Maths

There are 42 posts filed in Maths (this is page 2 of 5).

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 spread of diseases, this series of posts is what you are looking for.

The third, and final part of this course will focus on different strategies that can be used to explore different mechanisms of transmission, and possible interventions.

This online course is inspired by the recent COVID-19 pandemic. Now more than ever we need skilled and passionate people to focus on the complex subject of Epidemiology. I hope these articles will help some of you to get started.

All the revenue made from this article through Patreon will be donated to the National Emergencies Trust (NET) to help those most affected by the recent coronavirus outbreak. If you have recently become a patron for this reason, get in touch and I will add your contribution.

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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 spread of diseases, this series of posts is what you are looking for.

This online course is inspired by the recent COVID-19 pandemic. Now more than ever we need skilled and passionate people to focus on the complex subject of Epidemiology. I hope these articles will help some of you to get started.

All the revenue made from this article through Patreon will be donated to the National Emergencies Trust (NET) to help those most affected by the recent coronavirus outbreak. If you have recently become a patron for this reason, get in touch and I will add your contribution.

Become a Patron!

Continue reading →

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 robotic arms and tentacles. If you have not read them, do not fear: this new series will be self-contained, as it reviews the problem of Inverse Kinematics from a new perspective.

You can read the rest of this online course here:

A follow-up that focuses on 3D is also available:

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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 scattering, known as Mie Scattering.

You can find all the post in this series here:

You can download the Unity package for this tutorial at the bottom of the page.

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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 the Rayleigh scattering.

You can find all the post in this series here:

You can download the Unity package for this tutorial at the bottom of the page.

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The Mathematics of Rayleigh Scattering

This post introduces the Mathematics of Rayleigh Scattering, which is the optical phenomenon that causes the sky to appear blue. The equations derived in this tutorial will be translated into shader code in the next tutorial.

You can find all the post in this series here:

You can download the Unity package for this tutorial at the bottom of the page.

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CD-ROM Shader: Diffraction Grating – Part 2

This post completes the series on how to create a shader for CD-ROMs.

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.

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The Theory Behind Atmospheric Scattering

This is the second part of the tutorial on volumetric atmospheric scattering. In this post we will start deriving the equations that govern this complex, yet beautiful optical phenomenon.

You can find all the post in this series here:

You can download the Unity package for this tutorial at the bottom of the page.

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Intersecting The Atmosphere

 

You can find all the post in this series here:

You can download the Unity package for this tutorial at the bottom of the page.

Continue reading →