It’s hard to describe how paramount light is. Ultimately, it is the only thing we see. But just as important the presence of light is, so is its absence. To talk about light we have to start in darkness so let’s jump straight into it.

For the final part of this article we will remain inside that sphere of light, it will completely surround us and the scenes we will look at. In the demonstration above notice that every point of the surface is now exposed to the entire hemisphere of light with uniform intensity. This removes any differences between the points on the surface – they all receive the same light and end up with the same shading.

You may have seen a situation like that on an overcast day – the Sun isn’t directly visible and the entire sky emits light from every direction. In the last scene of this article let’s see what effects are created when a part of that surrounding light gets occluded. In the demonstration below you can control the position of the black tile and see the shadow it ends up creating:

The closer the black tile is to the gray plane the more light it obscures and the darker the shadow is. We can observe this easily using the hemisphere model. The yellow area represents the projection of the visible light:

This shadow is ultimately no different from the shadows cast by a rectangular wall that we saw before. Shadows are simply the absence of light.

Physically Based Rendering by Matt Pharr, Wenzel Jakob, and Greg Humphreys is the book on creation of photorealistic images with computer graphics. Over the course of the publication authors cover a wide variety of topics related to geometry, color, lights, and materials, while building a full-featured ray tracer at the same time. As of two years ago the complete book is available online, for free!

For a shorter overview of a production renderer I recommend Physically Based Rendering in Filament. This documentation provides more rigorous treatment of material properties than what I’ve presented here and it elaborates on many approximating models used in realtime computer graphics.

As the name implies, Vsauce’s What Is The Speed of Dark? discusses an interesting concept of a speed of darkness and it explains how shadows can break the speed of light, thankfully, without breaking the laws of physics.

It’s truly remarkable that what starts at light sources, what interacts with different objects, and what eventually ends up in our eyes is electromagnetic radiation with different wavelengths and of varying intensity. Math helps us understand how changes to those intensities happen.

With Lambertian surfaces and uniformly bright lights, we can simplify countless interactions of trillions of photons into relatively straightforward geometrical concepts, but even with more complicated materials and light sources, every step of the way can be simulated to create extremely convincing simulations of real life environments.

Naturally, it’s impossible to completely articulate the sheer intricacy and immensity of what spontaneously just happens in the physical world to every photon on a sunny day. Math, however, gives us the tools to raise above that complexity and see the bigger picture.