Alan Zucconi

Category: Maths

  • The Mathematics of Epidemics

    The Mathematics of Epidemics

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    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…

  • Inverse Kinematics in 2D – Part 2

    Inverse Kinematics in 2D – Part 2

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    You can read the rest of this online course here: A follow-up that focuses on 3D is also available:

  • Inverse Kinematics in 2D – Part 1

    Inverse Kinematics in 2D – Part 1

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    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,…

  • Atmospheric Scattering Shader

    Atmospheric Scattering Shader

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    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…

  • A Journey Through the Atmosphere

    A Journey Through the Atmosphere

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    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 Mathematics of Rayleigh Scattering

    The Mathematics of Rayleigh Scattering

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    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…

  • CD-ROM Shader: Diffraction Grating – Part 2

    CD-ROM Shader: Diffraction Grating – Part 2

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    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.

  • The Theory Behind Atmospheric Scattering

    The Theory Behind Atmospheric Scattering

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    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.

  • Intersecting The Atmosphere

    Intersecting The Atmosphere

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    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.

  • Fast Subsurface Scattering in Unity (Part 1)

    Fast Subsurface Scattering in Unity (Part 1)

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    Most (if not all) optical phenomena that materials exhibit can be replicated by simulating how the individual rays of light propagate and interact. This approach is referred in the scientific literature as ray tracing, and it is often too computationally expensive for any real-time application. Most modern engines rely on massive simplifications that, despite being…

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