Physics.ForceLayout

A simple, Haskell-native simulator for doing force-directed layout, e.g. of trees or graphs.

To use, just create an Ensemble like so:

import           Control.Lens        ((&), (.~))
import           Data.Default.Class  (def)
import qualified Data.Map            as M
import           Linear.Affine
import           Linear.V2
import           Physics.ForceLayout

e :: Ensemble V2 Double
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 . uncurry V2)
                    $ [ (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' :: Ensemble V2 Double
e' = forceLayout (def & damping     .~ 0.8
                      & energyLimit .~ Just 0.001
                      & stepLimit   .~ Nothing
                 )
                 e

See the diagrams-contrib package (http://github.com/diagrams/diagrams-contrib/) for more examples.

Data structures

data Particle v n

A particle has a current position, current velocity, and current force acting on it.

Constructors

Particle

Fields

_pos :: Point v n

_vel :: v n

_force :: v n

Instances

Eq (v n) => Eq (Particle v n)

pos :: forall v n. Lens' (Particle v n) (Point v n)

vel :: forall v n. Lens' (Particle v n) (v n)

force :: forall v n. Lens' (Particle v n) (v n)

initParticle :: (Additive v, Num n) => Point v n -> Particle v n

Create an initial particle at rest at a particular location.

type PID = Int

Used to uniquely identify particles.

type Edge = (PID, PID)

An edge is a pair of particle identifiers.

data Ensemble v n

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.

Constructors

Ensemble

Fields

_forces :: [([Edge], Point v n -> Point v n -> v n)]

_particles :: Map PID (Particle v n)

forces :: forall v n. Lens' (Ensemble v n) [([Edge], Point v n -> Point v n -> v n)]

particles :: forall v n. Lens' (Ensemble v n) (Map PID (Particle v n))

Pre-defined forces

hookeForce :: (Metric v, Floating n) => n -> n -> Point v n -> Point v n -> v n

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 :: (Metric v, Floating n) => n -> Point v n -> Point v n -> v n

coulombForce k computes the electrostatic repulsive force between two charged particles, with constant of proportionality k.

distForce :: (Metric v, Floating n) => (n -> n) -> Point v n -> Point v n -> v n

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 n

Options for customizing a simulation.

Constructors

FLOpts

Fields

_damping :: n

Damping factor to be applied at each step. Should be between 0 and 1. The default is 0.8.

_energyLimit :: Maybe n

Kinetic energy below which simulation should stop. If Nothing, pay no attention to kinetic energy. The default is Just 0.001.

_stepLimit :: Maybe Int

Maximum number of simulation steps. If Nothing, pay no attention to the number of steps. The default is Just 1000.

Instances

Fractional n => Default (ForceLayoutOpts n)

damping :: forall n. Lens' (ForceLayoutOpts n) n

energyLimit :: forall n. Lens' (ForceLayoutOpts n) (Maybe n)

stepLimit :: forall n. Lens' (ForceLayoutOpts n) (Maybe Int)

simulate :: (Metric v, Num n, Ord n) => ForceLayoutOpts n -> Ensemble v n -> [Ensemble v n]

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 :: (Metric v, Num n, Ord n) => ForceLayoutOpts n -> Ensemble v n -> Ensemble v n

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 :: (Additive v, Num n) => n -> Ensemble v n -> Ensemble v n

Simulate one time step for an entire ensemble, with the given damping factor.

particleStep :: (Additive v, Num n) => n -> Particle v n -> Particle v n

Simulate one time step for a particle (assuming the force acting on it has already been computed), with the given damping factor.

recalcForces :: (Additive v, Num n) => Ensemble v n -> Ensemble v n

Recalculate all the forces acting in the next time step of an ensemble.

kineticEnergy :: (Metric v, Num n) => Ensemble v n -> n

Compute the total kinetic energy of an ensemble.