Simple Verlet Physics for Games

Stuart Allen(aka FunkyPear)

Euler Integration

Simplest method of moving particles and objects Need to keep track of object position and speed Each frame/time step add speed to position:

X = X + speedX

Y = Y + speedY

Euler Integration

Verlet Integration

Also fairly simple, but expandable to be more accurate (outside scope of this talk)

Need to keep track of object current position and previous position

Each frame/time step, calculate distance travelled since last time, and add to current position:

X = X + (X - oldX)

Y = Y + (Y - oldY)

Verlet Integration

Demo 1

Euler & Verlet Particle Movement Demo

Constraints

Constraints ensure two particles stay a certain distance apart by moving them towards or away from each other

Demo 2

Particle Constraint Demo

Gravity & Other Forces

Forces applied directly to particle positions Gravity: y += 1

Verlet motion makes force persist (inertia)

Demo 3

Particle Constraint with Gravity Demo

Simple Four Step Verlet Engine

Step 1: Apply forces (gravity, wind, etc)

Step 2: Verlet update

Step 3: Constraints

Step 4: Collision Detection

Rope

Expanding from our last demo, rope can be simulated by having a chain of points connected in row with sticks

Demo 4

Multiple Constraints Rope Demo

Cloth

Cloth can be simulated by a grid of points that are connected to their neighbours

Demo 5

Rope Becomes Cloth Demo

Relaxation

Loop over constrain step multiple time to pull points together and make final result more rigid

Less constrain loops means a more bendy and bouncy structure

Engine Upgrade: Fixed Points

Fixed points do not move – other end of stick does all the moving

Structures & Towers

Adding fixed points allows us to build fixed but flexible structures

Towers (fixed points on ground) Bridges (fixed points on either edge of a gap) Dangling ropes (fixed point above rope)

Structures & Towers

Demo 6

Towers Editor Demo

Demo 7

Game Jam Tower Game Demo

Similar Mechanic:World of Goo (2D Boy)

Engine Upgrade: Stick Length Tolerance

Sticks previously had set length Modify sticks to have min and max lengths. Soft body dynamics possible due to addition valid

solutions

Blobs

Blobs attempt to mimic gooey / gelatinous objects

Multiple different configurations: Centre point makes blob seem more solid Double skinning helps stop edge points glitching More tolerance in inner sticks makes for a flatter,

more dynamic blob

Demo 8

Blobs Editor Demo

Blobs – Each Point Linked to Opposite

Blobs – With Central Point

Similar Mechanic:Gish (Chronic Logic)

Thanks for listening! :)

More info and source code at

www.funkypear.com/mochilondon2012