I found some more time to study Coq. One place where I stumble very frequently is case analysis of value-indexed inductive types. There are often cases that lead to contradiction. Other cases intuitively imply some variables to be equal. Vanilla match [...]

It’s time for one of flagship-features of ray tracing: reflection. Indeed this will be rather easy (again) – we basically did have every thing we need already – all that is left is to introduce some recursion in the tracing … Weiterlesen →

I just realized that I used a technique – projecting a vector on a line given by another vector – in my last post on ray-tracing that I did not justify in any way. Look at this picture: Given vector … Weiterlesen →

This time we are going to add specular lightning – this will add “shiny”ness on objects. The basic idea is simple: we reflect the currently traced ray, at the hit-point (using the normal of the object at this point) and … Weiterlesen →

This time we will see how to add shadows to our scene. Imagine this scene: that is generated by this snippet: The basic idea is to only use a directional light (ambient will always be used) if there is no … Weiterlesen →

Don Syme and several others sent tweets to correct my claims about boxing in F#. I made the mistake of assuming that structs cannot be used as interface implementations without being boxed and allocated on the heap. As it turns out, .NET constraints allo[...]

Finally we will produce some output. And after the work we did so far it will be rather easy. The last “hard” part will be the shading: First (very) simple shading The idea is very simple. A object will reflect … Weiterlesen →

(As usual, I will be sending the publisher a copy of this review to give them and the author a chance to reply to it before I publish it to the blog. Other than including their comments and correcting any factual mistakes they may point out, I don't inten[...]

In order to trace a ray we have to decide if a given ray hits a object in our scene. In this post I want to show you how to do this for the classic case of a sphere. Indeed … Weiterlesen →

This time we will have a look at two types that will help us on your way. First I will show you how I implemented a ray-type for representing the most important aspect of ray-tracing itself and then I will … Weiterlesen →