# Trisurf Plots in Python

How to make tri-surf plots in Python with Plotly. Trisurfs are formed by replacing the boundaries of a compact surface by touching triangles.

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Trisurf plots can be made using a figure factory as detailed in this page.

#### Torus¶

In [1]:
import plotly.figure_factory as ff

import numpy as np
from scipy.spatial import Delaunay

u = np.linspace(0, 2*np.pi, 20)
v = np.linspace(0, 2*np.pi, 20)
u,v = np.meshgrid(u,v)
u = u.flatten()
v = v.flatten()

x = (3 + (np.cos(v)))*np.cos(u)
y = (3 + (np.cos(v)))*np.sin(u)
z = np.sin(v)

points2D = np.vstack([u,v]).T
tri = Delaunay(points2D)
simplices = tri.simplices

fig = ff.create_trisurf(x=x, y=y, z=z,
simplices=simplices,
title="Torus", aspectratio=dict(x=1, y=1, z=0.3))
fig.show()


#### Mobius Band¶

In [2]:
import plotly.figure_factory as ff

import numpy as np
from scipy.spatial import Delaunay

u = np.linspace(0, 2*np.pi, 24)
v = np.linspace(-1, 1, 8)
u,v = np.meshgrid(u,v)
u = u.flatten()
v = v.flatten()

tp = 1 + 0.5*v*np.cos(u/2.)
x = tp*np.cos(u)
y = tp*np.sin(u)
z = 0.5*v*np.sin(u/2.)

points2D = np.vstack([u,v]).T
tri = Delaunay(points2D)
simplices = tri.simplices

fig = ff.create_trisurf(x=x, y=y, z=z,
colormap="Portland",
simplices=simplices,
title="Mobius Band")
fig.show()


#### Boy's Surface¶

In [3]:
import plotly.figure_factory as ff

import numpy as np
from scipy.spatial import Delaunay

u=np.linspace(-np.pi/2, np.pi/2, 60)
v=np.linspace(0, np.pi, 60)
u,v=np.meshgrid(u,v)
u=u.flatten()
v=v.flatten()

x = (np.sqrt(2)*(np.cos(v)*np.cos(v))*np.cos(2*u) + np.cos(u)*np.sin(2*v))/(2 - np.sqrt(2)*np.sin(3*u)*np.sin(2*v))
y = (np.sqrt(2)*(np.cos(v)*np.cos(v))*np.sin(2*u) - np.sin(u)*np.sin(2*v))/(2 - np.sqrt(2)*np.sin(3*u)*np.sin(2*v))
z = (3*(np.cos(v)*np.cos(v)))/(2 - np.sqrt(2)*np.sin(3*u)*np.sin(2*v))

points2D = np.vstack([u, v]).T
tri = Delaunay(points2D)
simplices = tri.simplices

fig = ff.create_trisurf(x=x, y=y, z=z,
colormap=['rgb(50, 0, 75)', 'rgb(200, 0, 200)', '#c8dcc8'],
show_colorbar=True,
simplices=simplices,
title="Boy's Surface")
fig.show()