Plotting a 3D trefoil knot

In this recipe, we will see how to plot a 3D trefoil knot. A trefoil knot is a closed curve with three crossings. In this recipe, we will draw not just a curve, but a solid 3D curve. This is beyond the plotly capabilities, and we will implement this functionality using a trick.

How to do it...

In this recipe, we will:

1. Generate all the points of the knot using parametric equations.

2. Organize the data as required by plotly.

3. Define a clean layout.

4. Invoke plotly to draw the chart:

   import numpy as np
   import plotly.plotly as py
   from plotly.graph_objs import Scatter3d, Data, Layout
   from plotly.graph_objs import Figure, Line, Margin, Marker
   
   from numpy import linspace,pi,cos,sin
   phi = linspace(0,2*pi,250)
   x = sin(phi)+2*sin(2*phi)
   y = cos(phi)-2*cos(2*phi)
   z = -sin(3*phi)
   
   traces = list()
   colors = ['rgb(%d,50,210)' % c for c in np.abs(z / max(z)) * 255]
   for i in linspace(-np.pi,np.pi,50):
       trace = Scatter3d(x=x+np.cos(i)*.5, y=y+np.sin(i)*.5, z=z,
                          mode...