Singulersum is a prototype 3D graphics rendering engine. It aims to be able to visualize STL files, freely defined 3D functions and other objects (like points, lines, planes, spheres, polygons) in a 3D environment. It's a pure python software pipeline for 3D and 2D graphics to do what normally a GPU would do.

First some important notes:

• this software is SLOW! It runs on the CPU (not a GPU) and is single threaded! Performance was NOT intended.
• this software is BUGGY and incomplete. It's a prototype!
• this software is not meant for production use

If you're looking for a 3D computer graphics software to create or visualize projects, I assume that you're better suited with something like Blender, GLC Player, Meshlab, Viewstl or something alike. For mathematical illustration you may want to look at Geogebra

Why did I create Singulersum

• it is and was fun to create. And a challenge!
• a graphics card and it's libraries offer all of that functionality out of the box. How ever: I wanted to see HOW it actually works, doing it all myself.
• it's cool to see the achievement
• main aim is to share and/or create interest. You can do something if you like to! Anything you want!
• in case you're interested in computer graphics or 3D graphics or projections. Take a look at the source code. But don't take it as ground truth! I'm not a graphics expert. I was just curious if I can do it with as little help as possible...

Some examples, videos and pictures:

/scripts/singulersum_gui.py, a Tkinter based GUI for Singulersum 3D rendering engine

Visualize binary and textual STL files (currently without color support):

Creation of animation videos using yaml configuration files (/scripts/singulersum_gui.py, using /yaml/sphericon_ascii_stl.yaml)

here some videos, created using Singulersum (/scripts/singulersum_video.py)

video of the function z=sin(x)+sin(y):

Creating graphical representations of mathematical functions

math calculus behind this software (one out of 16 pages):

Feature-Set of Singulersum:

• 3D objects that may contain other objects (recursive structure)
• z-Buffering
• different cameras (all with their own position and view angles in space)
• camera and object animation
  • either through mouse in GUI or
  • configured in yaml
• light sources (not yet supported)
• luminescence (by comparing normal vector of polygons with view vector of camera)
• object browser (not yet supported) to change properties of objects

My name is Philipp Hasenfratz (philipp.hasenfratz at protonmail.com). I'm a software developer based in Switzerland. This project was a fun side project of mine. I was wondering if I still had the mathematical skills to create and develop a 3D rendering engine prototype without any external tools, libraries, help or a GPU. After 20 years out of school I was a bit rusty doing the math (vector geometry, matrix calculation, dot and vector product (luminescence calculus), linear equation systems, linear algebra), but I got it back again with some help of wikipedia of course. But the main objective was to develop the whole math myself and for most part I did exactly that. So the math behind Singulersum (see ) is most probably not the same as in commonly used 3D software...

After two weeks and roughly 200 hours of work the prototype was ready and worked (more or less)...