Hexagon tiling of a sphere #

Image from Wikipedia

Recently two people asked me about making a tile-based game that uses a sphere topology. Some games have tile maps that wrap around. Civilization for example lets you go off the left side of the map and you warp to the right side. You can’t go off the top or bottom of the map. In 3D space, this would be a cylinder. Some games also let you go off the top side and warp to the bottom, and vice versa. In 3D space, this would be a torus. But most tile map games don’t use a sphere. Why? The sphere doesn't tile. I thought … can we almost tile it? The answer is yes!

I wrote up my notes here including a small interactive demo. This is a quick & dirty investigation and not one of my longer polished articles; see this post about my wanting to write pages more quickly.

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Outside the box #

I write interactive explanations; I'm always looking for simpler ways to explain things.

Think back to every technical paper you've read. The text connects to diagrams by using text such as "see figure 4". Maybe it's more specific and says "in figure 4 see circle 24". Maybe it's a hypertext link. However if I look at how I take notes on paper, I don't do that! I just draw an arrow to the thing I want to point to.

Figure 4. Sea of circles.

From an early age we have invisible boxes around text and diagrams, keeping them apart. It doesn't have to be this way. Pointing is the simplest way to direct attention to something. Why don't we do it more? I don't know, but these are the kinds of things I'm exploring on the web.

How did I implement this? The first guess would be that I'm using a giant SVG overlay that covers the area between the pointer and the target. I'm not! That's the only SVG element in this blog post. What's the trick? By default, the overflow for an SVG element is set to hidden; in some versions of IE it was visible and I had to set it back to hidden. That keeps the content inside its bounding box. But the IE situation made me wonder — if I set it to visible, what happens? It turns out you can draw outside the box! This seems to work across the browsers I've tried.

The second thing I need to do is construct an arrow path. The source and target of the arrow may be in different SVG elements, or they might not be SVG at all. For this page I use an invisible span in the text as the anchor. I use getBoundingClientRect() to get the coordinates on the page. Then I pick the midpoint of one side of the rectangle as the arrow source or target. I need to translate all the coordinates into the coordinate space of the SVG I'm drawing into.

For this demo I hard-coded the size, curvature, and directions of the arrows. I don't adjust them when the page is resized. For a reusable library, I think it'd be cleaner to have one svg per arrow anchor.

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