15-462 Graphics Project 3: Simulating a Jello Cube: Description of the world file

15-462 Graphics Project 3: Simulating a Jello Cube

Description of the world file

World file is a file version of the structure 'world', which is defined in the following way (you need not change this):

struct point
{
   double x;
   double y;
   double z;
};

struct world
{
  char integrator[10]; // "RK4" or "Euler"
  double dt; // timestep, e.g.. 0.001
  int n; // display only every nth timepoint
  double kElastic; // Hook's elasticity coefficient for all springs except collision springs
  double dElastic; // Damping coefficient for all springs except collision springs
  double kCollision; // Hook's elasticity coefficient for collision springs
  double dCollision; // Damping coefficient collision springs
  double mass; // mass of each of the 512 control points, mass assumed to be equal for every control point
  int incPlanePresent; // Is the inclined plane present? 1 = YES, 0 = NO
  double a,b,c,d; // inclined plane has equation a * x + b * y + c * z + d = 0; if no inclined plane, these four fields are not used
  int resolution; // resolution for the 3d grid specifying the external force field; value of 0 means that there is no force field
  struct point * forceField; // pointer to the array of values of the force field
  struct point p[8][8][8]; // position of the 512 control points
  struct point v[8][8][8]; // velocities of the 512 control points
};

Further explanation of the fields:

Field integrator specifies what method to use to solve the ordinary differential equation of motion. This method is called the integrator. There will be two choices for the integrator: Euler and Runge-Kutta 4th order (RK4). We provided implementations for both integrators in starter.c .
Field dt specifies the timestep for Euler or RK4 method.

Field n instructs that only every nth timepoint is to be shown as a frame (i.e. rendered by OpenGL). All the other timepoints are calculated only for the purposes of accuracy of internal calculations.

Example: dt=0.001 n=5
Now, timestep equals 0.001. Every fifth time point will actually be drawn,
i.e.
frame1 shown by display() <--> t = 0
no frame shown <--> t = 0.001
no frame shown <--> t = 0.002
no frame shown <--> t = 0.003
no frame shown <--> t = 0.004
frame2 shown by display() <--> t = 0.005
no frame shown <--> t = 0.006
...
no frame shown <--> t = 0.009
frame3 shown by display() <--> t = 0.010
no frame shown <--> t = 0.011
...
no frame shown <--> t = 0.014
frame4 shown by display() <--> t = 0.015
no frame shown <--> t = 0.016
no frame shown <--> t = 0.017
...
End of example

To display all the time points, set n=1. It is up to you to implement the functionality of displaying only certain timepoints. One good way to handle this:

...

(somewhere in doIdle() )

for (i=1; i<=jello.n; i++)
{
  if (jello.integrator[0]=='E') // Euler
    Euler(&jello);
  if (jello.integrator[0]=='R') // RK4
    RK4(&jello);
}

...

The physical parameters of the springs are specified by kElastic, dElastic, kCollision and dCollision. The parameters are assumed to be the same for structural, shear and bend springs. Also, they are assumed to be the same for all collision springs.
In the field 'mass', world file specifies the mass of each of the 512 control points. All control points are assumed to have equal mass. The mass information is necessary for computing accelerations, using Newton's second law F=ma.
Warning: world file specifies the mass of each of the 512 control points, not the total mass. Total mass equals 512 times the mass of a control point.
The presence of the inclined plane and its positions are specified by incPlanePresent and a,b,c,d. If there is no inclined plane, parameters a,b,c,d don't have any meaning, and they are not included in the world file.
If the field 'resolution' is non-zero, this indicates that there is no external force field. In this case, the structure forceField has no meaning. A positive value of resolution indicates that there is an external force field present. Then, the bounding box [-2,2]x[-2,2]x[-2,2] is divided into a rectangular grid with points at coordinates (-2 + i * 4 / (resolution - 1), -2 + j * 4 / (resolution - 1), -2 + k * 4 / (resolution - 1)) for i,j,k = 0,1,...,resolution-1 .
Field 'forceField' is a pointer to an array of points, giving the forces (in Newtons) at position corresponding to i,j,k. The force at i,j,k is a 3D vector and is given by the point (i.e. struct point) forceField[i * resolution * resolution + j * resolution + k].
Warning: world file specifies the force, not the acceleration. To obtain acceleration, use Newton's 2nd law F=ma. Here F is a 3D vector representing the force, m is a scalar representing the mass of a control point, and a is a 3D vector representing acceleration.
Fields p and v are 3D arrays, specifying the positions and velocities for every of the 512 control points. Each element of these arrays is of type 'point', i.e. a structure of 3 real numbers. When a world file is loaded, fields p and v contain initial positions and velocities. As time evolves inside the simulation, the arrays p and v will change. These are the only two fields of the world structure which actually change during the simulation. All the other fields are initialized to their values by loadWorld and then never change during a simulation.

How to create your own world files

You will need to create your own world files when you will be testing your program. Except for the header, you probably don't want to edit world files directly. The lines describing positions and velocities are meant to be machine-readable and not human-readable. Instead, use the createWorld application to generate your own files, and then use them for the simulation. Complete code for createWorld is provided together with the starter.code.

createWorld is a simple application that sets the fields of a world structure, and then uses writeWorld routine to write it to a disk file. To create different world files, you have to manually edit the code in the main() function of createWorld.c . Functionality to re-compile createWorld is included in the Makefile. To make different models, modify the fields of the jello world structure in main(). Also, modify the for loops to set the positions and velocities as you wish them for that particular world file. Don't forget to change the name of the output file in the call to writeWorld at the very end of main().

To use the world file you just created, load it with loadWorld in your main program.

Technical description of world files (taken from a comment in starter.c)

File should first contain a line specifying the integrator (EULER or RK4).
Example: EULER

Then, follows one line specifying the size of the timestep for the integrator, and
an integer parameter n specifying  that every nth timestep will actually be drawn
(the other steps will only be used for internal calculation)

Example: 0.001 5
Now, timestep equals 0.001. Every fifth time point will actually be drawn,
i.e. frame1 <--> t = 0
frame2 <--> t = 0.005
frame3 <--> t = 0.010
frame4 <--> t = 0.015
...

Then, there should be three lines for physical parameters and external acceleration.
Format is:
  kElastic dElastic kCollision dCollision
  fExternal.x fExternal.y fExternal.z
  mass
Here
  kElastic = elastic coefficient of the spring (same for all springs except collision springs)
  dElastic = damping coefficient of the spring (same for all springs except collision springs)
  kCollision = elastic coefficient of collision springs (same for all collision springs)
  dCollision = damping coefficient of collision springs (same for all collision springs)
  mass = mass in kilograms of each of the 512 points which model the jello cube
(mass assumed to be the same for all the points;
 total mass of the jello cube = 512 * mass)


Example:
  10000 25 10000 15
  -1 0 0
  0.002

Then, follow one or two lines for the inclined plane, with the obvious synax.
If there is no inclined plane, there should be only one line with a 0 value. There
is no line for the coefficient. Otherwise, there are two lines, first one containing 1,
and the second one containing the coefficients.
Example:
  1
  0.31 -0.78 0.5 5.39

Next, is the forceField block, first with the resolution and then the data, one point per row.
Example:
  30
  < here 30 * 30 * 30 = 27 000 lines follow, each containing 3 real numbers>

After this, there should be 1024 lines, each containing three floating-point numbers.
The first 512 lines correspond to initial point locations.
The last 512 lines correspond to initial point velocities.

There should no blank lines anywhere in the file.

Example of a valid world file

RK4
0.001000 1
10.000000 0.250000 1000.000000 0.250000
0.000000 0.000000 0.000000
0.001953
1
0.31 -0.78 0.5 5.39
0
0.000000 0.000000 0.000000
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