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Imagine that you are a person living in 4D, your eyes can see 3D images instead of 2D because the additional 4th direction makes your retina 3 dimensional. The poor 3D creatures (we) only have 2D visions, 3D images can only be seen by making voxels transparent, and this is what 4DViewer does. And we face another problem: Too many overlapping colors could make all things very blur, like a fog cluster. In order to solve this, we can select some cross sections(e.g. cross sections in the direction of x, y and z through retina's center) to cut the 3D retina, and show those cross sections separetly.

Guide：Tutorial of 4D Viewer

First meet

A simple example: Hypercube examples/hypercube.html

Use left and right button to drag to rotate camera, scroll mouse wheel to zoom in / out. Now you are inside the hypercube. Try to zoom out to get out of it and you can see the entire hypercube from outside. Hypercube(Also called tesseract) is made of 8 equillavent cubic cells(3D face). There are different spherical patterns painted at the center of each cell in order to distinguish them.

Regular polychora and other fundamental 4D shapes examples/polychora.html

You can select different shapes from the control panel.

Start walking in 4D

After understanding some basical 4D shapes, let us experience First-person perspective。 How to control:

  • Move front, back, left, right, ana and kata(two new 4th directions) by pressing key W S A D Q E.
  • Move upward/downward by holding space, when you relieve it you will fall down to the ground.
  • Move your mouse around or press key J L U O to look around horizontally(eg. look around left-right and ana-kata)
  • Scroll mouse wheel or press key I K to look upward/downward.
  • Press Z X to rotate the 3D retina.
  • Press C to toggle wireframe overlay, and press H to hide the control panel.

Examples：

Slope examples/slope.html

This is a simple scene with some slopes, a platform and a tunel.

  • Goal: Walk up to the platform, get through to the other side of the tunel.

Game Tetraspace remake examples/tetraspace.html

(Tetraspace is a free 4D game. Here I remade first 12 levels from tetraspace in the example.

  • Primary goal: Find the small white hypercube floating in the air without jumping. Touch it to get to the next level. Note: The blue hypercube block can be pushed by walking toward it, and the green hypercube is a laser emitter. You cannot touch the emitter and the laser beam.
  • Advanced goal: Pass through all levels with 3D voxel retina only (without three cross section thumbnails' help) (you can press the keyboard C to turn on the wireframe mode)

Take Adventure in 4D

4D version of Minecraft minecraft4d/

Minecraft4D detailed tutorial

infinity 4D Minecraft world based on random seeds, in which you can explore different biomes, build and destroy blocks.

4D rigid body physics engine

Some scenes

Parameters in control panel

Camera settings

  • Fov Field of view, which can be also adjusted by key 9 0.

Render settings

Note: In 4DViewer, the 3D retina is actually realised by layers of 2D cross sections.

  • Thickness Adjust gaps between 2D cross sections layers, you can also use key + -.
  • Flow Adjust layer opacity. It is recommended to keep the value moderate. A too large value will cause only the surface of the 3D retina to be visible. You can also use key [ ] to adjust it.
  • ThumbSize Adjust the size of the cross section thumbnail, you can also use key ; '.
  • WireFrameMode Toggle wireframe mode by press key C, use Ctrl+[ and Ctrl+] or Alt+[ and Alt+] to adjust the thickness.
  • bgColor4 Background color of the 4D scene (like the color of 4D sky)
  • bgColor3 Background color of the 2D screen on which 3D retina is projected. Use key , . to adjust th color in the range of black, gray and white.
  • Transparency When the scene is complex, we hope that some part of the 3D image could be more transparent. Hold on Alt+1, Alt+2, Alt+3 or Alt+4, and right click the color you want.(There aree 4 color slots to be transparent) Click anywhere while holding Alt will remove all the transparent colors.
  • if the FPS is too low, you can adjust the resolution by keyCtrl+, or Alt+, (decrease) and Ctrl+. or Alt+. (increase).

Here's a summary of shortcuts of rendering settings:(Alt can be replaced by Ctrl)

Shortcut Function
= Increase 2D cross section layers
- Decrease 2D cross section layers
] Increase opacity of voxels in 3D retina
[ Decrease opacity of voxels in 3D retina
; Decrease the size of cross sections
' Increase the size of cross sections
, Make background darker
. Make background brighter
9 Decrease camera FOV
0 Increase camera FOV
C Wireframe mode
Alt+[ Decrease wireframe width (Wireframe mode)
Alt+] Increase wireframe width (Wireframe mode)
Alt+, Decrease resolution
Alt+. Increase resolution
Alt+1 Use default rendering preset
Alt+2 Use preset for 3D retina (No cross sections, more layers and low resolution)
Alt+3 Use preset for cross sections (No 3D retina, big cross sections)
Arrow keys Rotate the 3D retina slightly

Solar control

  • Latitude Set latitude value from 0 to 90 degree (in Hopf coordination)
  • SouthernTime and NorthernTime Two different timing systems related to 2 longitude values in Hopf coordination.
  • Season The orbit phase angle of the planet；
  • SouthernTropic and NorthernTropic the minimum and the maximum latitude value on which sunlight can cast perpendicularly. eg. two obliquities of the ecliptic.
  • M-G Periode and W-E Periode are hours for one rotation at south and north pole respectively.
  • SunAngle and SunLatitude are only readable.
  • TimeStep adjust the time passing speed.

Inspiration (Thanks to)

Further probable works

  • 4D ray tracing offline renderer
  • 4D fluid?
  • A new 4D render engine "Tesserxel" with WebGPU