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Geometry Examples #3
Elevated Train Examples
Round Platform Examples
Scenery ExamplesThe blocks world is a half-infinite space, bounded by the ground and by a hemisphere at infinity. Things that are drawn on these boundaries I call scenery, since they're always in the background.
The examples and investigations here continue the train of thought that began with the navigation examples in "geom-nav" (Geometry Examples). In particular, I always use the same correspondence between colors and absolute directions: yellow for the sun up in the sky, brown for the ground, cyan for the initial forward direction (north), dark cyan for south, etc.
Reminder: the "Save" command doesn't work with scenery examples.
Hopefully the scenery in "sky3" fits reasonably well with your experience of the normal 3D world. There are four mountains off in the distance that just happen to lie in the four cardinal directions. There's some sky that's different shades of blue and purple in different directions, as if it were sunrise or sunset; but in fact the sun is straight overhead.
The scenery in "sky4" is unfamiliar but exactly analogous. There are six mountains off in the distance in the six cardinal directions, sky of different colors, and a sun overhead. If you move forward toward the block, you'll see it rise up and obstruct the mountain, just like in 3D.
If you'd like to have a sky background in any other scene, you can easily add one by adding lines like these to the scene file.
You can add any of the other scenery below, too, but you'll have to cut and paste because I didn't set up a separate include file.
I experimented with having another mountain range behind the first, hazy and purple with distance, but I didn't think the results were worth presenting. However, if you want to do some experiments of your own, the tools are all still there in the scene language; see Scenery Commands.
If you stared at the 4D sun, you probably noticed that it was made up of three orthogonal rings, and that for every vertex on the rings there was a sky-ray leading to a corresponding vertex on the horizon. That "mesh" of vertices can be changed.
The mesh in "4a" is the same as before, for comparison.
The mesh in "4b" is my favorite. In addition to the three rings, it has a cubical frame that makes the sun look nice and round and that also produces a nice pattern of squares on the ground. The only problem with this mesh is that the number of lines can be overwhelming if you're not used to it.
In "4c" the squares have been converted from 2x2 grids to 4x4 grids. This is almost certainly too many lines, but I admit it does have some appeal.
In "4d" the sun is a traditional sphere with lines of latitude and longitude. Unfortunately, this breaks the symmetry between the six cardinal directions. In spite of that, it does have some appeal: the sun looks nice, and the north and south mountains look like huge volcanic cones.
In these examples brown rings are drawn around you to show where the ground is. The rings move with you, but if you fly upward they stick to the ground and become smaller with distance. If you fly above the block and look down, you'll see that the rings line up nicely with the mat.
In 4D, notice how the ground rings line up with the mountain rings. (The ground mesh is the same as in "mesh4b" above.)
In these examples, magic compass points follow you around. In the "b" variants, ground rings are included to make a nice compass rose.
If all those circles and earth tones are too warm and fuzzy for you, well, here's a Cartesian coordinate grid in dark blue. The "a" examples have 1x1 grids in a circle of radius 3, the "b" examples have 5x5 grids in a circle of radius 15, and the "c" examples have both. I tried drawing the grids in square regions instead of circles, but it was just too jarring when a new grid line appeared all at once.
Like the ground rings and the compasses, the grids stay on the ground, so you can get a better perspective by flying upward. The grids were a nice idea, and they work well in 3D, but in 4D it's too hard to make sense of all those lines packed together near the horizon.
Finally, we have vanishing points - six in 3D, eight in 4D. These are hard to appreciate in align mode because the crosshairs are always covering them up, so it's better to switch to unaligned mode. These are the points that lines of perspective converge to.
The vanishing points don't really give any new information, since the bases of the mountains and the center of the sun were located in the same places, as were the blocks in the original navigation examples. I just thought it was interesting to see them. Also it's nice to know that you can create pretty much any scenery you can imagine—there are other options if you don't like the mountains and the sun.