Oops!… I violated ODR again


Often when you’re trying to debug a piece of code, the debugger steps into a block you didn’t expect it to. Most of the time this is because your code has a logic error, and it wasn’t doing what your mental model thought it would.

Other times it’s because you accidentally compiled with optimizations on, and the compiler did some magic to make the outcome the same even if the code was different.

This post talks about a scenario where it’s neither of those things. Instead it’s something much more dangerous and difficult to detect — a violation of the One Definition Rule (ODR).

In this post I’ll talk a little about C++’s One Definition Rule, and then discuss how one manifested itself in a project I was working on. I’ll talk about how to detect them, and how I resolved mine.
(I talk a lot about violating ODR in the context of a tool I use (SWIG), but the manner in which I violated ODR is applicable to any C++ library that links to another.)

Continue reading “Oops!… I violated ODR again”


The joys of forward declarations: results from the real world

This is not what you want your dependency graph to look like (graph generated using https://skanderkort.com/erdos_renyi_graph_generator_analyzer)

As a C++ project grows and matures, the following line is inevitably spoken: “The build is too slow”. It doesn’t really matter how long the build actually takes; it is just taking longer than it was. Things like this are an inevitability as the project grows in size and scope.

In this post I’ll talk specifically about my recent use of forward declarations to vastly improve build times on one of those projects, and how you can too.

Continue reading “The joys of forward declarations: results from the real world”

A true heterogeneous container in C++


Oftentimes I see questions StackOverflow asking something to the effect of

“Can I have a std::vector that holds more than one type?”

The canonical, final, never-going-to-change answer to this question is a thorough


C++ is a statically-typed language. A vector will hold an object of a single type, and only a single type.


Of course there are ways to work around this. You can hide types within types! In this post I will discuss the existing popular workarounds to the problem, as well as describe my own radical new heterogeneous container that has a much simpler interface from a client’s perspective. Continue reading “A true heterogeneous container in C++”

Representing plane intersections as a system of linear equations


When you are watching a digitally-rendered battle onscreen in the latest blockbuster movie, you don’t always think about the “camera” moving about that scene. In the real-world, cameras have a field of view that dictates how much of the world about them they can see. Virtual cameras have a similar concept (called the viewing frustum) whereby they can only show so much of the digital scene. Everything else gets chopped off, so to speak. Because rendering a digital scene is a laborious task, computer scientists are very interested in making it go faster. Understandably, they only want to spend time drawing pixels that you’ll see in the final picture and forget about everything else (outside the field of view, or occluded (hidden) behind something else).

Our friends in the digital graphics world make heavy use of planes everyday, and being able to test for plane-plane intersection is extremely important.

In this post, I’ll try to break down what a plane is in understandable terms, how we can create one given a triangle, and how we would go about testing for the intersection between two of them. Continue reading “Representing plane intersections as a system of linear equations”

Representing line intersections as a system of linear equations


(Note: this article was originally written in \LaTeX and transcribed to WordPress, so forgive the equation alignment. Get the original).

In a previous post, I outlined an analytical solution for intersecting lines and
ellipses. In this post I’m doing much the same thing but rather with lines on lines. I’ll point out why the normal slope-intercept form for a line is a poor representation, and what we can do about that.

Continue reading “Representing line intersections as a system of linear equations”

A programmer’s proof of the triangular numbers


The triangular numbers are an interesting mathematical phenomenon that appears constantly in computer science. When you, the programmer, talk about the Big-Oh complexity of a nested for loop that gets executed 1 + 2 + \ldots + n times, you might just slap O(n^2) on it and call it a day.

But do you ever think about what that summation actually is? In this article I’ll present an alternative formulation of the series that I think is satisfying from a programmer’s point of view, and also present some interesting results from looking at the series in different ways.

Continue reading “A programmer’s proof of the triangular numbers”

An Analytic Solution for Ellipse and Line Intersection

image of ellipse and line intersecting (Note: this article was originally written in \LaTeX and transcribed to WordPress, so forgive the equation alignment. Get the original). If you have a line and an ellipse, how can you tell where they intersect? This is a relatively simple problem that has worked-out examples all over the web if you Google for “line ellipse intersection”. However, what I’ve come to find is that nobody will actually give you the solution for an arbitrary line and an arbitrary ellipse. I’m here to do just that. Continue reading “An Analytic Solution for Ellipse and Line Intersection”