# Fill area under 3d curve PlotlyJS.jl

**URL:** https://discourse.julialang.org/t/fill-area-under-3d-curve-plotlyjs-jl/94556
**Category:** General Usage
**Tags:** plotting, plotlyjs
**Created:** [February 13, 2023, 1:02pm UTC](https://discourse.julialang.org/t/fill-area-under-3d-curve-plotlyjs-jl/94556 "2023-02-13T13:02:20Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![Maucejo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/maucejo/32/39090_2.png) [@Maucejo](https://discourse.julialang.org/u/Maucejo)
#### Post date: [February 13, 2023, 1:02pm UTC](https://discourse.julialang.org/t/fill-area-under-3d-curve-plotlyjs-jl/94556/1 "2023-02-13T13:02:20Z")

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Dear all,

I struggle with a problem for a few days. Indeed, I am trying to fill the area under a 3d curve using `PlotlyJS` without any success.

Here is the MWE:

```julia
using PlotlyJS

x = range(0., 2π, 100)
z = sin.(x)

X = [0.; collect(x); 2π]
Z = [minimum(z); z; minimum(z)]
Y = zeros(length(Z))

trace = scatter(x = X, y = Y, z = Z, type = "scatter3d", mode = "lines")
surf = mesh3d(x = X, y = Y, z = Z, delaunayaxis = "y", color = :white)

plot([trace, surf])

```

The results is the same using `plot(scatter(x = X, y = Y, z = Z, type = "scatter3d", mode = "lines", surfaceaxis = 1, surfacecolor=:white))`. For a better understanding of the problem, here is a picture of the output.

 ![image](https://global.discourse-cdn.com/julialang/original/3X/3/0/30951c8e4cbf4b301062fa760f7b3c0ee7213d3d.png)

It seems that this problem is a known issue of Plotly but I wonder if there is a julian workaround to this problem.

Note: I have no issues with `Makie` and `PyPlot`. Below, an example obtained with `Makie`:

 ![image](https://global.discourse-cdn.com/julialang/original/3X/b/2/b27ebe2dace6b59dde6a96cc7ec032f1b393dae6.png)

---

<div class="post-metadata">

### Author: ![empet](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/empet/32/221303_2.png) [@empet](https://discourse.julialang.org/u/empet)
#### Post date: [February 14, 2023, 5:39am UTC](https://discourse.julialang.org/t/fill-area-under-3d-curve-plotlyjs-jl/94556/2 "2023-02-14T05:39:14Z")

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If we want to fill the area below a 3d curve,  
γ: x=x(u), y=y(u), z=z(u), u ∈[a,b], then we have first to decide how much to fill below it.  
Let us say, up to the horizontal plane z=h, where h \<z(u), for all u. The ortogonal projection of this curve onto the plane is the curve prj: x=x(u), y=y(u), z=h.  
The “area” under our curve is a cylindrical surface generated by all  
3d segments of line, connecting the points on the given curve, with their projections onto the plane:  
\displaystyle\frac{x-x(u)}{0}=\displaystyle\frac{y-y(u)}{0}=\displaystyle\frac{z-h}{z(u)-h}=v

Hence we have to plot the surface  
`x=x(u), y=y(u), z=h+(z(u)-h)*v`  
with u ∈ [a, b], and v∈[0,1].

```
In your particular case, the curve γ is x=u, y=0, z=sin(u), u∈[0 2π],  

```

and h=-1.2. Hence we are plotting the surface  
x=u, y=0, z=-1+(sin(u)+1)v

```julia
using PlotlyJS
ul = range(0, 2*pi, 100)
vl = range(0, 1, 50)
u = ones(size(vl)) * ul'
v= vl * ones(size(ul))'
h = -1.2
fig = Plot(surface(x=u, y=zeros(size(u)), z=h .+ (sin.(u) .- h) .*v,
           colorscale=[[0, "#d22b2b"], [1, "#d22b2b"]], opacity=0.5, showscale=false),
           Layout(width=600, height=400))

```

![fillundercurve](https://global.discourse-cdn.com/julialang/original/3X/7/1/717359023ff9067f380566e7630b733ae6d49106.png)

---

<div class="post-metadata">

### Author: ![Maucejo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/maucejo/32/39090_2.png) [@Maucejo](https://discourse.julialang.org/u/Maucejo)
#### Post date: [February 14, 2023, 5:44am UTC](https://discourse.julialang.org/t/fill-area-under-3d-curve-plotlyjs-jl/94556/3 "2023-02-14T05:44:03Z")

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Many thanks @empet for this clear and accurate answer.