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A Journey Through the Atmosphere

This post describes how to model the density of the atmosphere at different altitude. This is a critical step, since the atmospheric density is one of the parameters necessary to correctly calculate...

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Atmospheric Scattering Shader

This tutorial finally concludes our journey to simulate Rayleigh Scattering for a planet’s atmosphere. The next (and final) part will show how to change the shader to also include an additional type of...

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Inverse Kinematics in 2D – Part 1

If you have been following this blog for a while, you might have noticed some recurring themes. Inverse Kinematics is definitely one them, and I have dedicated an entire series on how to apply it to...

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Inverse Kinematics in 2D – Part 2

You can read the rest of this online course here: Part 1. Inverse Kinematics in 2D: The Mathematics Part 2. Inverse Kinematics in 2D: The Code A follow-up that focuses on 3D is also available: Part 3....

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The Mathematics of Epidemics

This online course introduces the topic of modelling and simulating epidemics. If you are interested in understanding how Mathematicians, Programmers and Data Scientists are studying and fighting the...

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From an Outbreak to an Epidemic

This online course introduces the topic of modelling and simulating epidemics. If you are interested in understanding how Mathematicians, Programmers and Data Scientists are studying and fighting the...

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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: Part 1. An Introduction to Floating-Point...

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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. Part 1. An Introduction to Floating-Point Arithmetic...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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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...

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Unity 4D #4: Creating 4D Objects

To view this content, you must be a member of Alan Zucconi's Patreon at $5 or more - Click "Read more" to unlock this content at the source The post Unity 4D #4: Creating 4D Objects appeared first on...

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Unity 4D #1: Understanding the Fourth Dimension

This is the first part of a series of articles dedicated to extending Unity from 3D to 4D. In this instalment, we will explore the fourth dimension, from its representations in movies and video games,...

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Unity 4D #2: Extending Unity to 4D

This article will show how to extend Unity to support four-dimensional geometry. This is the second article in a series of four, and the first one which will probably start discussing the Mathematics...

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Unity 4D #3: Rendering 4D Objects

This article will explain how to render 4D objects in Unity, using three separate technique: orthographic projection, perspective projection and cross-section. You can find all the articles in this...

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