How to develop a simple 2D game with physics engineIVAN KUŠT, ANDROID TEAM LEADER

THE GAME

• Balls with random numbers 0

- 9 are falling from the sky

• User must catch as many as

possible in the bucket that

can move along the bottom

• Number of the ball defines

score for catching the ball

SO WHAT DO WE NEED?

• A way to spawn the objects on the top

• Simple physics - gravity and collisions

• Scoring and time limit

01SPAWNING OBJECTS

OBJECTS

• Each object in physics engine is either: • circle • rectangle

• Gravity can be applied or not

• Current position

• Current speed vector (x, y components)

SPAWNING OBJECTS

• Balls are spawned at a time

interval

• Random size (with min and

max values)

• Random position

• Once spawned, object is

added to physics engine (which applies gravity and

resolves collisions of the

object)

SPAWNING AREA

02COLLISIONS

02.1COLLISION DETECTION

AXIS ALIGNED BOUNDING BOXES

X

Y

• Rectangle that encloses an

object in the game

• Used for collision detection: • easiest • fastest

AABB COLLISION DETECTION

• Rectangles intersect

• Extreme case: • one rect encloses another

CIRCLES

• Distance between centers <=

sum of radiuses

CIRCLE VS AABB

• Distance between closest

point of rect and circle center

<= circle radius

02.2IMPULSE RESOLUTION

OBJECTS COLLIDED - NOW WHAT?

• Calculate new speed vectors for each object

• Two dimensional elastic collision

• Every object has an impulse or momentum:Impulse = mass * velocity

WHEN OBJECTS COLLIDE

• The relative velocity of one particle with respect to the other

is reversed by the collision

• The average of the momenta before and after the collision is

the same for both particles

CIRCLE VS CIRCLE

TANGENT

NORMAL

• Overall velocity split into two

perpendicular velocities

• One along common normal (line of collision)

• One perpendicular to

common normal

X

Y

CIRCLE VS AABB

TANGENT

NORMAL

• Calculate new velocities

depending on the masses of

the object

• Recalculate new velocities to

the x and y aligned velocity

components

X

Y

SIMULATING REALITY

• In reality, some kinetic energy is lost on collision(the ball never bounces back from the ground to the same

height)

• Restitution coefficient • multiply calculated velocities

• Feels more “real”

IN THE GAME

• Two rectangles on each side

of the bucket that collide with

the balls • mass = infinite

• Simulates bucket collisions

02.3SINKING

SINKING

• What if an object with low restitution hits a wall (or floor)

with infinite mass?

• It begins to sink (the expected behavior would be for the ball

to stay next to the wall or floor) • due to floating point error that accumulates over time

SOLUTION

TANGENT

NORMAL

• Solution: linear projection • move each object by a

small percentage of the

mass along collision

normal

03SCORING

SCORING

• Goal of the game is to collect as many balls as possible in a

limited amount of time

• Score for a “catch” is equal to number shown on the ball

SCORING

• A rectangular region is

defined • if a ball is in the region it is

removed from physics

engine and score is

increased

SCORING REGION

04ARCHITECTURE OVERVIEW

ENGINE ARCHITECTURE

PHYSICS ENGINESOLID

SOLID CIRCLE SOLID RECT

OBJECT GENERATOR

BALL GENERATOR

GAME IMPLEMENTATION

• Implemented as a custom View (no OpenGL)

• Constant redraw is forced • invalidate() posted in a loop using Handler

• On each frame:1. appliy gravity to all objects 2. check and resolve collisions3. generate new objects

4. draw new frame based on state of objects

CONCLUSIONS

• Simple game can be implemented without using OpenGL

• Various screen sizes must be taken into account: • easier to catch if resolution is higher

REFERENCES

• http://gamedevelopment.tutsplus.com/tutorials/how-to-

create-a-custom-2d-physics-engine-the-basics-and-

impulse-resolution--gamedev-6331

• http://gamedevelopment.tutsplus.com/tutorials/when-

worlds-collide-simulating-circle-circle-collisions--

gamedev-769

• https://en.wikipedia.org/wiki/Elastic_collision

• http://hypertextbook.com/facts/2006/restitution.shtml