Realtime soft body physics with Finite Elements

I’ve had a play with implementing soft body physics as described in the books Physics-based animation and Game Programming Pearls. (BTW I’ve no idea what’s going on with the price of Physics Based Animation on Amazon – I have a hardback copy available if anyone wants to buy it at that price :D)

The demo scene is a wall of cubes, anchored at the base of the wall. Each cube is made up of six tetrahedra. A force is applied to the top-right node causing the nodes to move and the elements to deform. The stiffness of the blocks is relatively low, and I haven’t applied any damping, so the resulting behaviour is as if the wall is made of jelly.

The description of the algorithm is described pretty similarly in both books, but there are enough subtleties it’s useful to cross-reference between the books where things are unclear. My code most closely follows Physics Based Pearls.

The code makes heavy use of the Eigen matrix library, and its conjugate gradient solver. As the Eigen library makes heavy use of proxy objects via template expressions, I did get caught out more than a couple of times with assigning the result of a matrix operation to an auto-declared variable.

The rendering is done in OpenGL ES 3.0, so that it runs on desktop graphics supporting OpenGL ES (tested on Intel Skylake), and more recent Android phones (tested on an LG G4).

I used Visual Studio’s cross-platform solution template to create the solution, so the bulk of the code is common between the desktop and mobile, with only a thin platform specific layer.

The code runs fluidly on the desktop with 192 elements and 90 nodes, but runs an order of magnitude slower on mobile.

Code is available on github:

RunKeeper Visualisations

My last post described how I’m using the Twitter API to receive tweets off the live stream.

Since then, I’ve used the API to filter for tweets containing the #runkeeper hashtag, and used that to scrape the user’s activity from the RunKeeper site (including the GPS points from the user’s exercise). I’ve stored that information in a MongoDB, which has allowed me to do some simple visualisation:

The above video (best played at 720p) shows activities plotted against time of day (the sun overhead in the video indicates midday for that region).

I haven’t charted this to confirm, but to my eyes it looks like amount of exercise activity peaks around sunrise and sunset, with almost none at night time (which isn’t really a surprise).

For the curious, this is what the colour of the dots indicate:

let createSphere (latitude:float) (longitude:float) (activityType:string=
    let color = match activityType with
                | "RUN" -> "Red"
                | "WALK" -> "Green"
                | "BIKE" -> "Blue"
                | "MOUNTAINBIKE" -> "Orange"
                | "SKATE" -> "Yellow"
                | "ROWING" -> "Cyan"
                | "HIKE" -> "Brown"
                | "OTHER" -> "Black"
                | _ -> "Black"

On a local scale, the actual GPS traces are of interest:


Activities are present in the more-populated regions of the UK. The blue and orange traces indicating cycling and mountain biking activities are clearly visible.

NOTE: if you think the map looks weird, it doesn’t have the usual aspect ratio – I’m not using a Mercator projection do plot the points, but am simply plotting the longitude and latitude linearly.

On an even smaller scale, landmarks around London are visible:



The GPS data contains altitude information, so there are more interesting visualisations that could be done, including generating contour plots. Also, the above only contains three days worth of data – with a larger data set it would be possible to plot to determine whether activities peak on a weekend etc.



The 3D plot of the globe was drawn using POV-Ray. The 3D globe model was from grabcad, with the converted to a POV-Ray model using PoseRay.

The UK outline was obtained from the NOAA.

The code was implemented in F# (which was a pleasure to get back to after the C++ I’ve been doing recently). I did try the MongoDB.FSharp library to store my data records, but they failed to deserialise from the database. In any case, I wanted more control over the data types saved (I wanted to store the GPS data as GeoJson3DGeographicCoordinates, with the first point stored separately as a GeoJson2DGeographicCoordinates with an index on this value). I could have created .NET classes and used the BSON serializer, but it seemed more effort than writing directly to the DB (and this is about the only time I’ve seen the benefit of C# implicit conversions, but I can live without them in F#).

Why use the Twitter API, and why not scrape the RunKeeper site directly? That’s because of times – the RunKeeper website displays the activity time, but it is displayed in local time, and it’s not clear whether that’s in the user’s timezone, or the timezone of the activity. It seems cleaner to instead assume that the tweet has been posted as soon as the activity is finished and store that time as UTC (this assumption may of course not be true, but the results seem realistic).

Show me the Code!

The code’s not in a bad shape, but I would like to tidy it up a little before releasing it into the world. I’m busy with other things at the moment, but if I get much interest I can go ahead and do that…

Bullet Physics and DirectX 11 on Windows 8 Metro

I’ve got a game idea which I think may work on a tablet so I’ve created the following ‘demo’. I’ve hooked together the Bullet Physics engine with some 3D graphics, and the falling wall of cubes could pretty much be the canonical “Hello, World” equivalent for a 3D game. I’m not sure how much time I’ll have to pursue my game idea, but it should in the worst case be a route to learning some new technologies.

The demo won’t win any awards for its graphics, and the video is pretty poor quality (I recorded the screen with my camera instead of using any screen capturing software).

Falling cubes

Microsoft seem to be definitely pushing for the use of C++ for game creation with Windows 8, with no announcement of a new version of XNA, but that seems to make sense; C++ is closer to the metal than C# and will get more performance out of lower power ARM tablets. Also, there’s quite a buzz with the C++ renaissance with C++11, and modern-style C++. The corresponding new technologies in VS 2010 (PPL) and VS 11 (auto-vectorization, C++ AMP) are especially cool.

I’m also keen to get back into C++ – the past year or so I’ve been working purely in C#, but all my prior experience was using a mixture of C# and C++, and I do miss C++ (even though I am more productive in C#). Also, my previous roles were generally in a modern style (use of STL, smart pointers etc.) but my most recent experience was “C with Classes” style code, so I’ve been relearning modern style as well as picking up the new C++11 features.

Building Bullet as a static lib was pretty easy, I just had to switch it over to use the Multi-threaded DLL c-runtime. Defining WINAPI_FAMILY=WINAPI_PARTITION_APP to detect any non-metro API usages revealed the usage of GetTickCount, which is unavailable on Metro apps, so I just turned off profiling by defining BT_NO_PROFILE 1 in btQuickprof.h

The Windows 8 samples including a couple of games which are decent guides on using DirectX 11. These demos aren’t supposed to be examples of a whole game engine, and don’t necessarily follow best practices: Marble Maze has a class DirectXBase which encapsulates all rendering logic, which is great, but the game logic is in a class MarbleMaze, which derives from this class. It’s nothing that would trip up an experienced developer, but beginners may follow the example. The Simple3DGame (which also demos DirectX and XAML interop) is better structured. The only strange thing in that example is that the render primitive classes are all C++/CX ref classes. This seems to contradict what I remember Herb Sutter saying in a Channel 9 video about sticking to ISO standard C++ where possible and only using C++/CX at the boundaries.

I’m not sure yet whether I’ll try to continue to create a simple demo of my game idea purely in C++, or create a C++/CX interop layer to facilitate writing the game logic in C# – I’m tempted to do this as I’m more productive in C#, and it’ll probably lead to a deeper understanding of WinRT which will be useful even when creating C# XAML applications.

I could have alternatively stayed purely in C# and used SharpDX, or a game framework such as ANX or Ogre (both of which say will soon be supporting XAML), but I was keen on having control of the whole game, C++ upwards – if after profiling any of the C# code any bottlenecks are found, it’ll be easier to re-implement those parts of the code in C++.

As to my experiences of developing the demo: The new version of C++ definitely feels more productive, and feels closer to C#. I love auto (var), lambdas (pretty much the same), for_each (foreach) and range for, and initializer lists. Also, async programming using PPL tasks feels very similar to .NET’s TPL. I’ve had to change mental gears a bit in thinking again about object ownership instead of relying on the garbage collector, and it took way longer than it should for me to figure out how to add a std::unique_ptr into a vector.

I could share the demo code if anyone would find it useful (I need to tidy it up a little bit, and can’t be bothered otherwise) – just post in the comments!

Faster boids

I used the built in performance profiler in VSTS to look at speeding the boids up (and there seems to be a bug in the profiler – when memory profiling was turned on, it seemed unable to resolve symbols, so I switched to the CLRProfiler to look at the memory being used).

Most of the time in the application was spent in calculating the boids’ steering behaviours.
The optimisations here were to try to reduce the time spent in calculating the forces – one optimisation was that instead of each behaviour (cohesion, separation, alignment) each scanning through the entire set of boids, the results of one of the behaviours could be used by both others.

Secondly, the cohesion force was not updated on each frame – the value is cached for 10 iterations. This should not be a fixed value – there should be some heuristic to determine how it should be varied once work is in to measure the “quality” of the flock.

This boosted the frame rate from approx 3fps to 10fps (dropping to 5 fps after some time).

Next came some micro-optimisations.

Changing the Vector to be a struct instead of a class (to avoid over-stressing the garbage collector) resulted in 14fps dropping to 8 fps after running.

Other micro-optimisations that I tried, but didn’t result in any real performance difference included:

Making the trail generator to use a fixed size array (instead of adding/removing from a list).

Removing IEulerRigidBody, calling onto objects directly instead of through an interface.

Changing all doubles to be floats (didn’t actually keep this change in the code).

For Scene8, the drawing code was the real bottleneck, changing the gluSphere to be drawn using VertexBufferObjects resulted in double the frame rate (and it isn’t particularly optimised – could use glDrawElements).

For Scene7, it’s limited by the O(n2) collision detection (this is the next thing to tackle).


An improvement of the flocking behaviour in Jabuka is available.

There are now very simplistic birds drawn, to give an idea of the boid’s orientation.

The separation behaviour has been fixed. The behaviour was garbage before, the force away from another boid was proportional to the distance away from it. Now the force increases the nearer another boid is.

The boid’s orientation is taken as the smallest angle between being aligned with the World’s x axis, and the boid’s velocity. The roll doesn’t behave realistically (see scene 13), but the boid’s behaviour isn’t realistic. A boid would really change its velocity by adjusting its orientation (change the wing shape to apply a torque to allow it to rotate…)

This paper describes how the steering behaviours should change the intention of the boid, instead of providing actual forces onto the boid.

A simple particle system has been introduced to allow the path of a few individual boids to be more easily seen.

Running under the Visual Studio profiler, most of the time was seen to be spent finding the flockmates in proximity of the boid.

The same calculation was being done twice, for both the cohesion and alignment behaviours. Adding a ProximityFinderCache increased the frame rate by 50%, with no change in the calculations. Adjusting the code so that the boids in proximity are only calculated on every third iteration added another 20% to the framerate (giving 15fps with only two TrailGenerators attached).

A change of approach/jabuka 0.6

As mentioned on the Jabuka website, I’m moving away from a tutorial-based approach, mainly because of lack of time. It’s much quicker to implement new code and then blog retrospectively, highlighting new features and interesting code/design decisions. In the tutorial based approach, making a change/bug fix in an earlier tutorial forces all later tutorials to be updated.

That being said, it’s worth discussing changes are in the latest version, 0.6, of Jabuka.
This code introduces a couple of simple steering behaviours, and flocking boids. Given the roadmap, why did I suddenly go off on a total tangent and implement boids? Well, apart from flocking behaviour being especially cool (look on youtube for the Carling Belong commercial, or starling flocks), I wanted to stress the engine (I use that term very loosely given the current functionality of Jabuka) as I’m itching to demonstrate multithreading and performance enhancements. This version of Jabuka has shown that it is still too early to look at performance, however, as the application still has some fundamental flaws to be addressed.

The flocking application implements a flock (based on the algorithms on Chris Reynolds website, and roughly based on the algorithms in the Killer Game Programming in Java book). The changes to Jabuka were that the force for a rigid body is obtained in the Update() method from introducing an IForceProvider interface, implemented by various behaviours.
If you look at the implementation of the steering behaviours, you can see that there is a large number of classes implementing this interface, each performing a simple operation such as aggregation/limitation. This does lead to a proliferation of classes, but I’m happy to live with it for now as it makes unit testing easier, and may lead to more easily changing behaviour dynamically at runtime.

The Update() method calling on the IForceProvider is not perfect in this case – the objects are iterated over, and each object’s Update() method calls on its IForceProvider. For the steering behaviours, the behaviour compares the body’s location to its neighbours to calculate its force and update its position. The problem is that the resulting locations are dependent on the order in which the bodies are updated. This has problems in measuring the flocking quality (more on this later), and it may be desired to update the steering forces independent of Update(), so we don’t do this in every time step (as it’s an expensive operation – O(2)?). Also, having the state of an object dependent on every other object on every timestep will get really messy when we introduce multithreading. Having each body’s Update() method independent of any other means that it’s much easier to parallelise/vectorise/split into multiple threads – it’s likely we’d want to avoid making every IEulerRigidBody thread safe, and would want to implement the thread safety at a higher level (though I won’t jump the gun, we’ll get there soon enough).

The sort of changes above hint that it may be better to have a Physics Manager class, that owns the Collision object, the rigid bodies, and also has knowledge of the IForceProviders and manages the overall sequence of operation.

The larger problem with having the currently flocking behaviour, including collision detection, is that I haven’t yet implemented resting contacts (well, any contact forces) apart from collisions, and as objects are forced towards each other, the simulation can halt. I’ve temporarily fixed this by introducing a scene where the boids don’t have any collision detection. I’ve also introduced a scene which demonstrates the halting, with only two spheres.

As to steering behaviours and flocking itself… I’ve introduced a scene for the seek behaviour, demonstrating that having the steering force directed towards the target is insufficient, the velocity tangential to the targed needs to be taken into account. The idea is to find the optimal trajectory towards the target. Reynolds copes with this by providing a force such that the body’s velocity is adjusted to be the maximum velocity towards the target. This is better, but does mean that the body needs a concept of its maximum velocity (this works OK on Earth, as air friction gives a terminal velocity, but in space this is arbitrary). Also, the maximum velocity may vary – the maximum velocity into the wind is less than having a following wind, and may depend on a body’s shape (or its orientation with respect to its velocity).

Looking at the arrive behaviour, where the speed is arbitrarily slowed down, the first thought that comes to mind is that a PID control towards the target would be desired. However, the problem is that the velocity tangential/perpendicular and distance from the target all need to be taken into account – a more complicated control scheme would need to be used, and that may be too computationally expensive.

The current boid implementation currently uses the same proximity distance for all individual behaviours (separation, alignment, cohesion). It may be that for separation, a smaller proximity should be used. Also, currently, I’m using a simple sphere without taking into account the blind spot behind the boid.

There are lots of tweaks to be made (and a Genetic Algorithm could be used to change these dynamically), but many of them are pointless without a method of measuring the quality of the flock. There is an interesting paper on that here. Some background on the flock theory / the underlying physics of flocking, can be found here, and here.