# Create a GeometryBasics convex polygon from an unordered set of points

**URL:** <https://discourse.julialang.org/t/create-a-geometrybasics-convex-polygon-from-an-unordered-set-of-points/96349>\
**Category:** General Usage\
**Tags:** question\
**Created:** [March 20, 2023, 3:26pm UTC](https://discourse.julialang.org/t/create-a-geometrybasics-convex-polygon-from-an-unordered-set-of-points/96349 "2023-03-20T15:26:19Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![prittjam](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/prittjam/32/21267_2.png) [@prittjam](https://discourse.julialang.org/u/prittjam)\
**Post date:** [March 20, 2023, 3:26pm UTC](https://discourse.julialang.org/t/create-a-geometrybasics-convex-polygon-from-an-unordered-set-of-points/96349/1 "2023-03-20T15:26:19Z")

</div>

I have a set of four 2d points and want to create a quadrilateral. Currently, I manually order the input points to ensure it is convex. Is there a function in GeometryBasiscs that crates a convex polygon from an unordered set of 2d points? If I don’t sort them properly then the lines intersect like an X

---

<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:** [March 20, 2023, 9:53pm UTC](https://discourse.julialang.org/t/create-a-geometrybasics-convex-polygon-from-an-unordered-set-of-points/96349/2 "2023-03-20T21:53:47Z")

</div>

If you have a set of unordered 2d points, that are vertices of a convex polygon, then you must first reorder them  
as follows:

- calculate the center of mass, c, of the given set of points;
- calculate the coordinates of vectors \vec{cp}=p-c, where p runs over  
the `points`, given as a vector of vectors;
- calculate the angle of each vector \vec{cp}=(x,y) with the positive x-axis, as `atan(y, x)`.
- `sortperm` the the computed angles, α, and a get the index vector `idx`.
- `points[idx]` represent the ordered points, and now you can plot the associated polygon with your favorite plotting library.  
I’m using PlotlyJS:

```julia
using PlotlyJS, Statistics
function reorderpoints(points)
   x= getindex.( points, 1)
   y= getindex.( points, 2) 
   c = [mean(x), mean(y)]
   v = [p-c for p in points]
   α =[atan(u[2], u[1]) for u in v]
   idx=sortperm(α)
   points[idx]
end 

points= [[-0.35, 1.6],
         [1.0, 0.0],
         [-0.4, -1.3],
         [-1.5, -1.2],
         [0.75, 1.5],
         [-1.0, 0.8]]
pts =reorderpoints(points)
push!(pts, pts[1])
fig =Plot(scatter(x=getindex.(pts, 1), 
                  y=getindex.(pts, 2), 
                  fill="toself", 
                  fillcolor="RoyalBlue"),
    Layout(width=400, height=400))

```

![convexpolygon](https://global.discourse-cdn.com/julialang/original/3X/8/4/84cacb97c91a7a68e29439315e547262bc34a8b2.png)