# Simple 4D Projector 1.1

HXCTCreations - Custom level - from AndroidDisplays wireframe of 2D perspective projection of 3D perspective projection of 4D perspective projection generated within the script. Still a WIP though, but it works! Currently the only object available is the hypercube.

Sliders from left to right rotate plane:

XZ, YZ, XY, XW, YW, ZW

-----Changelog:

---v1.0

-Initial release

---v1.1

-Re-written script to macth the 3D counterpart.

READ:

In 4D hyperspace there are 4 axis, 3 of them are normal axis in our 3D world (X, Y, Z) and the other one is W axis which is perpendicular to our 3D space. Seems impossible? Well, it's becaus our vision is only two dimensional. The case is the same as the Z axis is perpendicular to 2D plane (X, Z) and 2D beings (assume that they are exist) thinks that is impossible since their vision is limited to only one dimensional. (Shortly, an n-dimensional being has (n-1)-dimensional vision.

4D objects are much more complex than 3D objects due to extra degree of freedom. An 4D object is bounded by 3 dimensional faces called "cells". For example a hypercube (or tesseract, or 8-cell, or 4-cube, 4 dimensional analog of the cube) which is shown in the projector is bounded 8 cubical cells. It's like a cube is bounded 6 square faces, and a square is bounded by 4 line segments.

Cartesian coordinates for each vertex in hypercube are permutation of:

(+-1,+-1,+-1,+-1)

Normally when you look at the hypercube down the W axis, it's look like a cube inside another cube. The rest of the cubes are between those cubes, but they don't look like cubes. It's because the foreshortening effect of the perspective projection

The sliders to the left control rotation of x,y,z axis. If you use those sliders, the hypercube rotates just in first three dimension and nothing weird happens, just two cubes fixed to each other rotating in 3D.

Weird thing happens when you use sliders to the right. These sliders controls rotations involving W axis.

Views: 1610 Downloads: 665 Unique objects: 1 Total objects: 59

LEVEL ID: 22667

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