Shading

Badatcode123, SpinningCube, Robostew

Material

Diffuse objects are objects that reflect light completely randomly, meaning the outgoing and incoming directions have no relationship. This is often called lambertian reflectance.

Metals are objects that reflect light almost always in a specular way, meaning they often absorb transmissions.

Glasses usually refract light, but can also reflect light (more noticeable at steep angles, due to the fresnel effect).

Diffuse models

Many models, or BRDFs, exist for diffuse calculations, the most easiest and basic one is the lambertian diffuse model, it is defined simply as albedo/pi, with albedo being the reflectivity of the object. Other, more advanced models such as oren-nayar can represent diffuse objects more realistically at the cost of being more expensive to calculate and also needing many samples to converge because they use the microfact model.

Specular models

Diffuse models represent light that hits a surface and scatters in many directions due to small imperfections in the surface. It is common to include another type of lighting as well: specular lighting. This represents light that reflects as so:

The angle formed by the incoming ray and the surface is called the angle of incidence, and the angle formed by the reflected ray and the surface is the angle of reflection. These angles are the same for specular reflections.

If the reflected ray is pointing right at a light source¹, then, by the Helmholtz Reciprocity Principle, much of the light from that light source would be reflected off the surface and back towards the incoming ray’s origin.

This should cause a very bright area on the surface. Indeed, you can observe this in real life (go outside, touch grass, etc.) by taking any shiny object and looking for the reflection of lights on the object. These bright areas are called specular reflections, and they can look very sharp or kind of blurry depending on how rough the object is.

I am using rays and the concept of reflected light here, but this effect can be achieved with typical rasterized renderers.

For a simple specular reflection:

1. Find the incoming vector (the vector from the camera to the point you are shading).
2. Reflect that vector across the surface normal.
3. Normalize the reflection vector.
4. Take the dot product of the reflection vector with the vector to a light source (normalized). Clamp this value to the range 0-1 to discard negative values.
5. Raise this value to a power. Higher powers will result in sharper specular reflections.
6. This value represents the intensity of the specular highlight cast by a light on a surface.

Many models for specular reflections exist. Real time graphics in scratch usually use a simple model like the Phong Reflection Model.

Combined

In graphics, it is common to combine both the specular and diffuse models, alongside the ambient value, for more realistic shading than just using one model, as seen below

By SpinningCube

Shadows

Ray-based

Hard shadows can be achieved by shooting rays directly at the light sources from an object’s surface. If the ray is blocked by some object before reaching the light source, that point on the surface is in shadow.

Raymarching can make an approximation of soft shadows, explained in the raymarching section.

Depth-buffer based

Another method of shadow casting is rendering the scene to a depth buffer from the light’s point of view. Then, when figuring out if a pixel is in shadow, we find where the pixel is in the depth buffer of each light, and if there’s a depth value smaller than the depth value of the current pixel, projected onto the depth buffer, then we can safely conclude that it’s in shadow. This method however, can be quite costly, because of the fact we need to render a depth buffer for each light source, plus to get a good shadow resolution, the resolution of each depth buffer has to be quite high. Keep in mind that for point lights, the fov of the theoretical camera on the light will be 360 degrees, which will add to the resolution of the depth buffer. Plus, rendering an image for each light is just not possible considering the limitations of scratch or turbowarp, unless the scene is very simple and there’s only a couple of lights.

Rasterizer

WIP => talk about how to do shadows with rasterizers.

Baked lighting

WIP => about baked lighting methods in Scratch (texture based like The Mast by awesome-llama, polygon-based like Sub 1k Block Challenge by littlebunny06)