# Making a surface from scattered data
**URL:** https://discourse.julialang.org/t/making-a-surface-from-scattered-data/27622
**Category:** Visualization
**Created:** [August 16, 2019, 5:38pm UTC](https://discourse.julialang.org/t/making-a-surface-from-scattered-data/27622 "2019-08-16T17:38:58Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@Noel\_Araujo](https://discourse.julialang.org/u/Noel_Araujo)
#### Post date: [August 16, 2019, 5:38pm UTC](https://discourse.julialang.org/t/making-a-surface-from-scattered-data/27622/1 "2019-08-16T17:38:58Z")
I would to transform scattered data into a surface.
Google told me that is I could do it in Matlab[1,2] or Python [3] using Delaunay triangulation. But I cannot find a similar example in Julia with [VoronoiDelaunay.jl](https://github.com/JuliaGeometry/VoronoiDelaunay.jl) and its related pages.
Does anybody has an example ?
Thank you š
[1] [Making Surface Plots From Scatter Data - File Exchange - MATLAB Central](https://www.mathworks.com/matlabcentral/fileexchange/5105-making-surface-plots-from-scatter-data)
[2] [Delaunay triangulation - MATLAB delaunay](https://www.mathworks.com/help/matlab/ref/delaunay.html)
[3] [Use Python to plot Surface graphs of irregular Datasets](https://fabrizioguerrieri.com/blog/2017/9/7/surface-graphs-with-irregular-dataset)
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### Author:  [@lstagner](https://discourse.julialang.org/u/lstagner)
#### Post date: [August 16, 2019, 6:10pm UTC](https://discourse.julialang.org/t/making-a-surface-from-scattered-data/27622/2 "2019-08-16T18:10:41Z")
You can use a Thin Plate Spline / PolyharmonicSpline to do it.
Here is an [old gist](https://gist.github.com/lstagner/04a05b120e0be7de9915) that has an Julia v0.5ish implementation and example and here is an [updated version](https://github.com/lstagner/OrbitTomography.jl/blob/master/src/polyharmonic.jl) that works with Julia v1.0
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### Author:  [@Noel\_Araujo](https://discourse.julialang.org/u/Noel_Araujo)
#### Post date: [August 16, 2019, 6:35pm UTC](https://discourse.julialang.org/t/making-a-surface-from-scattered-data/27622/3 "2019-08-16T18:35:28Z")
just for anyone that needs an example with Julia v1.x:
```julia
ENV["MPLBACKEND"]="tkagg" # if you need
using PyPlot
using LinearAlgebra
include("polyharmonic_spline.jl")
# contain all code from https://github.com/lstagner/OrbitTomography.jl/blob/master/src/polyharmonic.jl
# and `interpolate()`definition from https://gist.github.com/lstagner/04a05b120e0be7de9915
x,y = randn(500),randn(500)
z = exp.(-(x.^2 .+ y.^2))
S2 = PolyharmonicSpline(2,[x y],z)
n=20
xgrid = ones(n)*range(-3,stop=3,length=n)'
ygrid = range(-3,stop=3,length=n)*ones(n)'
xx = reshape(xgrid,n*n)
yy = reshape(ygrid,n*n)
zz = interpolate(S2,xx,yy)
zgrid = reshape(zz,n,n);
plot_surface(xgrid,ygrid,zgrid,alpha=0.5)
scatter3D(x,y,z,color="r")
show()
```
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### Author:  [@lstagner](https://discourse.julialang.org/u/lstagner)
#### Post date: [August 16, 2019, 6:46pm UTC](https://discourse.julialang.org/t/making-a-surface-from-scattered-data/27622/4 "2019-08-16T18:46:47Z")
With the updated version you donāt need the `interpolate` method. The constructor for the spline returns a interpolating āfunctionā. You can simplify the code to be
```julia
using PyPlot
using LinearAlgebra
include("polyharmonic_spline.jl")
# contain all code from https://github.com/lstagner/OrbitTomography.jl/blob/master/src/polyharmonic.jl
x,y = randn(500),randn(500)
z = exp.(-(x.^2 .+ y.^2))
S2 = PolyharmonicSpline(2,[x y],z)
n=20
xgrid = ones(n)*range(-3,stop=3,length=n)'
ygrid = range(-3,stop=3,length=n)*ones(n)'
zgrid = S2.(xgrid,ygrid) #Take advantage of dot broadcasting
plot_surface(xgrid,ygrid,zgrid,alpha=0.5)
scatter3D(x,y,z,color="r")
show()
```
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### Author:  [@jlchan](https://discourse.julialang.org/u/jlchan)
#### Post date: [February 13, 2020, 2:29pm UTC](https://discourse.julialang.org/t/making-a-surface-from-scattered-data/27622/5 "2020-02-13T14:29:12Z")
Iām not sure why we need spline interpolation to do this. Using the default GR backend, seems like `surface` naturally interpolates via Delaunay triangulation. The following code
```julia
using Plots
x = randn(1000)
y = randn(1000)
z = @. sin(x)*sin(y)
surface(x,y,z,camera=(0,90))
```
gives something like
