The inside of a curve

Hi, I am shuba, and I'll be using this blog to dicuss various computer graphics topics I find interesting. I might also disgress on C++, which is my main programming language.

For my first article, I'll try and answer a question that's not as simple as it seems: onto what did I click? How did the program know what I clicked on? We're used to be able to click on various kinds of button, rectangular or circular. But when using image editing software such as The Gimp or Inkscape, we want to select the freeform shapes we create.

Tail-recursive map in OCaml

The List.map function of the OCaml standard lib is not implemented tail-recursively. The current version (as of 4.00 on my computer) is

let rec map f = function
    [] -> []
  | a::l -> let r = f a in r :: map f l

Debugging with DOT

Rationale

I'm starting a PhD on first-order automated theorem proving, which is the reason I'm writing an experimental theorem prover in OCaml. Theorem provers are full of complicated algorithms (that I plan to write on later), and my usual techniques for debugging are twofold:

  1. Writing a lot of assert to make sure invariants are not broken
  2. Printing debug information on stdout, if required, to get an idea of what the prover is doing. This allows me to choose the level of detail of what is printed, depending on which incorrect behavior I'm tracking.

The second technique, also known as printf debugging, is quite powerful (especially since OCaml does not feature a great debugger as an alternative). However, text is not great for representing structured data, and especially graphs. Here is where I bring DOT into play.