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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Meshes / Surfaces
Meshes (or surfaces) in ipyvolume consist of triangles, and are defined by their coordinate (vertices) and faces/triangles, which refer to three vertices.
Step1:  Triangle meshes
Lets first construct a 'solid', a tetrahedron, consisting out of 4 vertices, and 4 faces (triangles) using plot_trisurf
Step2:  Surfaces
To draw parametric surfaces, which go from $\Bbb{R}^2 \rightarrow \Bbb{R}^3$, it's convenient to use plot_surface, which takes 2d numpy arrays as arguments, assuming they form a regular grid (meaning you do not need to provide the triangles, since they can be inferred from the shape of the arrays). Note that plot_wireframe has a similar api, as does plot_mesh which can do both the surface and wireframe at the same time.
Step3:  Colors
Vertices can take colors as well, as the example below (adapted from matplotlib) shows.
Step4:  Texture mapping
Texture mapping can be done by providing a PIL image, and UV coordiante (texture coordinates, between 0 and 1). Note that like almost anything in ipyvolume, these u & v coordinates can be animated, as well as the textures.
Step5:  We now make a small movie / animated gif of 30 frames.
Step6:  And play that movie on a square
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Python Code:
import ipyvolume as ipv
import numpy as np
Explanation: Meshes / Surfaces
Meshes (or surfaces) in ipyvolume consist of triangles, and are defined by their coordinate (vertices) and faces/triangles, which refer to three vertices.
End of explanation
s = 1/2**0.5
# 4 vertices for the tetrahedron
x = np.array([1.,  -1, 0,  0])
y = np.array([0,   0, 1., -1])
z = np.array([-s, -s, s,  s])
# and 4 surfaces (triangles), where the number refer to the vertex index
triangles = [(0, 1, 2), (0, 1, 3), (0, 2, 3), (1,3,2)]
ipv.figure()
# we draw the tetrahedron
mesh = ipv.plot_trisurf(x, y, z, triangles=triangles, color='orange')
# and also mark the vertices
ipv.scatter(x, y, z, marker='sphere', color='blue')
ipv.xyzlim(-2, 2)
ipv.show()
Explanation: Triangle meshes
Lets first construct a 'solid', a tetrahedron, consisting out of 4 vertices, and 4 faces (triangles) using plot_trisurf
End of explanation
# f(u, v) -> (u, v, u*v**2)
a = np.arange(-5, 5)
U, V = np.meshgrid(a, a)
X = U
Y = V
Z = X*Y**2
ipv.figure()
ipv.plot_surface(X, Z, Y, color="orange")
ipv.plot_wireframe(X, Z, Y, color="red")
ipv.show()
Explanation: Surfaces
To draw parametric surfaces, which go from $\Bbb{R}^2 \rightarrow \Bbb{R}^3$, it's convenient to use plot_surface, which takes 2d numpy arrays as arguments, assuming they form a regular grid (meaning you do not need to provide the triangles, since they can be inferred from the shape of the arrays). Note that plot_wireframe has a similar api, as does plot_mesh which can do both the surface and wireframe at the same time.
End of explanation
X = np.arange(-5, 5, 0.25*1)
Y = np.arange(-5, 5, 0.25*1)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = np.sin(R)
from matplotlib import cm
colormap = cm.coolwarm
znorm = Z - Z.min()
znorm /= znorm.ptp()
znorm.min(), znorm.max()
color = colormap(znorm)
ipv.figure()
mesh = ipv.plot_surface(X, Z, Y, color=color[...,:3])
ipv.show()
Explanation: Colors
Vertices can take colors as well, as the example below (adapted from matplotlib) shows.
End of explanation
# import PIL.Image
# image = PIL.Image.open('data/jupyter.png')
# example how put a png as texture
import PIL.Image
import requests
import io
url = 'https://vaex.io/img/logos/spiral-small.png'
r = requests.get(url, stream=True)
f = io.BytesIO(r.content)
image = PIL.Image.open(f)
import ipyvolume as ipv
import numpy as np
fig = ipv.figure()
ipv.style.use('dark')
# we create a sequence of 8 u v coordinates so that the texture moves across the surface.
u = np.array([X/5 +np.sin(k/8*np.pi)*4. for k in range(8)])
v = np.array([-Y/5*(1-k/7.) + Z*(k/7.) for k in range(8)])
mesh = ipv.plot_mesh(X, Z, Y, u=u, v=v, texture=image, wireframe=False)
ipv.animation_control(mesh, interval=800, sequence_length=8)
ipv.show()
Explanation: Texture mapping
Texture mapping can be done by providing a PIL image, and UV coordiante (texture coordinates, between 0 and 1). Note that like almost anything in ipyvolume, these u & v coordinates can be animated, as well as the textures.
End of explanation
# this doesn't work anymore with modern ipykernel
# frames = 30
# ipv.movie('movie.gif', frames=frames)
Explanation: We now make a small movie / animated gif of 30 frames.
End of explanation
# so we also need to skip this
# ipv.figure()
# x = np.array([-1.,  1,  1,  -1])
# y = np.array([-1,  -1, 1., 1])
# z = np.array([0., 0, 0., 0])
# u = x / 2 + 0.5
# v = y / 2 + 0.5
# # square
# triangles = [(0, 1, 2), (0, 2, 3)]
# m = ipv.plot_trisurf(x, y, z, triangles=triangles, u=u, v=v, texture=PIL.Image.open('movie.gif'))
# ipv.animation_control(m, sequence_length=frames)
# ipv.show()
Explanation: And play that movie on a square
End of explanation
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