Basic physics using fixed-point or integers. For determinism, stability and consistency across all setups (useful for networked simulations using the lockstep model).
Prerequisites for the test program are SDL2 and SDL2_ttf.

Evolution and known problems -- Please read before reviewing --

I was initially planning to implement this physics engine the way I'm used to : have collision primitives, and write functions to detect collisions between them.
The following (legacy) files show my initial efforts :

• include/boulette/aabb.hpp
• include/boulette/box.hpp
• include/boulette/disk.hpp

But soon I needed to implement velocity and acceleration, so I figured I'd do it the old way :

void Physics::update() {
    //For each object...
    obj.position += obj.velocity;
    obj.velocity += obj.acceleration;
}

I saw no problems with it, until I saw this article from Gaffer on Games and basically learned that what I was doing sucked pretty bad because of the accuracy loss over time (the example shown by the author is really convincing).
I then moved all my efforts into implementing a Verlet Integration-based physics system, which is, right now, this project's main selling point.
It (the algorithm) appears quite good for cloth simulation, and was also used in "Hitman : Codename 47" for ragdolls and other stuff.

The file is include/boulette/verlet.hpp. One can test it using various types, by changing the unit and real typedefs in include/TestVerlet.hpp (this is documented in that file).

There's no render-time simulation-space to screen-space transformation, but it would be a nice feature for TestVerlet to implement (and perhaps it would allow integer-based simulations, since the simulation wouldn't be limited by the window's size).

Known problems

• Picking vertices with the mouse deforms the edges - this is because the update step's frequency is known to be slower than the display rate. I tried a lot a things to fix this, but none are satisfying (it either caused jitter or made the code more obscure).
• Sometimes, enabling friction seems to "extend" bodies as if they grew invisibly. I haven't been able to prove why.
• The test program can get slow pretty easily - I blame it on SDL2's renderer which doesn't allow me to cleanly render all of my objects at the same time. I would probably be wise to do this in proper OpenGL.

On Data-Oriented Design

I also took it as an opportunity to put what I've learned about Data-Oriented Design (DOD) into practice. However, since it looks like OOP's nemesis (while still valuing understandable code), the Verlet System's code is a bit unusual, so I took extra time to document it.

DOD values the understanding of the target hardware and assembly, which is why I concern myself with the layout of the data, the access patterns, and the assembly output (even though it's pointless because SDL2's renderer is one big overhead).
The files in sse2_tests show my experiments with SIMD instructions, and finally helped me understand why the assembly output of my program was not what I expected :

• First, methods seem to be inlined, which is why GDB's disas won't allow me to inspect most of them. This can be "solved" using GCC's __attribute__((noinline)).
• The compiler cannot prove that my arrays are aligned on a 16-bytes boundary, so it has to generate some extra instructions to handle potentially misaligned data.
• The compiler cannot prove that my float/int arrays have an element count that is a multiple of 4 (the SIMD loop could cause a segmentation fault because of this, so extra checks are performed).