Category Archives: Mathematics

Implementing Multidimensional Arrays in JavaScript

The past few months I’ve been working to move more of my work into JavaScript, and in particular the node.js ecosystem.  I hope that by doing this I will be able to create better demos and applications that are easier … Continue reading

Posted in Mathematics, Programming | 19 Comments

Comparing Sequences Without Sorting

This is a post about a silly (and mostly pointless) optimization.  To motivate this, consider the following problem which you see all the time in mesh processing: Given a collection of triangles represented as ordered tuples of indices, find all … Continue reading

Posted in Mathematics, Programming | 24 Comments

Shapes and Coordinates

In a previous post, I talked a bit about solid modeling and discussed at a fairly high level what a solid object is.  This time I’m going to talk in generalities about how one actually represent shapes in practice.  My … Continue reading

Posted in Mathematics, Shape Modeling | 1 Comment

Conway’s Game of Life for Curved Surfaces (Part 2)

(This is the sequel to the following post on SmoothLife.  For background information go there, or read Stephan Rafler’s paper on SmoothLife here.) Last time, we talked about an interesting generalization of Conway’s Game of Life and walked through the … Continue reading

Posted in Game of Life, Mathematics, Programming | Tagged , , , , , , , | 7 Comments

Conway’s Game of Life for Curved Surfaces (Part 1)

Conway’s Game of Life is one of the most popular and iconic cellular automata.  It is so famous that googling it loads up a working simulation right in your browser!  The rules for the Game of Life (GoL) can be stated … Continue reading

Posted in Game of Life, Mathematics, Programming | Tagged , , | 12 Comments

Turning 8-Bit Sprites into Printable 3D Models

Continuing in the recreational spirit of this blog, this week I want to write about something purely fun.  In particular, I’m going to tell you how to convert retro 16 x 16 sprites into 3D miniatures: This project was motivated … Continue reading

Posted in Mathematics, Programming, Voxels | 34 Comments

What is a solid?

In this post, I am going to go into a bit of a mathematical digression about the fundamentals of solid modeling.  In a nutshell, solid modeling is the study of digital representations of physical shapes.  This was a hot topic … Continue reading

Posted in Mathematics, Shape Modeling | Tagged , | 1 Comment