```
using CairoMakie
using StableRNGs
points = [(0.0, 0.0), (2.0, 0.0), (1.0, 2.0)]
tri = triangulate(points)
fig, ax, sc = triplot(tri)
fig
add_point!(tri, 1.0, 0.5)
fig, ax, sc = triplot(tri)
fig
add_point!(tri, 0.0, 1.0)
fig, ax, sc = triplot(tri)
fig
delete_ghost_triangles!(tri)
add_point!(tri, 2.0, 1.5)
DelaunayTriangulation.has_ghost_triangles(tri)
add_ghost_triangles!(tri)
DelaunayTriangulation.has_ghost_triangles(tri)
get_convex_hull_vertices(tri)
convex_hull!(tri)
fig, ax, sc = triplot(tri, show_convex_hull=true)
fig
rng = StableRNG(123)
for _ in 1:1000
new_point = 2rand(rng, 2)
add_point!(tri, new_point)
end
fig, ax, sc = triplot(tri)
fig
vertices_to_delete = Iterators.filter(each_solid_vertex(tri)) do i
p = get_point(tri, i)
r2 = (getx(p) - 1.0)^2 + (gety(p) - 1.0)^2
return r2 < 1 / 2^2
end
for i in vertices_to_delete
delete_point!(tri, i)
end
fig, ax, sc = triplot(tri)
fig
```

Hi, this is in the documentation of triangulation, I want to do a delete point operation similar to the above, but im facing issues. Getting error vertex. not found. I tried to run the exact code in the docs, it also fails.

What is your error? The code you posted works fine for me. The only error is on Line 19, but if you read the docs that error is intentionally made to make a point about ghost triangles. An MWE would be best.

Taking part of it:

```
using CairoMakie
using StableRNGs
points = [(0.0, 0.0), (2.0, 0.0), (1.0, 2.0)]
tri = triangulate(points)
fig = Figure()
ax = Axis(fig[1, 1])
add_point!(tri, 1.0, 0.5)
delete_point!(tri, (0.0, 1.0))
add_point!(tri, 2.0, 1.5)
triplot!(ax, tri)
display(fig)```
ERROR: Graph does not contain requested vertex
Stacktrace: @line 11 delete operation
```

You cannot put coordinates into `delete_point!`

. Only vertices - meaning integers, as mentioned in the docs:

Let us now demonstrate how to delete points. To do this, we use `delete_point!`

. This function takes vertices rather than coordinates, identifying the corresponding point in `points`

by its index

how can i get vertices closest to the points?

In my function:

```
for (i, j) in enumerate(each_polygon_index(svorn))
p = DelaunayTriangulation.get_centroid(svorn, i)
density = get_density_value(normalized_density_values, p)
if density != 0
push!(points_to_add, p)
else
delete_point!(tri, j)
end
end
```

Im looping through the voronoi cells and checking certain value and adding or deleting points. Is this the correct way to do?

There are very fast ways to do this, but here are some naive ways. Can probably do some nearest neighbour type methods for this too if you construct a KDTree to work with (GitHub - KristofferC/NearestNeighbors.jl: High performance nearest neighbor data structures (KDTree and BallTree) and algorithms for Julia.).

```
# If you know that your given coordinates (x, y) appear *EXACTLY* in points
function get_vertex(tri, p) # p is the point (x, y) to find the vertex of
for i in DelaunayTriangulation.each_point_index(tri)
get_point(tri, i) == p && return i
end
return 0 # 0 ⟹ point not found, you can error if you prefer
end
# If you only have an approximate form of the coordinates
function get_closest_vertex(tri, p)
x, y = getxy(p)
i = argmin(DelaunayTriangulation.each_point_index(tri)) do v
x′, y′ = get_point(tri, v)
(x - x′)^2 + (y - y′)^2
end
return i
end
```

No. The triangulation is changing as you are doing the loop, so the density values will constantly be changing. Moreover, `svorn`

will not be in sync with `tri`

- you need to keep updating `vorn`

after each update of `tri`

. You should find the points to add / delete in a loop, then update the triangulation afterwards and then recompute your Voronoi tessellation.

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