# 3D Mesh Plots in Julia

How to make 3D Mesh Plots

### Basic 3D Mesh example

The mesh3d trace type draws a 3D set of triangles with vertices given by x, y and z. If only coordinates are given, an algorithm such as Delaunay triangulation is used to draw the triangles. Otherwise the triangles can be given using the i, j and k parameters (see examples below).

using PlotlyJS, CSV, DataFrames, HTTP

df = CSV.File(
HTTP.get("https://raw.githubusercontent.com/plotly/datasets/master/mesh_dataset.txt").body;
delim=" ",
) |> DataFrame

plot(df, kind="mesh3d", x=:Column1, y=:Column2, z=:Column3, opacity=0.50)

### 3D Mesh example with Alphahull

The alphahull parameter sets the shape of the mesh. If the value is -1 (default value) then Delaunay triangulation is used. If >0 then the alpha-shape algorithm is used. If 0, the convex hull is represented (resulting in a convex body).

using PlotlyJS, CSV, DataFrames, HTTP

df = CSV.File(
HTTP.get("https://raw.githubusercontent.com/plotly/datasets/master/mesh_dataset.txt").body;
delim=" ",
) |> DataFrame

plot(df, x=:Column1, y=:Column2, z=:Column3,
kind="mesh3d",
alphahull=5,
opacity=0.4)

### Mesh Tetrahedron

In this example we use the i, j and k parameters to specify manually the geometry of the triangles of the mesh.

using PlotlyJS

plot(mesh3d(
x=[0, 1, 2, 0],
y=[0, 0, 1, 2],
z=[0, 2, 0, 1],
colorbar_title="z",
colorscale=[[0, "gold"],
[0.5, "mediumturquoise"],
[1, "magenta"]],
# Intensity of each vertex, which will be interpolated and color-coded
intensity=[0, 0.33, 0.66, 1],
# i, j and k give the vertices of triangles
# here we represent the 4 triangles of the tetrahedron surface
i=[0, 0, 0, 1],
j=[1, 2, 3, 2],
k=[2, 3, 1, 3],
name="y",
showscale=true
))


### Mesh Cube

using PlotlyJS

plot(mesh3d(
# 8 vertices of a cube
x=[0, 0, 1, 1, 0, 0, 1, 1],
y=[0, 1, 1, 0, 0, 1, 1, 0],
z=[0, 0, 0, 0, 1, 1, 1, 1],
colorbar_title="z",
colorscale=[[0, "gold"],
[0.5, "mediumturquoise"],
[1, "magenta"]],
# Intensity of each vertex, which will be interpolated and color-coded
intensity = 0:8,
# i, j and k give the vertices of triangles
i = [7, 0, 0, 0, 4, 4, 6, 6, 4, 0, 3, 2],
j = [3, 4, 1, 2, 5, 6, 5, 2, 0, 1, 6, 3],
k = [0, 7, 2, 3, 6, 7, 1, 1, 5, 5, 7, 6],
name="y",
showscale=true
))


### Intensity values defined on vertices or cells

The intensitymode attribute of mesh3d can be set to vertex (default mode, in which case intensity values are interpolated between values defined on vertices), or to cell (value of the whole cell, no interpolation). Note that the intensity parameter should have the same length as the number of vertices or cells, depending on the intensitymode.

Whereas the previous example used the default intensitymode='vertex', we plot here the same mesh with intensitymode='cell'.

using PlotlyJS

plot(mesh3d(
# 8 vertices of a cube
x=[0, 0, 1, 1, 0, 0, 1, 1],
y=[0, 1, 1, 0, 0, 1, 1, 0],
z=[0, 0, 0, 0, 1, 1, 1, 1],
colorbar_title="z",
colorscale=[[0, "gold"],
[0.5, "mediumturquoise"],
[1, "magenta"]],
# Intensity of each vertex, which will be interpolated and color-coded
intensity = 0:12,
intensitymode="cell",
# i, j and k give the vertices of triangles
i = [7, 0, 0, 0, 4, 4, 6, 6, 4, 0, 3, 2],
j = [3, 4, 1, 2, 5, 6, 5, 2, 0, 1, 6, 3],
k = [0, 7, 2, 3, 6, 7, 1, 1, 5, 5, 7, 6],
name="y",
showscale=true
))