# 3D volume plot for spherical coordinate grid points

**URL:** <https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668>\
**Category:** Visualization\
**Tags:** glmakie, meshes\
**Created:** [June 5, 2025, 11:52am UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668 "2025-06-05T11:52:44Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![raman\_kumar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raman_kumar/32/26782_2.png) [@raman\_kumar](https://discourse.julialang.org/u/raman_kumar)\
**Post date:** [June 5, 2025, 11:52am UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/1 "2025-06-05T11:52:44Z")

</div>

How to get volume plot for the following spherical coordinate positions? 🧒  
I have a lot of blocks each having such r, θ and ϕ spherical coordinate position vectors and i want to create 3D volume plot for each block vectors and finally combine them to create a single 3D volume plot.

```julia
r = Float32[1.677044, 1.8385518, 2.0156136, 2.2097273, 2.4225352, 2.6558375, 2.911608, 3.1920104, 3.499417, 3.8364286, 4.205896, 4.6109447, 5.055002, 5.5418243, 6.0755296, 6.660634, 7.3020864, 8.005314]
θ = Float32[0.049087387, 0.14726216, 0.24543692, 0.3436117]
ϕ = Float32[0.19634955, 0.5890486, 0.9817477, 1.3744467, 1.7671459, 2.1598449, 2.552544, 2.9452431, 3.3379421, 3.7306414, 4.12334, 4.5160394, 4.9087386, 5.3014374, 5.6941366, 6.086836]

```

---

<div class="post-metadata">

**Author:** ![JM\_Beckers](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jm_beckers/32/22482_2.png) [@JM\_Beckers](https://discourse.julialang.org/u/JM_Beckers)\
**Post date:** [June 5, 2025, 11:59am UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/2 "2025-06-05T11:59:09Z")

</div>

What do you mean by “volume plot”? Your vectors do not have the same length, so what do they represent ?

> [@raman\_kumar](#):
>
> ```julia
> x = Float32[1.677044, 1.8385518, 2.0156136, 2.2097273, 2.4225352, 2.6558375, 2.911608, 3.1920104, 3.499417, 3.8364286, 4.205896, 4.6109447, 5.055002, 5.5418243, 6.0755296, 6.660634, 7.3020864, 8.005314]
> y = Float32[0.049087387, 0.14726216, 0.24543692, 0.3436117]
> z = Float32[0.19634955, 0.5890486, 0.9817477, 1.3744467, 1.7671459, 2.1598449, 2.552544, 2.9452431, 3.3379421, 3.7306414, 4.12334, 4.5160394, 4.9087386, 5.3014374, 5.6941366, 6.086836]
> 
> ```

---

<div class="post-metadata">

**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [June 5, 2025, 12:41pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/3 "2025-06-05T12:41:39Z")

</div>

Here is one way to define a `RectilinearGrid` with `Spherical` coordinates:

```julia
using Meshes
using CoordRefSystems

import GLMakie as Mke

r = Float32[1.677044, 1.8385518, 2.0156136, 2.2097273, 2.4225352, 2.6558375, 2.911608, 3.1920104, 3.499417, 3.8364286, 4.205896, 4.6109447, 5.055002, 5.5418243, 6.0755296, 6.660634, 7.3020864, 8.005314]
θ = Float32[0.049087387, 0.14726216, 0.24543692, 0.3436117]
ϕ = Float32[0.19634955, 0.5890486, 0.9817477, 1.3744467, 1.7671459, 2.1598449, 2.552544, 2.9452431, 3.3379421, 3.7306414, 4.12334, 4.5160394, 4.9087386, 5.3014374, 5.6941366, 6.086836]

g = RectilinearGrid{𝔼,typeof(Spherical(0,0,0))}(r, θ, ϕ)

viz(g)

```

 ![image](https://global.discourse-cdn.com/julialang/original/3X/2/3/235a2c82d5d74897d4ab2e2516fb672e438e1e83.jpeg)

The type parameters in the constructor are a bit low-level, but I think they match what you have in mind. The first type parameter `𝔼` refers to the manifold where the geometries live. In this case this is the Euclidean manifold. The second type parameter is the coordinate reference system type, which I am producing with a `typeof(Spherical(0,0,0))` call.

You can also define the periodicity of each coordinate. Below you can find an alternative code that considers one of the angular coordinates to be periodic. First, it creates a `GridTopology` with the number of elements in the grid and the periodicity information, and then it feeds the topology as the second argument of the `RectilinearGrid`:

```julia
# grid topology with given number of elements per dimension
# the last coordinate is periodic so we set (false, false, true)
t = GridTopology((length(r)-1, length(θ)-1, length(ϕ)-1), (false, false, true))

g = RectilinearGrid{𝔼,typeof(Spherical(0,0,0))}((r, θ, ϕ), t)

viz(g)

```

 ![image](https://global.discourse-cdn.com/julialang/original/3X/f/6/f678ec634a4a74c425550659c433ddcb195ad483.jpeg)

Notice how the cone is now full-filled compared with the previous one.

---

<div class="post-metadata">

**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [June 5, 2025, 12:54pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/5 "2025-06-05T12:54:32Z")

</div>

I’ve updated the answer to include a variation that you might be interested in.

---

<div class="post-metadata">

**Author:** ![raman\_kumar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raman_kumar/32/26782_2.png) [@raman\_kumar](https://discourse.julialang.org/u/raman_kumar)\
**Post date:** [June 5, 2025, 1:09pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/6 "2025-06-05T13:09:10Z")

</div>

@juliohm Thank you very much. I will also map Density on these 3D points.

> [@juliohm](#):
>
> Notice how the cone is now full-filled compared with the previous one.

For me first plot would be fine.

---

<div class="post-metadata">

**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [June 5, 2025, 1:15pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/7 "2025-06-05T13:15:10Z")

</div>

You can map colors to every element of the grid with

```julia
viz(g, color=1:nelements(g))

```

Notice the length of the vector. It must match the number of elements in the grid, not the number of vertices. Some `viz` methods also support colors for every vertex, but I don’t remember if this is the case with `RectilinearGrid`. You can try and see.

---

<div class="post-metadata">

**Author:** ![raman\_kumar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raman_kumar/32/26782_2.png) [@raman\_kumar](https://discourse.julialang.org/u/raman_kumar)\
**Post date:** [June 5, 2025, 1:21pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/8 "2025-06-05T13:21:40Z")

</div>

I got this error below. Please update you reply and replace first line with

```julia
using Meshes, CoordRefSystems, GLMakie

```

so that people don’t have misunderstanding while reading your solution later.

> julia\> g = RectilinearGrid{𝔼,typeof(Spherical(0,0,0))}(r, θ, ϕ)  
> ERROR: UndefVarError: `Spherical` not defined in `Main`  
> Suggestion: check for spelling errors or missing imports.  
> Hint: a global variable of this name may be made accessible by importing CoordRefSystems in the current active module Main

---

<div class="post-metadata">

**Author:** ![JoshuaLampert](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/joshualampert/32/205964_2.png) [@JoshuaLampert](https://discourse.julialang.org/u/JoshuaLampert)\
**Post date:** [June 5, 2025, 1:34pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/9 "2025-06-05T13:34:56Z")

</div>

> [@raman\_kumar](#):
>
> Can many such block plots be combined to get final single plot? 🙉

Sure, just create another `RectilinearGrid` in the same way with the other coordinates and call `viz!` instead of `viz` to plot it in the same figure.

---

<div class="post-metadata">

**Author:** ![raman\_kumar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raman_kumar/32/26782_2.png) [@raman\_kumar](https://discourse.julialang.org/u/raman_kumar)\
**Post date:** [June 6, 2025, 12:39pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/10 "2025-06-06T12:39:15Z")

</div>

Thanks to you all. I got this plot of Athena++ Black Hole simulation but color of density plot looks not so smooth and real. 🙉

 ![image](https://global.discourse-cdn.com/julialang/original/3X/e/a/ea08c44c213504626c3dea1025904bd940714848.png)  
and for `alpha = 0.3` it looks  
 ![image](https://global.discourse-cdn.com/julialang/original/3X/6/b/6bf7c26aa701719380076ff9ecc993821758c133.png)  
Is there any way to interpolate color to smooth them?

---

<div class="post-metadata">

**Author:** ![sdanisch](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sdanisch/32/1406_2.png) [@sdanisch](https://discourse.julialang.org/u/sdanisch)\
**Post date:** [June 10, 2025, 3:02pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/11 "2025-06-10T15:02:59Z")

</div>

First thing should be to use `transparency=true` for the second image 😉

---

<div class="post-metadata">

**Author:** ![raman\_kumar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raman_kumar/32/26782_2.png) [@raman\_kumar](https://discourse.julialang.org/u/raman_kumar)\
**Post date:** [June 10, 2025, 5:34pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/12 "2025-06-10T17:34:01Z")

</div>

On using

```julia
viz!(g, color = nrho, transparency=true, alpha = 0.3)

```

i got this plot. But still it don’t look smooth.

 ![image](https://global.discourse-cdn.com/julialang/original/3X/b/4/b45b6c8e00a7b0de2cf6c621fb824879aaa02393.png)  
and cone segment looks as shown below.  
 ![image](https://global.discourse-cdn.com/julialang/original/3X/4/4/44e3fc56d409fdc729d866371a3b504d6bb186d1.png)

---

<div class="post-metadata">

**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [June 10, 2025, 5:45pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/13 "2025-06-10T17:45:26Z")

</div>

We currently don’t forward the `transparency` option to the underlying Makie.jl function. It should be easy to submit a PR with a fix.

---

<div class="post-metadata">

**Author:** ![sdanisch](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sdanisch/32/1406_2.png) [@sdanisch](https://discourse.julialang.org/u/sdanisch)\
**Post date:** [June 10, 2025, 6:57pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/14 "2025-06-10T18:57:05Z")

</div>

As a work around, if you can access the plot object from what `viz!` returns, you could do `plot.transparency=true`.  
If it’s a recipe, you’ll find the mesh plot in `plot.plots`.

---

<div class="post-metadata">

**Author:** ![raman\_kumar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raman_kumar/32/26782_2.png) [@raman\_kumar](https://discourse.julialang.org/u/raman_kumar)\
**Post date:** [June 11, 2025, 7:33pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/15 "2025-06-11T19:33:11Z")

</div>

```julia
scene = viz!(g, color = nrho, transparency=true, showsegments = false, alpha = 0.3)
scene.plots[1].transparency = true

```

On using above code i still get patchy rough plot.

 ![image](https://global.discourse-cdn.com/julialang/original/3X/5/5/55c52561c67a7af55fb853f65d2b4198e30a8c0e.png)

---

<div class="post-metadata">

**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [June 11, 2025, 7:38pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/16 "2025-06-11T19:38:41Z")

</div>

@raman_kumar by “patchy rough plot” you mean discrete color transitions? The `color` option is assigned to each element of the grid/mesh so this is an expected result. If the colors were assigned to vertices, the graphics card would perform an additional interpolation to make the final color map look “smooth”.

---

<div class="post-metadata">

**Author:** ![raman\_kumar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raman_kumar/32/26782_2.png) [@raman\_kumar](https://discourse.julialang.org/u/raman_kumar)\
**Post date:** [June 11, 2025, 7:47pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/17 "2025-06-11T19:47:09Z")

</div>

Thanks, I should plot to vertices and not elements. 🥶

> [@juliohm](#):
>
> If the colors were assigned to vertices, the graphics card would perform an additional interpolation to make the final color map look “smooth”.

I have `nelements(g) = 765` and ` nvertices(g) = 1152` but i have `size(nrho) = (1152,)`.

- How to assign color to vertices and not elements?

---

<div class="post-metadata">

**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [June 11, 2025, 7:55pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/18 "2025-06-11T19:55:48Z")

</div>

In theory all you need to do is pass the vector of colors with the correct length. Some `viz` recipes will have specializations for vertices, but I don’t think the recipe with `RectilinearGrid` has this specialization at the moment.

You can try with a `CartesianGrid(10,10)` to see the difference:

```julia
viz(CartesianGrid(10,10), color=1:100) # color elements
viz(Cartesiangrid(10,10), color=1:121) # color vertices

```

---

<div class="post-metadata">

**Author:** ![sdanisch](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sdanisch/32/1406_2.png) [@sdanisch](https://discourse.julialang.org/u/sdanisch)\
**Post date:** [June 11, 2025, 8:23pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/19 "2025-06-11T20:23:25Z")

</div>

> [@raman\_kumar](#):
>
> `scene.plots[1].transparency = true`

Hm, that still doesn’t look like propper transparency…  
Is this GLMakie?

---

<div class="post-metadata">

**Author:** ![raman\_kumar](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/raman_kumar/32/26782_2.png) [@raman\_kumar](https://discourse.julialang.org/u/raman_kumar)\
**Post date:** [June 11, 2025, 10:19pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/20 "2025-06-11T22:19:00Z")

</div>

Yes, I am using GLMakie.jl.

> [@raman\_kumar](#):
>
> ```julia
> r = Float32[1.677044, 1.8385518, 2.0156136, 2.2097273, 2.4225352, 2.6558375, 2.911608, 3.1920104, 3.499417, 3.8364286, 4.205896, 4.6109447, 5.055002, 5.5418243, 6.0755296, 6.660634, 7.3020864, 8.005314]
> θ = Float32[0.049087387, 0.14726216, 0.24543692, 0.3436117]
> ϕ = Float32[0.19634955, 0.5890486, 0.9817477, 1.3744467, 1.7671459, 2.1598449, 2.552544, 2.9452431, 3.3379421, 3.7306414, 4.12334, 4.5160394, 4.9087386, 5.3014374, 5.6941366, 6.086836]
> 
> ```

@juliohm Above 👆 are the `r`, `θ` and `ϕ` values of cell centers along x1/x2/x3-direction in mesh.  
But when i supply in code different `r`, `θ` and `ϕ` denoting values of interface locations along x1/x2/x3-direction 👇

```julia

r = Float32[1.6, 1.754088, 1.9230156, 2.1082115, 2.311243, 2.5338273, 2.7778475, 3.0453684, 3.3386526, 3.6601818, 4.012676, 4.3991165, 4.8227735, 5.287231, 5.7964177, 6.354642, 6.9666257, 7.637547, 8.373081]
θ = Float32[0.0, 0.09817477, 0.19634955, 0.2945243, 0.3926991]
ϕ = Float32[0.0, 0.3926991, 0.7853982, 1.1780972, 1.5707964, 1.9634954, 2.3561945, 2.7488935, 3.1415927, 3.5342917, 3.9269907, 4.3196898, 4.712389, 5.105088, 5.497787, 5.8904862, 6.2831855]

```

then i get grid without cracks as in second plot of your post ⬇ .

> [@juliohm](#):
>
> Notice how the cone is now full-filled compared with the previous one.

---

<div class="post-metadata">

**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [June 11, 2025, 10:35pm UTC](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668/21 "2025-06-11T22:35:15Z")

</div>

If these are grid centers you will need some additional processing to convert into vertices for the RectilinearGrid

[Next page](https://discourse.julialang.org/t/3d-volume-plot-for-spherical-coordinate-grid-points/129668.md?page=2)