Welcome to everyone who has come here from Rudy Rucker’s blog, from Vimeo, or from my LKL talk. I have attempted here to give a a bit more explanation of my recent 4D rotation animations, in as non-technical a way as possible.


OK. here it is, The applet for inversion with respect to a sphere as a Rhino4 plugin available for free download from:

Any questions or comments please let me know. I’d love to be able to post images or links to show any ways anybody finds of using it.

Well I’m now happy that this script is ready. In the morning I’m going to wrap it up in a plugin and post it on the Rhino developer site. Here are some demonstrations of what it does:

Inside the Outside of a horse

Inverted Stanford Bunny

Inverted Stanford BunnyInverted Stanford Bunny

Inverted Head
Inverted Head Inverted Head

and here are some videos, just to make clear that these are not just 2D transformations

Each one of the images and videos above is produced by a single application of my transformation script – the only variable being the position of the object relative to the inversion sphere.

There are so many incredibly serious and tasteful sites about Rhinoscripting, all about making gently undulating arrayed surfaces and stuff like that – Well now Im here to give you the really useful stuff you need- like tools for turning horses inside out!

I wrote my inversion script mainly for 3D objects , but I realised afterwards it had the nice byproduct of being able to invert bitmaps :


Notice how the globe remains circular – circles always map to circles

invertedroom.jpgI have written a program for Rhino which performs the mathematical transformation of ‘inversion with respect to a sphere’. This transformation has many beautiful properties and reveals some surprising symmetries. It also relates in a deep and beautiful way to Einstein’s theory of Relativity.



Have you ever wondered why perspective drawing using vanishing points works ?

What are these mysterious points that all lines point towards ?, Where are they ?

Well I can do better than just tell you where they are – I can show you what it looks like from there ! (more…)