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- Turning 8-Bit Sprites into Printable 3D Models
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# Category Archives: Mathematics

## Geometry without geometric algebra

When I was younger I invested a lot of time into studying geometric algebra. Geometric algebra is a system where you can add, subtract and multiply oriented linear subspaces like lines and hyperplanes (cf. Grassmanian). These things are pretty important if … Continue reading

Posted in Geometry, Mathematics, Rambling
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## A level of detail method for blocky voxels

Large voxel terrains may contain millions of polygons. Rendering such terrains at a uniform scale is both inefficient and can lead to aliasing of distant objects. As a result, many game engines choose to implement some form of level of … Continue reading

Posted in Geometry, Programming, Voxels
2 Comments

## Collision detection (part 3): Benchmarks

Previously in this series we covered the basics of collision detection and discussed some different approaches to finding intersections in sets of boxes: Collision detection (part 1): Overview Collision detection (part 2): Box intersection Today, we’ll see how well this … Continue reading

Posted in Collision detection, Geometry, Mathematics, Programming
10 Comments

## Collision detection (part 2): Box intersection

Last time, we discussed collision detection in general and surveyed some techniques for narrow phase collision detection. In this article we will go into more detail on broad phase collision detection for closed axis-aligned boxes. This was a big problem in the 1970’s … Continue reading

Posted in Collision detection, Geometry, Mathematics, Programming
8 Comments

## Collision detection (part 1): Overview

Collision, or intersection, detection is an important geometric operation with a large number of applications in graphics, CAD and virtual reality including: map overlay operations, constructive solid geometry, physics simulation, and label placement. It is common to make a distinction … Continue reading

Posted in Collision detection, Geometry, Mathematics, Programming, Video games
2 Comments

## Relations are hard to model in category theory

WARNING: This is a somewhat rambling post about category theory. If half-baked mathematical philosophy is not your thing, please consider navigating away right now. Anyway, the thing that I want to write about today is the difference between category theory … Continue reading

Posted in Mathematics, Rambling
2 Comments

## ndarray modules

In the last two posts I introduced ndarrays, and explained the rationale and implementation details of the library. In this post I am going to show a few of the libraries that I have written using ndarrays. All of this … Continue reading

Posted in Mathematics, Programming
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## 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