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### Top Posts & Pages

- Turning 8-Bit Sprites into Printable 3D Models
- An Analysis of Minecraft-like Engines
- Ambient occlusion for Minecraft-like worlds
- Implementing Multidimensional Arrays in JavaScript
- Texture atlases, wrapping and mip mapping
- Meshing in a Minecraft Game
- Conway's Game of Life for Curved Surfaces (Part 1)
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- Comparing Sequences Without Sorting
- Smooth Voxel Terrain (Part 1)

# Category Archives: Mathematics

## Cache oblivious array operations

I must confess that secretly the article I wrote last time (in which I introduced ndarrays) was just a pretext to introduce the stuff that I am going to write about today: which is the cwise library for array operations … Continue reading

Posted in Mathematics, Programming
3 Comments

## 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

## 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 game of life, smooth life, surfaces
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