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Iso Surface in Python

How to make Iso Surface in Python with Plotly.

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Plotly Isosurfaces Defined as Trisurfs

A surface, F(x,y,z) = c is discretized by a triangular mesh, extracted by the Marching cubes algorithm from a volume given as a (M, N, P) array of doubles.
The scikit image function, measure.marching_cubes(F, c) returns the vertices and simplices of the triangulated surface.

First, define a grid within the parallelepiped [-2,2] x [-2,2] x [-2,2], and give the function F, defining a surface of equation F(x,y,z) = 0:

In [1]:
import plotly.plotly as py
from plotly.graph_objs import *
from plotly.tools import FigureFactory as FF

import numpy as np
from skimage import measure

X,Y,Z = np.mgrid[-2:2:40j, -2:2:40j, -2:2:40j]
surf_eq = X**4 + Y**4 + Z**4 - (X**2+Y**2+Z**2)**2 + 3*(X**2+Y**2+Z**2) - 3   

Triangulate the Given Surface:

In [2]:
vertices, simplices = measure.marching_cubes(surf_eq, 0)
x,y,z = zip(*vertices)  

Color According to a colormap and Plot:

In [3]:
colormap=['rgb(255,105,180)','rgb(255,255,51)','rgb(0,191,255)']
fig = FF.create_trisurf(x=x,
                        y=y, 
                        z=z, 
                        plot_edges=False,
                        colormap=colormap,
                        simplices=simplices,
                        title="Isosurface")
py.iplot(fig)
Out[3]:

Reference

In [4]:
help(FF.create_trisurf)
Help on function create_trisurf in module plotly.tools:

create_trisurf(x, y, z, simplices, colormap=None, show_colorbar=True, color_func=None, title='Trisurf Plot', plot_edges=True, showbackground=True, backgroundcolor='rgb(230, 230, 230)', gridcolor='rgb(255, 255, 255)', zerolinecolor='rgb(255, 255, 255)', edges_color='rgb(50, 50, 50)', height=800, width=800, aspectratio={'x': 1, 'y': 1, 'z': 1})
    Returns figure for a triangulated surface plot
    
    :param (array) x: data values of x in a 1D array
    :param (array) y: data values of y in a 1D array
    :param (array) z: data values of z in a 1D array
    :param (array) simplices: an array of shape (ntri, 3) where ntri is
        the number of triangles in the triangularization. Each row of the
        array contains the indicies of the verticies of each triangle
    :param (str|tuple|list) colormap: either a plotly scale name, an rgb
        or hex color, a color tuple or a list of colors. An rgb color is
        of the form 'rgb(x, y, z)' where x, y, z belong to the interval
        [0, 255] and a color tuple is a tuple of the form (a, b, c) where
        a, b and c belong to [0, 1]. If colormap is a list, it must
        contain the valid color types aforementioned as its members
    :param (bool) show_colorbar: determines if colorbar is visible
    :param (function|list) color_func: The parameter that determines the
        coloring of the surface. Takes either a function with 3 arguments
        x, y, z or a list/array of color values the same length as
        simplices. If None, coloring will only depend on the z axis
    :param (str) title: title of the plot
    :param (bool) plot_edges: determines if the triangles on the trisurf
        are visible
    :param (bool) showbackground: makes background in plot visible
    :param (str) backgroundcolor: color of background. Takes a string of
        the form 'rgb(x,y,z)' x,y,z are between 0 and 255 inclusive
    :param (str) gridcolor: color of the gridlines besides the axes. Takes
        a string of the form 'rgb(x,y,z)' x,y,z are between 0 and 255
        inclusive
    :param (str) zerolinecolor: color of the axes. Takes a string of the
        form 'rgb(x,y,z)' x,y,z are between 0 and 255 inclusive
    :param (str) edges_color: color of the edges, if plot_edges is True
    :param (int|float) height: the height of the plot (in pixels)
    :param (int|float) width: the width of the plot (in pixels)
    :param (dict) aspectratio: a dictionary of the aspect ratio values for
        the x, y and z axes. 'x', 'y' and 'z' take (int|float) values
    
    Example 1: Sphere
    ```
    # Necessary Imports for Trisurf
    import numpy as np
    from scipy.spatial import Delaunay
    
    import plotly.plotly as py
    from plotly.tools import FigureFactory as FF
    from plotly.graph_objs import graph_objs
    
    # Make data for plot
    u = np.linspace(0, 2*np.pi, 20)
    v = np.linspace(0, np.pi, 20)
    u,v = np.meshgrid(u,v)
    u = u.flatten()
    v = v.flatten()
    
    x = np.sin(v)*np.cos(u)
    y = np.sin(v)*np.sin(u)
    z = np.cos(v)
    
    points2D = np.vstack([u,v]).T
    tri = Delaunay(points2D)
    simplices = tri.simplices
    
    # Create a figure
    fig1 = FF.create_trisurf(x=x, y=y, z=z,
                             colormap="Blues",
                             simplices=simplices)
    # Plot the data
    py.iplot(fig1, filename='trisurf-plot-sphere')
    ```
    
    Example 2: Torus
    ```
    # Necessary Imports for Trisurf
    import numpy as np
    from scipy.spatial import Delaunay
    
    import plotly.plotly as py
    from plotly.tools import FigureFactory as FF
    from plotly.graph_objs import graph_objs
    
    # Make data for plot
    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
    
    # Create a figure
    fig1 = FF.create_trisurf(x=x, y=y, z=z,
                             colormap="Greys",
                             simplices=simplices)
    # Plot the data
    py.iplot(fig1, filename='trisurf-plot-torus')
    ```
    
    Example 3: Mobius Band
    ```
    # Necessary Imports for Trisurf
    import numpy as np
    from scipy.spatial import Delaunay
    
    import plotly.plotly as py
    from plotly.tools import FigureFactory as FF
    from plotly.graph_objs import graph_objs
    
    # Make data for plot
    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
    
    # Create a figure
    fig1 = FF.create_trisurf(x=x, y=y, z=z,
                             colormap=[(0.2, 0.4, 0.6), (1, 1, 1)],
                             simplices=simplices)
    # Plot the data
    py.iplot(fig1, filename='trisurf-plot-mobius-band')
    ```
    
    Example 4: Using a Custom Colormap Function with Light Cone
    ```
    # Necessary Imports for Trisurf
    import numpy as np
    from scipy.spatial import Delaunay
    
    import plotly.plotly as py
    from plotly.tools import FigureFactory as FF
    from plotly.graph_objs import graph_objs
    
    # Make data for plot
    u=np.linspace(-np.pi, np.pi, 30)
    v=np.linspace(-np.pi, np.pi, 30)
    u,v=np.meshgrid(u,v)
    u=u.flatten()
    v=v.flatten()
    
    x = u
    y = u*np.cos(v)
    z = u*np.sin(v)
    
    points2D = np.vstack([u,v]).T
    tri = Delaunay(points2D)
    simplices = tri.simplices
    
    # Define distance function
    def dist_origin(x, y, z):
        return np.sqrt((1.0 * x)**2 + (1.0 * y)**2 + (1.0 * z)**2)
    
    # Create a figure
    fig1 = FF.create_trisurf(x=x, y=y, z=z,
                             colormap=['#604d9e',
                                       'rgb(50, 150, 255)',
                                       (0.2, 0.2, 0.8)],
                             simplices=simplices,
                             color_func=dist_origin)
    # Plot the data
    py.iplot(fig1, filename='trisurf-plot-custom-coloring')
    ```
    
    Example 5: Enter color_func as a list of colors
    ```
    # Necessary Imports for Trisurf
    import numpy as np
    from scipy.spatial import Delaunay
    import random
    
    import plotly.plotly as py
    from plotly.tools import FigureFactory as FF
    from plotly.graph_objs import graph_objs
    
    # Make data for plot
    u=np.linspace(-np.pi, np.pi, 30)
    v=np.linspace(-np.pi, np.pi, 30)
    u,v=np.meshgrid(u,v)
    u=u.flatten()
    v=v.flatten()
    
    x = u
    y = u*np.cos(v)
    z = u*np.sin(v)
    
    points2D = np.vstack([u,v]).T
    tri = Delaunay(points2D)
    simplices = tri.simplices
    
    
    colors = []
    color_choices = ['rgb(0, 0, 0)', '#6c4774', '#d6c7dd']
    
    for index in range(len(simplices)):
        colors.append(random.choice(color_choices))
    
    fig = FF.create_trisurf(
        x, y, z, simplices,
        color_func=colors,
        show_colorbar=True,
        edges_color='rgb(2, 85, 180)',
        title=' Modern Art'
    )
    
    py.iplot(fig, filename="trisurf-plot-modern-art")
    ```

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