Stuart Allen instructs how to utilize verlet physics for more elegant motion in games.

1. Simple Verlet Physics for
Games
Stuart Allen
(aka FunkyPear)

2. 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

3. Euler Integration

4. 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)

5. Verlet Integration

6. Demo 1
Euler & Verlet Particle Movement Demo

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

8. Demo 2
Particle Constraint Demo

9. Gravity & Other Forces

Forces applied directly to particle positions

Gravity: y += 1

Verlet motion makes force persist (inertia)

10. Demo 3
Particle Constraint with Gravity Demo

11. Simple Four Step Verlet Engine
Step 1: Apply forces (gravity, wind, etc)
Step 2: Verlet update
Step 3: Constraints
Step 4: Collision Detection

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

13. Demo 4
Multiple Constraints Rope Demo

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

15. Demo 5
Rope Becomes Cloth Demo

16. 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

17. Engine Upgrade: Fixed Points

Fixed points do not move – other end of
stick does all the moving

18. 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)

19. Structures & Towers

20. Demo 6
Towers Editor Demo

21. Demo 7
Game Jam Tower Game Demo

22. Similar Mechanic:
World of Goo (2D Boy)

23. 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

24. 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

25. Demo 8
Blobs Editor Demo

26. Blobs – Each Point Linked to Opposite

27. Blobs – With Central Point

28. Similar Mechanic:
Gish (Chronic Logic)

29. Thanks for listening! :)
More info and source code at
www.funkypear.com/mochilondon2012