Stores graph as a list of nodes and a list of edges.

Short version of what happens:

Coulomb's law pushes elements which are on top of one another away.

Hookes' law pulls (or pushes) elements that should be near one another via spring physics.

Parameters for the solver:

• stiffness: how stiff springs are
• repulsion: how strongly nodes push away from one another
• damping: a moderator where nodes lose speed while traveling
• minimum energy threshold: if total energy in the graph goes below this then solving stops
• maximum speed: maximum speed a node can travel
• timestep: 0.03 in orignal; controls how many seconds are run in each simulation step

Coulomb's Law

Run on a pairwise list of nodes.

d         <- point1 - point2
distance  <- magnitude(d) + 0.1
distance2 <- distance^2
direction <- normalize(d)

applyForce(point1, (direction * repulsion) / (distance2 *  0.5))
applyForce(point2, (direction * repulsion) / (distance2 * -0.5))

• 0.1 is added to distance to avoid math blowing up near zero

Hookes Law

Run on each spring.

d            <- point2 - point1
displacement <- spring.length - magnitude(d)
direction    <- normalize(d)

applyForce(point1, direction * (spring.k * displacement * -0.5))
applyForce(point2, direction * (spring.k * displacement *  0.5))

• 0.1 is added to distance to avoid math blowing up near zero

Attract to Center

Run on each node.

direction <- -point.p
applyForce(point.p, direction * (repulsion / 50.0))

Updating Velocity

Run on each node.

point.v <- (point.v + (point.a * timestep)) * this.damping
if magnitude(point.v) > maxSpeed:
   point.v <- normalize(point.v) * maxSpeed
point.a = (0, 0)

Had a developer remark about if this (and update position) are the only places the integration code exists.

Applying force

a <- a + (force / mass)

Updating Position

Run on each node.

point.p <- point.p + (point.v * timestep)

Had a developer remark about if this (and update velocity) are the only places the integration code exists.

Calculating total energy

Sum this formula over all nodes:

speed  <- magnitude(point.v)
energy <- 0.5 * point.m * speed^2

Laying out the graph

Repeat until the total energy in the system is below some cutoff:

<< Coulomb's Law >>
<< Hookes Law >>
<< Attract to Center >>
<< Updating Velocity >>
<< Updating Position >>