Programming Assignment Checklist: Atomic Nature of Matter

Sorry, no pairs programming on this assignment.

Frequently Asked Questions

How do I read in the .jpg files? Use our Picture.java data type, described in Section 3.1 of the textbook. To see it in action, program Threshold.java takes the name of a picture file as a command line argument, displays it on the screen, converts all pixels to grayscale, and displays all those pixels with a grayscale value ≥ 180 in white. It relies on the helper program Luminance.java (Program 3.1.3) to convert from color to grayscale.

Are diagonal pixels considered adjacent? No, use only the 4 ordinal neighbors (N, E, S, and W).

For Bead.java, do I need to store the locations of all of the constituent pixels? No, it's much easier to only keep track of the statistics, either

• (number of points, x-coordinate center of mass, and y-coordinate center of mass) or
• (number of points, sum of x-coordinates, and sum of y-coordinates) needed to compute the center-of-mass.

What should I do if several of the beads in frame t+1 have the same bead in frame t as their closest bead? That happens from time to time, but don't worry about it. For our purposes, it is fine to ignore this case since the beads aren't supposed to get too close. If they do get close, there's no good way to track them anyway. Our posted solutions do not check for that rare case and we just let the same bead in frame t get paired a second time.

My physics is a bit rusty. Do I need to worry about converting units? No, we have provided all of the constants in SI units. The only conversion you should need to do is to convert from distances measured in pixels (the radial displacements) to distances measured in meters using the conversion factor of 0.175 × 10^-6 meters per pixel.

Will all of the frames be 640-by-480? Will all of the runs be comprised of 200 runs? Yes, yes. However, do not hardwire any of these constants into your program. Instead use picture.width() and picture.height() for the width and height, and use args.length for the number of command-line arguments.

How do I specify the 200 image names on the command line? One way is to type them all in.

% java BeadTracker run_1/frame00000.jpg run_1/frame00001.jpg run_1/frame00002.jpg ...

% java BeadTracker run_1/*.jpg

Is there a way to make the toString() method format numbers in a nice way? Yes. String.format() works like System.out.printf(), but returns the resulting string instead of printing it. Here is our toString() method in Bead.

public String toString() {
    return String.format("%2d (%8.4f, %8.4f)", mass, cx, cy);
}

How long should my program take? It depends on the speed of your computer. Ours takes about 30 seconds to process a set of 200 frames.

How much memory should my program use? Ours uses less than 5m. You may be using substantially more if you have references to multiple Picture objects at the same time, or if you have more over-sized temporary arrays than you need. Pay attention to this. We will be looking at memory use when we run your code.

How accurate of an estimate should I get? You should get within 10% or so of the exact value for Avogadro's number (6.022142 × 10²³). The standard deviation of the radius of the beads is about 10%, so you shouldn't expect results more accurate than that.

Do I have to follow the API? Yes, you must follow the API and your client program may not call methods not in the API. However, you may add private methods (which are only accessible in the class in which they are declared).

Input, Output, and Testing

Testing. Test your main() methods in BeadFinder, BeadTracker, and Avogadro.

• BeadFinder. For reference, beads_run_1.txt contains a list of all of the beads identified in each of the 200 frames in the run_1 dataset, using a grayscale threshold of 180 and a minimum bead size of 25. For example,

  % java BeadFinder run_1/frame00000.jpg
  37 (220.0270, 122.8919)
  36 (297.8333, 394.5000)
  39 (312.3077, 215.8205)
  31 (433.7742, 375.4839)
  32 (475.5000,  44.5000)
  31 (525.2903, 443.2903)
  35 (632.7714, 154.5714)
  

• BeadTracker. For reference, displacements-run_1.txt contains a list of all of the displacements (again using a grayscale threshold of 180 and a minimum bead size of 25); it was obtained by running

  % java BeadTracker run_1/*.jpg
   7.183
   4.793
   2.169
   5.529
   5.429
   4.396
  ...
  

• Avogadro. For reference, the estimate of Avogadro's number using the data from run_1 is 6.6 × 10⁺²³. Here are our outputs using run_1 and run_2.

  % java BeadTracker run_1/*.jpg | java Avogadro
  Boltzmann = 1.254e-23
  Avogadro  = 6.633e+23
  

  % java BeadTracker run_2/*.jpg | java Avogadro
  Boltzmann = 1.420e-23
  Avogadro  = 5.855e+23
  

Submission

Use the following readme file template.

Possible Progress Steps

These are purely suggestions for how you might make progress. You do not have to follow these steps.

• Download the directory atomic to your system. It contains the data files, Picture.java, and StdIn.java. Each directory run_[1-9] contains a sequence of 200 JPEG images. In total, these data files consume 70MB of space.
• Bead data type. Implement the Bead data type. If you think carefully, you do not need to store all of the individual pixels that comprise a bead - three numeric fields should suffice. Be sure to thoroughly test your data type before proceeding.

• BeadFinder data type. Implement the BeadFinder data type. This is the most difficult part.

  • Review Section 2.4 in the textbook, especially the part on depth-first search. Finding all the pixels in a bead is similar to finding a percolating path.

  • The crux of this part is to write a recursive method dfs(int i, int j) that locates all of the foreground pixels in the same blob as the foreground pixel (i, j). To do, this use depth-first search: mark (i, j) as in the current blob, then recursively mark all of its foreground neighbors as in the current blob (but don't recur if the pixel has previously been marked or the pixel indices are out-of-bounds).

  • Now, implement a nonrecursive method private findBeads() that runs dfs(i, j) from each unmarked pixel (i, j). All of the pixels you encounter by calling dfs(i, j) are in one blob. Store all of the beads (blobs of sufficient size) in a Bead array (of sufficient capacity).

  • Implement a main() method that takes the name of a JPEG file as a command line parameter and prints out all of the beads. The threshold and minimum bead size should be set as named constants in the main() method.

• BeadTracker client. The main() method in BeadTracker takes an arbitrary number of command line parameters, args[0], args[1], and so forth.

• Avogadro client. The main() method in Avogadro reads a sequence of real numbers from standard input and prints out the estimate of Avogadro's number using the formulas provided in the assignment. To calculate σ², use the second formula listed with radial displacements; these are the results from BeadTracker. To test your program, use the file displacements-run_1.txt.

  % java Avogadro < displacements-run_1.txt
  Boltzmann = 1.254e-23
  Avogadro  = 6.633e+23
  

What is polystyrene? It's an inexpensive plastic that is used in many everyday things including plastic forks, drinking cups, and the case of your desktop computer. Styrofoam is a popular brand of polystyrene foam. Computational biologists use micron size polystyrene beads (aka microspheres, latex beads) to "capture" a single DNA molecule, e.g., for a DNA test.

What's the history of measuring Avogadro's number? In 1811, Avogadro hypothesized that the number of molecules in a liter of gas at a given temperature and pressure is the same for all gases. Unfortunately, he was never able to determine this number that would later be named after him. Johann Josef Loschmidt, an Austrian physicist, gave the first estimate for this number using the kinetic gas theory. In some places, this number is known as Loschmidt's number. In 1873 Maxwell estimated the number of be around 4.3 × 10²³; later Kelvin estimated it to be around 5 × 10²³. Perrin gave the first "accurate" estimate (6.5 - 6.8 × 10²³) of, what he coined, Avogadro's number. Here's a reference on estimating Avogadro's number. The most accurate estimates for Avogradro's number and Boltzmann's constant are computed using x-ray crystallography: Avogadro's number is approximately 6.022142 × 10²³; Boltzmann's constant is approximately 1.3806503 × 10^-23 J K^-1.