Visualization in notebooks

It is possible to visualize pyddg objects in jupyter notebooks. For this we use the python package k3d.

Objects in this package can be displayed as interactive widgets in a jupyter notebook or in even in a static html page.

On the top right of the widgets there is a k3d panel that allows to take screenshots, show the widget in fullscreen or modify objects.

import ddg
import numpy as np

Converting pyddg objects to drawable objects

Default conversion

quadric = ddg.geometry.Quadric(np.diag((1, 1, -1, -1)))

To visualize this quadric as a smooth surface, we first need to convert it to an instance of k3d.objects.Drawable.

hyperboloid = ddg.jupyter.convert(quadric)
type(hyperboloid)

k3d.objects.Group

k3d.objects.Drawable objects can be previewed direclty when outputed from a jupyter cell:

hyperboloid

Special conversions

To convert to a k3d.objects.Drawable containing only the edges of an object, run:

hyperboloid_edges = ddg.jupyter.edges(quadric)
hyperboloid_edges

To get only the points of an object, run:

hyperboloid_points = ddg.jupyter.vertices(quadric)
hyperboloid_points

Visualizing a 3D scene

To create a 3D scene from k3d.objects.Drawable objects, one must add them to a k3d.plot.Plot. We provide a utility function to render them in a clean and higher quality render setting. One can combine objects to create more complex scenes:

ddg.jupyter.show_3d(hyperboloid, hyperboloid_points, hyperboloid_edges)

Visualizing a 2D scene

To create a 2D scene, we provide a similar function:

I = (-1, 0, 1)
conics = [ddg.geometry.Quadric(np.diag((i, j, k))) for i in I for j in I for k in I]
kobjs = [ddg.jupyter.convert(c) for c in conics]
ddg.jupyter.show_2d(*kobjs)

Compared to 3D scenes, 2D scenes just have flat colors and the camera looks from the top by default.

Interactive visualization

One can make interactive visualizations using widgets, like the ones from ipywigets. Let’s make an empty plot for the visualization:

pencil = ddg.geometry.Pencil(quadric, ddg.geometry.Quadric(np.diag((1, 1, 1, -1))))
plot = ddg.jupyter.show_3d()
plot

Now let’s create a slider widgets and define a callback function that places a quadric in the scene for each value of the slider.

from ipywidgets import FloatSlider, interact


@interact(i=FloatSlider(value=0, min=-2, max=2))
def callback(i):
    global plot
    ddg.jupyter.clear_plot(plot)
    quadric = pencil.quadric(i)
    plot += ddg.jupyter.convert(quadric)

(The slider will take effect in the jupyter notebook, but not here in the docs.)