Particle System
A. The procedure animate() is define in ParticleMain.cpp
There is another procedure animate2() which double check
the
correct result is return.
B. In my system the user is able to adjust lambda, r0 and a factor
that limit the magnitude of force. Since it is possible
that
when time step is not small enough, two particle would be
very close and 1/r will got pretty big. This cause the
system
very unstable.
r0 is default to be the initial particle distance in grid.
Gravity is added in the system which can be turn on/off via
the 'Add Gravity' checkbox.
C. The floor is define as bottom of window (y = 0). There
are two objects in the scene. One is a square on the floor,
another is a rectangle floating in the air. In additional
ceiling (y = 1) , left (x = 0) and right (x = 1) wall
boundaries
are added to contain particle if necessary.
There are 2 checkbox for these. 'Add obstacles' is used to
turn on/off the square and rectangle obstacle.
'Add boundary' is used to turn on/off the left, right and
ceiling.
D. For floor, collision detection is check for y < 0. The particles
is projected to the closest outside point for new position.
If the velocity just computed (from new force) dot plane
normal
is positive, it is used as response velocity.
Otherwise, the old velocity vertical component (to plane
normal)
is reverse, multiple by friction, and add back to
horizontal
component to form new response velocity.
For Rectangle, the point containment test is used. To
compute the
response. We need to figure out which one of 4 plane
should use
for collision response.
Given a rectangle, it divide the space into 9 parts with
itself
in the center. If the old position (i.e. the one without
collision)
lie in the top/bottom/right/left region we know which
plane to use.
If the old position lie in the four corner regions. We use
the
current position to see which 2 planes in the corner is
closer
and select that one for collison response similar to floor.
My system allow user to adjust friction in GUI through
friction
edit box.
E. The procedure handleCollision() is written in
ParticleMain.cpp
Besides the input & output for position/velocity.
There are 2
more arguments. One to specify friction and another to
specify
a vector of Shape2D as obstacle. There are currently 2
Shape2D
implementation: Rect.cpp and Plane2D.cpp. Both implement
the
collision, response and intersect function from base class.
F. The user is able to pick a particle in the system (highlight by
yellow) and drag the particle around. A spring is attach
to it
with default stiffness, damp and natural length (=0). They
all
are adjustable through the edit box GUI.
G. The demo start with 3x3 grid and gravity, boundary, obstacles on.
H. The scene is partition into 2x2 grid to store particle. The size
of grid is 2*r0. Each grid store a vector of particles and
list
of obstacles (e.g. floor, left wall, square on floor ..)
fall into
it. Only the 8 neighbors grid and itself is considered
when computing
forces. As a result it run in nearly linear time and can
support
100x100 particles with > 30fps. To show the partition,
check the
'show partition' checkbox. Different paritition will show
particle
in it with different color.
I. The number of particle is adjustable in grid size edit box.
The user can also adjust the timestep of the
simulation.
Note that all attributes, except timestep, add gravity
& show partition,
will not take into effect unless user press the Restart
button.
Note that for larger grid size, you need to set bigger
gravity constant
in the editbox. For 3x3 I use 0.1, for 30x30 it is
recomment to use 9.8.
The system will display current frame rate and time.
There are 14 attribues in my partition system that user
can play around
and produce a variety of effect.
Download program
Have fun !