# Contour plots on non-rectangular domain

**URL:** <https://discourse.julialang.org/t/contour-plots-on-non-rectangular-domain/47193>\
**Category:** New to Julia\
**Tags:** pyplot, plots\
**Created:** [September 24, 2020, 8:16am UTC](https://discourse.julialang.org/t/contour-plots-on-non-rectangular-domain/47193 "2020-09-24T08:16:44Z")\
**Posts on this page:** 7\
**Page:** 1

<div class="post-metadata">

**Author:** ![Stein](https://avatars.discourse-cdn.com/v4/letter/s/5f8ce5/32.png) [@Stein](https://discourse.julialang.org/u/Stein)\
**Post date:** [September 24, 2020, 8:16am UTC](https://discourse.julialang.org/t/contour-plots-on-non-rectangular-domain/47193/1 "2020-09-24T08:16:44Z")

</div>

Is there any way to use the `contour` and `contourf` commands from the `Plots.jl` package to produce figures with non-rectangular domains? Or what would be the most flexible/complete alternative?

Suppose I have the following plot in polar coordinates:

```julia
using Plots
r = 1:0.1:2
θ = 0:0.05π:0.5π
f(r,θ) = r^2+sin(θ)
contourf(r, θ, f)

```

How would I plot this as a quarter annulus in the Cartesian frame? I am not looking for anything specific for polar coordinates though, that’s just an example.

---

<div class="post-metadata">

**Author:** ![tomerarnon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomerarnon/32/3170_2.png) [@tomerarnon](https://discourse.julialang.org/u/tomerarnon)\
**Post date:** [September 24, 2020, 10:49am UTC](https://discourse.julialang.org/t/contour-plots-on-non-rectangular-domain/47193/2 "2020-09-24T10:49:31Z")

</div>

You can use `plot(..., proj=:polar)` to make a polar plot. See: [http://docs.juliaplots.org/latest/generated/plotly/#plotly-ref27](http://docs.juliaplots.org/latest/generated/plotly/#plotly-ref27)

Just to note, you data is not currently a quarter annulus. In a polar plot, it seems ranges for theta and r iterate together, rather than independently (basing that on just the example) so you wont get the contour you’re expecting.  
You could always convert (r, θ), and f to (x, y) domain to use contourf as expected.

---

<div class="post-metadata">

**Author:** ![yha](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/yha/32/3502_2.png) [@yha](https://discourse.julialang.org/u/yha)\
**Post date:** [September 24, 2020, 10:57am UTC](https://discourse.julialang.org/t/contour-plots-on-non-rectangular-domain/47193/3 "2020-09-24T10:57:03Z")

</div>

This is supported on the pyplot backend.

```julia
pyplot()
r = 1:0.1:2
θ = 0:0.05π:0.5π
f(θ,r) = r^2+sin(θ)
contourf(θ, r, f, proj=:polar)

```

(note that the order of the arguments (`θ` and `r`) is the other way round from your code)

---

<div class="post-metadata">

**Author:** ![Stein](https://avatars.discourse-cdn.com/v4/letter/s/5f8ce5/32.png) [@Stein](https://discourse.julialang.org/u/Stein)\
**Post date:** [September 24, 2020, 11:48am UTC](https://discourse.julialang.org/t/contour-plots-on-non-rectangular-domain/47193/4 "2020-09-24T11:48:18Z")

</div>

Thank you both for your quick replies.  
Maybe my example of polar coordinates was a bit unfortunate. As I am indicating in my original post, that is really just an example. I am looking for something that can handle arbitrary transformations.

Does the proj key word argument only take predefined symbols, or can I also pass transformation functions? Or is there some sort of “projection recipe” that I can write?

---

<div class="post-metadata">

**Author:** ![yha](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/yha/32/3502_2.png) [@yha](https://discourse.julialang.org/u/yha)\
**Post date:** [September 24, 2020, 3:12pm UTC](https://discourse.julialang.org/t/contour-plots-on-non-rectangular-domain/47193/5 "2020-09-24T15:12:14Z")

</div>

This is not directly supported by `Plots`, and I’m not aware of any existing recipes for doing that.  
If your non-rectangular domain can be represented as a transformation of a rectangular domain (as in the polar example), maybe you can compute the contours in the rectangular domain (using `Contour.jl`), and then transform and plot them.

---

<div class="post-metadata">

**Author:** ![Stein](https://avatars.discourse-cdn.com/v4/letter/s/5f8ce5/32.png) [@Stein](https://discourse.julialang.org/u/Stein)\
**Post date:** [September 25, 2020, 11:04am UTC](https://discourse.julialang.org/t/contour-plots-on-non-rectangular-domain/47193/6 "2020-09-25T11:04:40Z")

</div>

As it happens, my use case does indeed exclusively involve mapped rectangular domains. I can use the `Contour.jl` package that you’re suggesting to make the basic contour plots work. However, getting filled contour plots to work (which is really the interesting case) still seems like a significant implementation effort. I’d be happy to hear of any packages that can help with that.

In case anyone is interested, here is a working example that can handle various transformations (mostly copied from the `Contour.jl` tutorial):

```julia
using Plots
using Contour
gr()

transformation(r,θ) = (@.r*cos(θ) ,@.r*sin(θ))

r = 1:0.01:2
θ = 0:0.01π:0.5π
f(r,θ) = cos((r-0.5)*3)+sin(θ)
p1 = Plots.contour(r,θ,f,nlev=20)

p2 = plot()
z = [f(ri,θi) for ri in r, θi in θ]
conts = contours(r,θ,z,20)
for cl in levels(conts)
    for line in lines(cl)
        xline,yline = transformation(coordinates(line)...)
        plot!(xline,yline, label="")
    end
end
plot(p1,p2,size=(500,250))

```

which produces:

![image](https://global.discourse-cdn.com/julialang/original/3X/c/9/c94d5338c92afa05ec4e0d069f0a3baf28e728b8.png)

---

<div class="post-metadata">

**Author:** ![Aran](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/aran/32/32584_2.png) [@Aran](https://discourse.julialang.org/u/Aran)\
**Post date:** [April 28, 2022, 11:17am UTC](https://discourse.julialang.org/t/contour-plots-on-non-rectangular-domain/47193/7 "2022-04-28T11:17:59Z")

</div>

Good afternoon all, sorry to revive an old thread.  
However I too am looking to plot a contour in the quarter annulus only, i.e. I do not wish the frame of the plot to include the range π/2 \< θ \< 2π. Currently the command

```julia
contour(θ, r, f, proj=:polar)

```

Produces a full cirlce regardless of the theta domain specified.

Although converting to Cartesians would be a potential work around, it would be nice to have the ranges supported intrinsically.

Does this anyone know how to do this ?  
I have used the Contour.Jl package but colouring of the contours seems to be strange.  
Many thanks