My PyVista artworks

I like the Python library PyVista very much. In this blog post I show a sample of the animations I realized with this library.

Github repositories

PyVistaMiscellanous contains numerous pictures and animations.

A 3-30 duoprism, realized with the method given here.

Some Hopf tori in orbit, forming like a Steiner chain.

Some connected linked cyclides, looking like a flower.

The orbit of the modular tessellation, with spheres instead of circles.

A bouquet of roses. It’s surprising that one can obtain such a realistic rose with parametric equations. Here is an interactive three.js version.

The metamorphosis of a torus to a solid Möbius strip, with an electric texture.

A metamorphosis of three tori to a kind of cage. Credit to ICN5D, a member of the Hi.gher Space forum.

The PyApollony repository contains three Apollonian fractals.

The PyCyclides repository hosts a package to draw some linked cyclides. It contains a PyVista application to play with them:

PyPlaneGeometry is a Python version of my R package PlaneGeometry. I call this animation the Malfatti-Apollonian gasket:

And here is an elliptical nested Steiner chain:

PySteiner is a package to draw nested Steiner chains. Here is one, with its enveloping cyclides:

PyTorusThreePoints is a package allowing to draw a torus whose equator passes through three points. Actually you don’t need that with PyVista: it is easy to get a circle passing through three points, and with PyVista you can easily make it tubular.

PyHyperbolic3D is a package allowing to draw hyperbolic triangles and tubular hyperbolic segments, with the help of Ungar’s theory presented in this post.

There’s also PyMobiusHyperbolic which provides functions to draw hyperbolic stuff, also based on Ungar’s theory, but it deals with the Poincaré model, whereas PyHyperbolic3D deals with the hyperboloid model. In fact these two packages are not restricted to 3D graphics, 2D pictures are possible too, but do not involve PyVista:

PyPlaneGeometry (see above) has been used to draw this hyperbolic tessellation.

Gists

I also use some gists to store my animations. Here are twenty Hopf tori:

In this gist you can find a rotating Hopf torus with an electric texture:

A compound of five hyperbolic tetrahedra, made with the help of Ungar’s theory:

Here there is an animation of some slices of the tiger:

In this gist there is a pretty stereographic duoprism:

This gist shows an animation made from the runcinated tesseract, a 4D polytope. It is stereographically projected in 3D but I kept only the tetrahedrals cells, and it is in rotation in the 4D space.

I hope you enjoyed the presentation.