Mathematics

There is surprising little information available on hex-coordinates, despite how many games use hex grids. In this article I will explain some of the math so that you can do basic geometry in a hex grid, and design more elegant algorithms for your hex-grid games.

Geometry with Hex Coordinates

31 Aug, 2013 in Mathematics tagged hex coordinate / hex grid / vector math by Herman Tulleken

This tutorial provides some algorithms useful for working with Bézier curves: determining the length of a piece of curve; interpolating a set of points with a Bézier path; and reducing a large point set to a smooth Bézier curve.

Bézier Path Algorithms

23 Jun, 2011 in Mathematics / Programming tagged algorithm / bezier curve / bezier path / curve length / interpolation / sampling by Herman Tulleken

A Bézier curve is a type of curve that is easy to use, and can describe many shapes. This guide gives instructions for implementing algorithms for using Bézier curves in your games.

Bézier Curves for your Games: A Tutorial

5 Apr, 2011 in Development / Mathematics / Programming tagged algorithm / bezier curve / bezier path / path / racing line / vector mathematics by Herman Tulleken

This tutorial covers basic algorithms with vectors.

Basic Vector Recipes

25 Aug, 2009 in Development / Mathematics tagged algorithm / geometry / math / tutorial / vectors by Herman Tulleken

Geometry plays a central role in game programming, underlying not only graphics, but also physics and spatial AI. A lot has happened since geometry was first formalised by the Greeks more than two thousand years ago, most notably the invention of coordinates and vectors. These inventions are indispensible for doing […]

Vector Fundamentals

12 Aug, 2009 in Development / Mathematics tagged explanation / math / vector operation / vectors by Herman Tulleken

This article originally appeared in Dev.Mag Issue 29, released in February 2009. Last month we covered some of the very basic ways of testing whether object A hits object B. But, while the techniques we covered could quite likely take you very far, you’ll inevitably encounter a time when they […]

Basic Collision Detection in 2D – Part 2

17 Apr, 2009 in Development / Mathematics / Programming tagged collision detection / explanation / intersection / issue29 / math / tutorial by Claudio de Sa

This article originally appeared in Dev.Mag Issue 28, released in January 2009. Almost every video game needs to respond to objects touching each other in some sense, a practice commonly known as collision detection. Whether it’s simply to prevent the player character from walking through the walls of your maze […]

Basic Collision Detection in 2D – Part 1

13 Apr, 2009 in Development / Mathematics / Programming tagged collision detection / explanation / issue28 / math / tutorial by Claudio de Sa

This article originally appeared in Dev.Mag Issue 16, released in August 2007 Welcome back, fellow coders! Prepare yourselves for the final, bumper episode of the Trig Trilogy, where I cover a whole lot of awesome trig techniques for your game-making pleasure. We’ve got a lot to cover, so let’s jump […]

Trigonometry: Part 3

24 Mar, 2009 in Development / Mathematics tagged explanation / issue16 / math / trigonometry by Gazza_N

This article originally appeared in Dev.Mag Issue 12, released in July 2007 Previously… Last issue we covered the core principles of trigonometry and learned how to use these to calculate unknown sides in a triangle. Well, I hope you’re rested and ready Commander, because we’ll be jumping straight back in […]

Trigonometry: Part 2

24 Mar, 2009 in Development / Mathematics by Gazza_N

This article originally appeared in Dev.Mag Issue 14, released in June 2007. Trigonometry. The mere mention of it strikes terror into the minds of bewildered high school students. Confusing ratios, bizarre diagrams, trying to find the sine of the cosine of the tangent of theta – many people struggle to […]

Trigonometry: Part 1

24 Mar, 2009 in Development / Mathematics tagged explanation / issue14 / math / trigonometry by Gazza_N

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