The Mathematics of Thin-Film Interference

This post continues our journey through the Mathematical foundations of iridescence. This time, we will discuss a new way in which material can split light: thin-film interference. This is how bubbles (and car paint) get their unique reflections.

You can find the complete series here:

A link to download the Unity project used in this series is also provided at the end of the page.

Continue reading

The Extended Kalman Filter

This is the third part of the series dedicated to one of the most popular sensor de-noising technique: Kalman filters. This article will explain how to model non-linear processes to improve the filter performance, something known as the Extended Kalman Filter.

You can read all the tutorials in this online course here:

Continue reading

Modelling Kalman Filters

This is the third part of the series dedicated to one of the most popular sensor de-noising technique: Kalman filters. This article will explain how to model processes to improve the filter performance.

You can read all the tutorials in this online course here:

Continue reading

The Mathematics of the Kalman Filter

This is the second part of the series dedicated to one of the most popular sensor de-noising technique: Kalman filters. This article will introduce the Mathematics of the Kalman Filter, with a special attention to a quantity that makes it all possible: the Kalman gain.

You can read all the articles in this online course here:

Continue reading

Colour Curve Correction

This is the third and final part of the tutorial dedicated to one of the most used Mathematical tools in Game Development: linear interpolation! In this part, we will explore how to use it to correct colour curves.

You can find a link to download the C# scripts and the Unity package used at the end of this post.

Continue reading

Piecewise Interpolation

This is the second part of the tutorial dedicated to one of the most used Mathematical tools in Game Development: linear interpolation! In this part, we will explore how to extend the concept of linear interpolation to non-linear mappings. The final part will explore how to use them to correct colour curves.

You can find a link to download the C# scripts and the Unity package used at the end of this post.

Continue reading

Linear Interpolation

This tutorial will explore one of the most used Mathematical tools in Game Development: linear interpolation! This first post will focus on its Mathematical definition and implementation. The following parts of this series will explore how to extend linear interpolation to non-linear mappings, and how to use them to correct colour curves.

You can find a link to download the C# scripts and the Unity package used at the end of this post.

Continue reading

Inverse Kinematics in 3D

This tutorial will teach you how to master inverse kinematics in 3D: the technique that solves the problem of moving a robotic arm to reach for a specific target.

You can read the rest of this online course here:

A link to download the entire Unity package can be found at the end of this tutorial.

Continue reading

Improving Floating-Point Precision in C#

This tutorial continues the journey to understand floating-point arithmetic, and how to improve the precision of modern programming language types.

At the end of this article, you will find a link to download a simple C# library that provides a new type which improves the precision of traditional floatĀ and doubleĀ variables.

Continue reading

An Introduction to Floating-Point Arithmetic

This tutorial will introduce you to floating-point arithmetic, and how many modern languages—C# included—represent real numbers. This is a series in two parts:

At the end of this article, you will find a link to download a simple C# library that provides a new type which improves the precision of traditional floatĀ and doubleĀ variables.

Continue reading