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Assignment 2: Cloth & Fluid Simulation
The goal of this assignment is to implement and experiment with
two different physical simulation engines: a spring-mass cloth system
and a grid-based fluid system. The bulk of the rendering,
visualization, and interaction code including the basic data
structures is provided.
In the cloth simulation a 2D grid of point masses are connected
with structural, shear, and flexion/bend springs. To mitigate the
"super-elastic" effect of these springs without increasing
the stiffness (which requires a smaller timestep) you will implement
the correction term described in
"Deformation Constraints in a Mass-Spring Model to Describe Rigid
Cloth Behavior", Xavier Provot, 1995.
For the fluid simulation, you will track a collection of
marker particles as they move through a 3D grid of cells, monitoring
the cell pressure and velocity through each face of each cell. The
implementation requires tri-linear interpolation of the velocities, handling
free-slip and no-slip boundary conditions, and adjustment for incompressible
flows as described in
"Realistic Animation of Liquids", Foster and Metaxas, 1996.
- Download the provided source code and the sample test datasets.
Compile it on your favorite platform and try the command lines below.
There are a number of visualization options for the cloth system.
Press 'm' to toggle drawing of the masses/particles in the spring-mass
particle system. Press 'w' to toggle drawing of the wireframe
(springs). Press 's' to toggle drawing of the surface represented by
the masses & springs. 'v' and 'f' are used to toggle visualizations
of the velocity and forces at each mass position. Finally, 'b' is
used to toggle the bounding box of the original mass positions.
- First implement basic animation of the masses. You'll need
to compute the spring forces and track the position, velocity, and
acceleration of each particle as time progresses. Simple
forward/explicit Euler integration is sufficient. You can access the
timestep and gravity from the ArgParser class. Initially test your
code on the small example shown below and verify that each of the
spring forces (structural, shear, and bend/flexion) and the force due
to gravity are correct. Pressing 'a' will toggle the animation on and
off. Each loop of this continuous animation will call
Cloth::Animate() 10 times and then refresh the screen. To
take just one step of animation, press the space bar. You can restart
the animation from the beginning by pressing 'r'.
simulation -cloth small_cloth.txt -timestep 0.001
You will need to complete the implementation for the force
visualization. Your visualization does not need to match the one
above (the blue lines), as long as you find its output informative and
helpful in your debugging.
- Once your basic spring-mass system is working, test it on the
larger example below. As illustrated by Provot, the springs at the
corner will stretch too much. Implement the iterative
correction/adjustment method for springs that have stretched beyond
the specified threshold. The provided code will visualize the
"over-stretched" springs in cyan (shown below).
simulation -cloth provot_original.txt -timestep 0.001
simulation -cloth provot_correct_structural.txt -timestep 0.001
simulation -cloth provot_correct_structural_and_shear.txt -timestep 0.001
- When you are confident that your implementation is complete,
test it on the examples below which use different parameter values to
mimic different types of cloth. Now experiment with your system and
try adjusting the many different parameters. How stable is the
simulation? Discuss in your README.txt. Make at least one
interesting new test scene. You may extend the input file format as
necessary for your new example(s). Describe your new example and how
to run it in your README file.
simulation -cloth denim_curtain.txt -timestep 0.001
simulation -cloth silk_curtain.txt -timestep 0.001
simulation -cloth table_cloth.txt -timestep 0.005
- In your experimentation, you undoubtedly caused the cloth to
"explode" at least once. In theory this instability can always be
fixed by using a smaller timestep. So now, let's implement an
adaptive timestep for the simulator. Start with the timestep provided
on the command line, but if the simulation is too stiff (unstable at
that timestep), back up, halve the timestep, and try again. What
criteria did you use to detect that the system is unstable? Discuss
in your README.txt
- Now for the second part --- fluid simulation, which is
launched like this:
simulation -fluid fluid_random_xy.txt -timestep 0.01
The images below show some visualizations of this dataset of
random particles on a 5x5x1 grid. On the left we see the random
particles (approximately 64 per cell) and the random initial
velocities measured at the center of each cell. Marker particle
visualization and velocity visualization are toggled by pressing the
'm' and 'v' keys. Remember that the velocities are actually stored as
vectors perpendicular to the face of each cell, visualized by red (x)
and green (y) triangles (toggled by pressing the 'e' key). The
velocity at the center of each cell is computed by averaging the
velocities at the faces on either side of the cell.
To move particles within the field, we need to compute the
velocity at each point within the volume. The simplest thing to do is
just use the velocity at the center of the cell for all particles in
that cell. The image below left shows this discontinuous velocity
field (press 'd' to visualize this "dense" velocity field). Go ahead
and press 'a' to animate the particles within this field and you
should see why this isn't a good assignment of velocities.
So, your first task is to implement proper velocity interpolation
as described in Foster & Metaxas. Once you've carefully implemented
the interpolation in the xy plane, run the above simulation again and
you should see dense velocity fields like the ones above middle and
right. NOTE: In the implementation provided, each cell stores the
face velocities (u, v, & w) for the face it
shares with the cell in the positive direction along each axis. That
is, celli,j,k stores
ui+1/2,j,k, vi,j+1/2,k, and
wi,j,k+1/2. These values are stored in the
variables u_plus, v_plus, and w_plus, and
the corresponding accessors get_u_plus(),
get_v_plus(), and get_w_plus().
To perform 3D fluid simulations your interpolation scheme must
correctly account for the z direction as well. Here are 3 test cases
to help you verify that your interpolation is working in 3D. The
resulting animation should be similar in each of the 3 axis-aligned
simulation -fluid fluid_spiral_xy.txt -timestep 0.01
simulation -fluid fluid_spiral_yz.txt -timestep 0.01
simulation -fluid fluid_spiral_zx.txt -timestep 0.01
- Now let's address the issue of compressibility/incompressibility.
You may have noticed that your simulations are a little "bouncy". To
emphasize the fact, try this simulation:
simulation -fluid fluid_compressible.txt -timestep 0.01
You can press "p" to visualize the pressure in each cell by drawing
little cubes for each cell colored by pressure. Initially all the
cells are white (pressure == 0). After just a few timesteps a
negative pressure (blue) appears in the middle of the grid surrounded
by a ring of positive pressure (red). Later in the simulation these
values are quite chaotic, introducing noise into the velocity field.
In order to enforce the incompressibility of the flow, you will
need to implement the divergence correction originally described by
Harlow & Welch and later by Foster & Metaxas. Compute the divergence
of each "full" cell and adjust each non-boundary face velocity to
absorb its share of excess inflow or outflow. When correctly
implemented, the pressure in each cell should be (within epsilon of)
zero throughout the simulation and the flow should no longer "bounce".
NOTE: You can swap between compressible and incompressible
simulation by editing the following line in the simulation data file
and then pressing 'r' to restart the simulation:
- Up to this point, all of the cells in our fluid simulation
have been full (had at least one particle). Now let's look at some
interesting cases showing the interaction between air and water. Try
the examples below. Press "c" to visualize the Marker-And-Cell (MAC)
voxels: red == FULL and blue == SURFACE. Press "s" to enable a
triangular mesh rendering of the surface using Marching Cubes/Marching
simulation -fluid fluid_drop.txt -timestep 0.01
simulation -fluid fluid_dam.txt -timestep 0.01
To perform these simulations you will need to extend your
incompressibility code to handle surface cells. The divergence of
inflow or outflow should be dissipated over the "free" faces of the
cell (i.e., faces that this cell shares with EMPTY cells).
Note: You can edit the dimensions of your grid by editing the top
line of the simulation data file. The "drop" and "dam" shapes will
adjust to your new dimensions.
WARNING: Despite spending many hours on the solution
implementation, I was not able to sufficiently stabilize these last
two examples to match results from the papers we have read. It could
be that the timestep was too large (ultimately due to the inherent
instability of explicit numerical integration schemes), that the units
are not consistent (e.g., grams vs. kilograms), that I've
misinterpreted the implementation described in the papers, or that
there are bugs in my code. If you are more successful, please let us
- Harlow & Welch, "Numerical Calculation of Time-Dependent Viscous
Incompressible Flow of Fluids with Free Surface," Phys. Fluids,
Vol. 8, p. 2182, 1965. (paper copy handed out in lecture).
Practical animation of liquids,
Foster & Fedkiw,
simulation of smoke, Fedkiw, Stam & Jensen, SIGGRAPH 2001
"Melting and Flowing"
Carlson, Mucha, Van Horn III & Turk,
ACM SIGGRAPH Symposium on Computer Animation 2002
Ideas for Extra Credit
Include a short paragraph in your README.txt file describing
- Implement an alternate integration method (Midpoint, Runge-Kutta,
implicit Euler, etc.) Compare the performance of each method.
- Experiment with the provided Marching Cubes implementation in
the fluid simulator. Try different isosurface values (a command line
option and keyboard shortcut --- press '+'/'-') and render the
isosurfaces of different scalar fields such as density or pressure or
divergence (for compressible flows). Discuss in your
README.txt file. If you're really motivated, add gouraud
shading to the marching cubes surface!
- Implement a new visualization/rendering mode (maybe you already
did to debug an earlier step).
- Create a new fluid test scene (you can create it procedurally,
or create a new input file). A fun test scene could include source
and sink cells where mass is created and deleted or a spatial- or
time-varying force field (instead of a uniform gravity).
- Having two physical simulation engines within the same program
makes it possible for us to experiment with coupled simulations.
Compose a cloth simulation and fluid simulation in the same scene
(just load 2 files on the command line). The cloth motion can be
driven by the fluid's velocity field, or the fluid motion can be
driven by the cloth, or both!
- Basic Code (vectors.h, matrix.h, matrix.cpp, argparser.h,
camera.h, camera.cpp, glCanvas.h, glCanvas.cpp, main.cpp,
boundingbox.h, boundingbox.cpp, utils.h, Makefile)
Similar to Assignments 1 & 2.
- Cloth (cloth.h, cloth.cpp)
A class to store, animate, and paint a 2D grid of masses & springs.
- Cloth test scenes (small_cloth.txt, provot_original.txt,
- Fluid (fluid.h, fluid.cpp, cell.h, marching_cubes.h,
- Fluid test scenes (fluid_random_xy.txt,
fluid_spiral_xy.txt, fluid_spiral_yz.txt, fluid_spiral_zx.txt,
fluid_compressible.txt, fluid_drop.txt, fluid_dam.txt)
Please read the Homework information page again before submitting.