for adjacency and AOE coverage.

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As noted above, Mike Krahulik of Penny Arcade modeled spherical, planar combat in D&D in the Elemental Chaos part 1 and D&D in the Elemental Chaos part 2.

A concern exists that LOE and AOE in Krahulik's models, as well as, prolonged combat and movement were not possible in the models documented.

However, both context of Krahulik's efforts and his entries, he notes that the oddites of modeling the grid on the sphere as well as the success of the models in play.

Krahulik talks about "...I was drawing these squares on a curved surface they got sort of wonky in some places, but that is why I made separate [areas] of grid zones on each planet." The photo of these grids clearly shows Krahulik "solving for wonky" with compromises to aesthetic problems by ignoring the curvature of the sphere and scale at the polar coordinates.

enter image description here
Image © Copyright 1998-2013 Penny Arcade, Inc.

The disconnected grid addresses the "wonkiness" as well as LOS...and likely solved for AOE too (constrained within the "separate areas of grid zones"). Nearby grid zones could be handled as a "hand wave" or even built-in as player-GM expectation.

Both articles are great resources for creatively solving a problem and delivering an exciting table experience.

Hexagons

Read Geodesic Discrete Global Grid Systems by Kevin Sahr, Denis White, and A. Jon Kimerling. I skimmed it, but it offers some great ideas to achieve full coverage with hexagons. The research is quite detailed and expounds at length regarding the popularity and resolution available with hexagons.

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I'm explicitly trying to avoid the need to "hand wave" the interaction on the sphere, and don't want the sphere broken into zones. –  dlras2 Oct 7 '13 at 21:21
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I sympathize, but you may be constrained by geometry. You could possibly compromise by finding the latitude at which the 5' squares becomes impractical as you near the poles then limit the disconnected zones to the poles. However, I'm not sure how you can get "squares" without a) such o compromise or b) flattening the map with any number of possible projections and creating a practical LOS method a la dots and curvature limits and height relativity. –  javafueled Oct 7 '13 at 23:44
    
I'm suddenly reminded of GDW's Harpoon. –  javafueled Oct 7 '13 at 23:52

I would print out a flattened geodesic sphere for the minis alongside a printed out and assembled version of the same, using post-it notes or similar to reference where the minis map to on the sphere.

For movement, it's triangles instead of squares. Movement along a side is adjacent triangles. I would probably disallow movement across corners, just to make things simpler.

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Nice. I wonder if triangles would be a good compromise? Triangles certainly solve for surface area mapped. Without assembly though LOS might be lost. –  javafueled Oct 8 '13 at 0:26
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Without assembly, it's probably hard to get your head around, unless you want to draw connecting lines or you have mathematically inclined players. –  okeefe Oct 8 '13 at 23:38
  1. Buy a soccer ball
  2. Add velcro
  3. ???
  4. Profit

On a more serious note, you'd need to sort out how movement would work, and possibly subdivide each patch into 5 or 6 triangles depending on the size of the pieces you're velcroing on.

Additionally, you might want to prop the soccer ball up on stilts so that you could have units on the entire world.

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If you are free to alter the dimensions of your planet, you can use any one of these nice projections of a sphere's surface.

Note that the projections have 24 squares across and top to bottom (15 degrees lat/long each) ie. a 24x24 grid. At 5' per grid square you end up with a circumference of 120' and a 19' radius.

Note that most projections lose a lot of latitude squares near the poles.

Now the trick becomes distance to visual horizon. But again the internet provides a handy calculator.

Using this tool, assuming 6' person gives a surface to horizon of 13'. Making an assumption that double that is hidden. So absolute LOS = 26' = 5 or 6 squares. For fun give anyone in squares 5 and 6 a cover save.

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3d movement in D&D is made by dividing the space in cubes. Each cube that's less than 50% filled is a void space, each cube that's not is all filled. If you build a sphere made of cubes you'll get sections similar to a small circle drawn in Paint.

If you get a sphere, sunlight (which rays are parallel) and a transparent sheet with parallel lines you can trace the projection of these lines on the sphere. Rotating thee sphere exactly 90° on the 3 axis of the sheet will get you a gridded sheet. The elements of the grrid near to the axes will be squared, the boundaries between those areas will feature triangular elements.
It's fine, I've explained earlier what they are, corners of a cube. Despite being triangular, they still count as squares.


As an alternative, this really is a cube, but it looks like a sphere
http://origin-ars.els-cdn.com/content/image/1-s2.0-S0377042711000276-gr1.jpg

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