Maintainer  byorgey@cis.upenn.edu 

A simple, Haskellnative simulator for doing forcedirected layout, e.g. of trees or graphs.
To use, just create an Ensemble
like so:
e = Ensemble [ (edges, hookeForce 0.05 4) , (allPairs, coulombForce 1) ] particleMap where edges = [(1,2), (2,3), (2,5), (3,5), (3,4), (4,5)] allPairs = [(x,y)  x < [1..4], y < [x+1..5]] particleMap = M.fromList . zip [1..] . map (initParticle . P) $ [ (2.0, 3.1), (6.3, 7.2) , (0.3, 4.2), (1.6, 1.1) , (4.8, 2.9) ]
Then run a simulation using either simulate
(to get the list of
all intermediate states) or forceLayout
(to get only the ending
state):
e' = forceLayout (FLOpts { damping = 0.8 , energyLimit = Just 0.001 , stepLimit = Nothing } ) e
See the diagramscontrib package (http://patchtag.com/r/byorgey/diagramscontrib/home) for more examples.
 data Particle v = Particle {}
 pos :: forall (~>) v. Arrow ~> => Lens ~> (Particle v) (Point v)
 vel :: forall (~>) v. Arrow ~> => Lens ~> (Particle v) v
 force :: forall (~>) v. Arrow ~> => Lens ~> (Particle v) v
 initParticle :: AdditiveGroup v => Point v > Particle v
 type PID = Int
 type Edge = (PID, PID)
 data Ensemble v = Ensemble {}
 forces :: forall (~>) v. Arrow ~> => Lens ~> (Ensemble v) [([Edge], Point v > Point v > v)]
 particles :: forall (~>) v. Arrow ~> => Lens ~> (Ensemble v) (Map PID (Particle v))
 hookeForce :: (InnerSpace v, Floating (Scalar v)) => Scalar v > Scalar v > Point v > Point v > v
 coulombForce :: (InnerSpace v, Floating (Scalar v)) => Scalar v > Point v > Point v > v
 distForce :: (InnerSpace v, Floating (Scalar v)) => (Scalar v > Scalar v) > Point v > Point v > v
 data ForceLayoutOpts v = FLOpts {}
 simulate :: (InnerSpace v, Ord (Scalar v), Num (Scalar v)) => ForceLayoutOpts v > Ensemble v > [Ensemble v]
 forceLayout :: (InnerSpace v, Ord (Scalar v), Num (Scalar v)) => ForceLayoutOpts v > Ensemble v > Ensemble v
 ensembleStep :: VectorSpace v => Scalar v > Ensemble v > Ensemble v
 particleStep :: VectorSpace v => Scalar v > Particle v > Particle v
 recalcForces :: forall v. AdditiveGroup v => Ensemble v > Ensemble v
 kineticEnergy :: (InnerSpace v, Num (Scalar v)) => Ensemble v > Scalar v
Data structures
A particle has a current position, current velocity, and current force acting on it.
initParticle :: AdditiveGroup v => Point v > Particle vSource
Create an initial particle at rest at a particular location.
An Ensemble
is a physical configuration of particles. It
consists of a mapping from particle IDs (unique integers) to
particles, and a list of forces that are operative. Each force
has a list of edges to which it applies, and is represented by a
function giving the force between any two points.
Predefined forces
hookeForce :: (InnerSpace v, Floating (Scalar v)) => Scalar v > Scalar v > Point v > Point v > vSource
hookeForce k l p1 p2
computes the force on p1
, assuming that
p1
and p2
are connected by a spring with equilibrium length l
and spring constant k
.
coulombForce :: (InnerSpace v, Floating (Scalar v)) => Scalar v > Point v > Point v > vSource
coulombForce k
computes the electrostatic repulsive force
between two charged particles, with constant of proportionality
k
.
distForce :: (InnerSpace v, Floating (Scalar v)) => (Scalar v > Scalar v) > Point v > Point v > vSource
distForce f p1 p2
computes the force between two points as a
multiple of the unit vector in the direction from p1
to p2
,
given a function f
which computes the force's magnitude as a
function of the distance between the points.
Running simulations
data ForceLayoutOpts v Source
Options for customizing a simulation.
FLOpts  

simulate :: (InnerSpace v, Ord (Scalar v), Num (Scalar v)) => ForceLayoutOpts v > Ensemble v > [Ensemble v]Source
Simulate a starting ensemble according to the given options,
producing a list of all the intermediate ensembles. Useful for,
e.g., making an animation. Note that the resulting list could
be infinite, if a stepLimit
is not specified and either the
kinetic energy never falls below the specified threshold, or no
energy threshold is specified.
forceLayout :: (InnerSpace v, Ord (Scalar v), Num (Scalar v)) => ForceLayoutOpts v > Ensemble v > Ensemble vSource
Run a simluation from a starting ensemble, yielding either the
first ensemble to have kinetic energy below the energyLimit
(if
given), or the ensemble that results after a number of steps
equal to the stepLimit
(if given), whichever comes first.
Otherwise forceLayout
will not terminate.
Internals
ensembleStep :: VectorSpace v => Scalar v > Ensemble v > Ensemble vSource
Simulate one time step for an entire ensemble, with the given damping factor.
particleStep :: VectorSpace v => Scalar v > Particle v > Particle vSource
Simulate one time step for a particle (assuming the force acting on it has already been computed), with the given damping factor.
recalcForces :: forall v. AdditiveGroup v => Ensemble v > Ensemble vSource
Recalculate all the forces acting in the next time step of an ensemble.
kineticEnergy :: (InnerSpace v, Num (Scalar v)) => Ensemble v > Scalar vSource
Compute the total kinetic energy of an ensemble.