How to fill a volume plot of a vector valued functions (with 3 variables)

Again, I'm ascending new ground, now dealing with volume plots. I'm aware of Matlabs documentary concering this topic. But it doesn't seem to cover my problem. It's about plotting:

where

To the best of my knowldege this function will map a cuboid to . So it should be representable without reducing any dimension. I feel like inconvenient doing this in Matlab, since there doesn't seem to exist some nice functions like mesh or surf for volumes, so I just can't

[u,v,w] = meshgrid(-1:0.1:1);
x = u.^2+u;
y = v.^2+v;
z = z.^2+z;

mesh(x,y,z) %... just defined for surfaces. 

Nevertheless Is there some equivalence for volumes?

[darova]

Maybe isosurface

[KSSV]

Have a look on slice

[Niklas Kurz]

Isn't slice made for plotting scalar functions of 4th dimension? I haven't been using isosurface yet, but its plots look like 2-dimensional manifolds. For my purpose you must think about a filled cube, that is being deformed in by the function φ. At least that's how I think about it. Briefly speaking I search for a function like mesh that maps a plane of points in and inderpolates the distance between the resulting mapping. Just for Volumes.

Answer 1

[Matt J]

See quiver3.

https://www.mathworks.com/help/matlab/ref/quiver3.html

[Niklas Kurz]

would work in case φ would be a vector Field. But it's a vector valued Function.

[Matt J]

But a vector field is a vector-valued function from R^3 to R^3. Is that not what you want?

[u,v,w] = meshgrid(-1:0.1:1);
x = u.^2+u;
y = v.^2+v;
z = w.^2+w;

quiver3(u,v,w,x,y,z)

[Niklas Kurz]

Yea, that's true: a vector field is a vector valued function, but a vector falued function is not a vector field. Here I'm just given a vector valued function, whose mapped domain I'd like to visulaize (as connected points, like mesh)

[Niklas Kurz]

probably matlab lecks the ability of doing that, because I haven't seen fully 3D filled objects being plotted yet. Just the outline. So maybe I've to finde a parametrization of the outer surface. What's kinda odd.