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This is a tool to display 4d point clouds. You might know how we cannot actually draw in 3d, and instead must make further things smaller and closer to the center. This is also done in all 3d games. Here, it is done two times: the first projects from 4d to 3d, and then 3d is projected to 2d.

Because your screen probably has only 2 dimensions, and the cardinallity of the set of all people such that the set of their belongings does not contain a keyboard is nonzero some people don't have a keyboard, there are instead many planes you can move. XZ is the default one (left/right + up/down), YW is the weird one (ana/kata + forward/backward, which both have perspective effects that overlap), and 4 others, since there are 6 main planes in 4d (and thus 6 rotations). 4d also has 6 whole rotations, although 2 of them are just rolling. These rotations come in two types: turns and sping. There are 3 of each, and turns are the ones that turn your view (they include the forward direction). They are yaw, pitch, and reel (reel is looking ana/kata). Spins look like they change what you can see, but that's only because you have 3 spatial dimensions. All they are is just the ways you can roll in 4d: roll, twirl, and tumble. Because you most likely have evolved on a planet, roll is not implemented for spins to make things less confusing, and turns apply horizontal turning before pitch, meaning the twirl and tuble rotations just look like rotating the 3d view (because they basically are).

Note that all objects almost always look translucent, or end up cluttering. This is because the retnia is 3d. A 4d creature would see the entire 3d retnia at once, but as 3d creatures with 2d retnias our only hope of seeing anything close to the whole retnia is making literally everything translucent. Oh, also, without the slice renderer enabled, occlusion isn't accurate.

The slice render can be enabled by setting slice count to something other than 0. It renders the 4d scene in a lot of slices, which for more than 1 slice is less performant, and has 2 uses: if you set the slice count to 1, you can render a cross-section view, and otherwise it can be used for more accurate rendering. It can be disabled by setting slice count back to 0, in which case the renderer just double-projects every point instead with no slicing. Note that not all things will appear if they are too far ana/kata, because that's the slicer's axis. Also, I reccoment starting with the projection view, since it shows a much more complete view than cross-sections.

In 4d, there are double-rotations, since rotations are planar, and so there can be 2 of them (ex. pitch+twirl). They are chiral in 4d: in the same way that 2d rotations cannot be flipped in 2d, 4d double rotations cannot be flipped in 4d, and here, there is a ratio: it can be 1:1 (isoclinic dexter), 1:-1 (isoclinic sinister, and yes there are very different), 1:0 (single rotation, which is rare in 4d), and a lot of others (ex. 1:π or 1:3). If the spin rates are the same, the rotation is isoclinic, but if not, it's just a double rotation.

Also related to the extra space: a 2d surface (like a triangle) does not have a normal anymore! Let's say I have an XY plane. There is now a circle of normal vectors: Z and W are both normal to XY, and so are combinations of ZW. This is also why people say that you rotate "around" planes, since for whatever reason they don't just say the plane you rotate in. Anyways, the only surfaces in 4d that *do* have normals are volumes, like the ground, where you can move 3 ways in them, and the 4th way is the normal. For example, with a 4d sphere, you can move in 3 ways (called artitude, longitude, and colongitude) and the remaining direction (of altitude/radius) is the normal. Of course, you can still flip it, but usually there is one more sensible way (ex. lighting).

In fact, the ground in 4d is actualy a 3d thing. If you tumble (as in the 4d rotation) by 90 degrees and are a 3d being, not only will you probably be stuck without help, but also you'll not see the up direction anymore, instead seeing the ana/kata, left/right, and forward/backward directions. One way this makes 4d different is looping racetracks: in 3d, further loops are more distance, but in 4d, you can just arrange them ana/kata of each other (or whatever way is normal to the track's plane), which is like stacking a lot of rings, and the distances are now constant. Yes, in 3d, you *could* stack the tracks, however doing so is clearly enough of an enginerring hassle for people *not* to do it.

Also, importantly, this is NOT the first time this has been done. 4d blocks by Jhon McIntosh, 4d viewer Minecraft4D and Tesserxel all by wxyhly, and 4d sim by ascyt are all great projects by others.

Made by Catzcute4.

changelog:

fundamentalChange.newThing.tweak.bugfix

• 0.7.1: twirl-pitch, fixed planet moon star
• 0.7: scene.hplane, scene.tetra, scene.merge, and scene.shade added, along with a basic vec4 and mat4 library, terrain has normals, diffuse shading no longer shades alpha, depthmaps fixed, and also pentachoron added
• 0.6: slice renderer! renders slices so culling works! oh, and yes, this also means a new way to explode a chrombook.
• 0.5.2: fixed it not working (and yes, "it" as in the whole thing). oh also very tiny performance improvment maybe
• 0.5.1: code eval fixed, added caveat in scene.docs.globals. objects that skew do NOT work well with normal vectors
• 0.5: animation suppourt, isoclinic and standard double rotations added, sicne saveload always crashes it now runs code (try scene.docs.docs), inside of tessract removed, normals added for lambertian shading, positions are now in a Float32Array, and a scene object is added with documentation of this
• 0.4: rotations actually work fully now, yay! since it's quaternions everything is slightly more performant, and so a full mandelbrot (wih escape time display) and performant mandelbrot (only points in set) are here... good job if you can interpert those messes. sadly, you can't measure euler angles easily from quaternions, so only pitch and tumble are displayed. oh also pitch and tumble are now complex numbers internally
• 0.3: planet added (no, it will not explode your computer, unless you're on a chromebook, then it might), rotations should be a bit more performant, also turn horizontally now does something (4d yaw and reel) but still absolute glitchy (twirl isn't accumulated)
• 0.2: improved terrain generation, controls, and depth sort (now sorts 3d depth)
• 0.1: glome and tiger added
• 0.0: first version, "forked" from gravity 4-alpha 3.5