How to draw an object in 4 dimensional space using matlab ?

Hi all,

Do you know how to draw an object in 4 dimensional space, namely the gif pictures showed in this wiki link (https://en.wikipedia.org/wiki/Four-dimensional_space)?

I need to draw ‘regular triangular pyramid’，‘cube' and 'sphere' of 4 dimensional space using matlab and show them by gif pictures.

I need algorithms or useful math expressions in detail.

Thanks you very much!

Wish you good!

Answer 1

[Walter Roberson]

Create your points and connection list in 4D. When you need to draw it, do a Projection into 3D and draw the result.

You likely will not want to bother with a formal projection matrix: you will probably just want to use a rotation matrix and then drop the last coordinate.

[William]

Hi Walter,

Thank you very much! I just don't know how to creat those points or connections in 4D.Do you know the coputation method in detail? The papers and links gives operable computing method will also be very helpful.

I.P.

[Walter Roberson]

https://en.wikipedia.org/wiki/5-cell#Geometry

Coordinates for the hypercube are trivial, all 0's and 1's

For the 3-sphere you are going to need to choose a subset of points on the surface.

On the other hand, rotating a true 3-sphere around its center is going to result in the same 3-sphere, so in a sense there is no point doing the rotation. The same would be true of a sufficiently dense approximation of a 3-sphere; it is not, however, true of an approximation to a 3-sphere. And of course if you have colored the 3-sphere non-uniformly then it might be worth rotating.