Graphical representation of vectors in 4 dimensional space

Question

I want to draw the 4-dimensional vectors. The vectors' restrictions are:

all elements are more than 0.
all vectors' sum of the all elements is the same.

If 3-dim, we can draw them in an 2-dim equilateral triangle like this.

It means that we can reduce the dimension by using this kind of figure, so if 4-dim vectors, we can represent them by a regular tetrahedron.

I'm looking for a software or program library for drawing 4-dim vectors in such a regular tetrahedron.

I'm sorry if this question is not relevant to this forum.

I wouldn't use a tetrahedron then, I would instead make a pie chart or some percentage based chart. — Rushabh Mehta, Sep 12 '19 at 14:01

score 1 · Answer 1 · answered Sep 12 '19 at 14:11

1

Legit 3D plots are most of the time are confusing when people cant' interact with them, because the depth is harder to perceive on a flat image.

However, if you still want to follow that path, you can normalize your vector, so the sum of the elements is $1$ and use baricentric coordinates in tetrahedron: $$ u_i=\frac{v_i}{\sum_{j=1}^4 v_j},\qquad \vec U=\sum_{i=1}^4\vec P_iu_i, $$ where $\vec P_i$ is coordinates of $i$-th tetrahedron vertex.

It can be done in any software sophisticated enough. For example, in Wolfram Mathematica:

answered Sep 12 '19 at 14:11

Vasily Mitch

10,129

Thanks a lot. What vectors did you draw in your figure above? Could you show me the case where (3, 2, 2, 1), (2, 3, 2, 1), (2, 2, 3, 1), (3, 2, 3, 0)? – Sato Sep 12 '19 at 14:23
See https://i.imgur.com/KLXsMiD.png – Vasily Mitch Sep 12 '19 at 14:30
Do you know the free software or programming language to implement this, e.g., python? – Sato Sep 12 '19 at 14:41
python can do this too – Vasily Mitch Sep 12 '19 at 14:49
Thank you very much! – Sato Sep 12 '19 at 15:39

Graphical representation of vectors in 4 dimensional space

1 Answers1