Chapter 14 Bending and Folding Your Mazes

Mazes for Programmers — by Jamis Buck (95 / 121)

👈 Your Turn | TOC | Cylinder Mazes 👉

It’s been a wild ride, but we’re nearly done. Maze algorithms, grids born of non-rectangular tesselations, circles, weaves, and braids, and even building those mazes out in three and four dimensions — it’s all brought us to this point.

Let’s go out with a bang. Let’s blow some minds.

Consider those mazes you’ve generated up to now, all of them neatly built on flat, predictable surfaces. Even the three-dimensional ones were composed of neatly planar levels. But what would happen if you were to take one of those mazes and bend it a bit, warping the surface so that it curves in one or more dimensions? What if you were to even go so far as to fold it?

Those first-person shooters take on an entirely different feel when the corridors wrap around the surface of a sphere, or carry you around the inside of a ribbon. Picture a game where you can see your goal above you as the maze arches overhead, or where monsters may be lurking just down the passage, hidden by a not-so-distant horizon!

These are what are called planair mazes, an unusual name for an unusual kind of puzzle. Mazes on cylinders, cubes, cones, pyramids, spheres, and toruses are all examples of these planair mazes, and I’ll be honest: this is a topic that could easily be an entire book in its own right. We’ve only got time for a brief taste, but hopefully that’ll be enough to set you exploring some more on your own.

We’ll look at four different surfaces in this chapter: cylinders, Möbius strips, cubes, and spheres. In each case, you’ll learn how to generate a maze on that surface. For the first three, we’ll use simple paper-crafting techniques to visualize the resulting mazes, and for the last we’ll resort to using a 3D renderer to draw our maze on the surface of a sphere.

👈 Your Turn | TOC | Cylinder Mazes 👉

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