Programming Assignment Checklist: Atomic Nature of Matter

Pair programming. On this assignment, you are encouraged (not required) to work with a partner provided you practice pair programming. Pair programming "is a practice in which two programmers work side-by-side at one computer, continuously collaborating on the same design, algorithm, code, or test." One partner is driving (designing and typing the code) while the other is navigating (reviewing the work, identifying bugs, and asking questions). The two partners switch roles every 30-40 minutes, and on demand, brainstorm. Before pair programming, you must read the article All I really need to know about pair programming I learned in kindergarten.

You may choose a partner from any precept. Only one member of the partnership will turn in the assignment. Both partners must submit readme.txt files. Both partners will receive the same grade.

Frequently Asked Questions

Do I need to follow the prescribed API? Yes, we will be testing the methods in the API directly. If your method has a different signature or does not behave as specified, you will lose a substantial number of points. You may not add public methods to the API; however, you may add private methods (which are only accessible in the class in which they are declared).

Are the PowerPoint slides from precept available? Here they are.

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 a luminance value, and displays all those pixels with a luminance value ≥ 180 in white. It relies on the helper program Luminance.java (Program 3.1.3) to convert from color to luminance.

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

Do I have to output the blobs, beads and displacements in the same order as shown on the assignment web page? No, although keeping it in the same order makes it easier for you (and us) to check.

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.

Why do I have to compare each bead in frame t+1 to each bead in frame t? Why can't I do it the other way around? It's an arbitrary choice. We require you do it this way to make it easier to check your answer.

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.

Can I assume that all of the frames be 640-by-480 and that all of the runs will consist of 200 frames? No, do not hardwire any of these constants into your program. Use picture.width() and picture.height() for the width and height, and use args.length for the number of command-line arguments.

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 Blob.

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

See p. 125 of the textbook to learn more about formatted printing.

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

% java BeadTracker 25 180.0 25.0 run_1/frame00000.jpg run_1/frame00001.jpg run_1/frame00002.jpg ...

An easier alternative is to use the wildcard capability of your command line: for example, the following specifies (in alphabetical order) all .jpg files in the run_1 directory.

% java BeadTracker 25 180.0 25.0 run_1/*.jpg

How can I estimate the running time of my program? Use the Stopwatch object from Section 4.1. When you execute BeadTracker, redirect the output to a file to avoid measuring the time to print the output to the terminal. On OS X or Linux, you can use the wildcard capability of the command-line to run 5 frames, 10 frames, 20 frames, 40 frames, 80 frames, and 160 frames:

% java BeadTracker 25 180.0 25.0 run_1/frame0000[0-4]*.jpg > temp.txt

% java BeadTracker 25 180.0 25.0 run_1/frame000[0]*.jpg    > temp.txt

% java BeadTracker 25 180.0 25.0 run_1/frame000[0-1]*.jpg  > temp.txt

% java BeadTracker 25 180.0 25.0 run_1/frame000[0-3]*.jpg  > temp.txt

% java BeadTracker 25 180.0 25.0 run_1/frame000[0-7]*.jpg  > temp.txt

% java BeadTracker 25 180.0 25.0 run_1/frame000*.jpg run_1/frame001[0-5]*.jpg > temp.txt

On Windows, the best way is to create several subirectories with the desired number of frames.

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 5 MB. You will receive a deduction if you use substantially more. The most common way to waste memory is to hold references to an array of Picture objects in BeadTracker instead of only two at a time. You can use the -Xmx option to limit how much memory Java uses: for example, the following command limits the memory available to Java to 5 MB.

% java -Xmx5m BeadTracker 25 180.0 25.0 run_1/*.jpg

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 this.

Input, Output, and Testing

Testing. For testing, create main() methods in BlobFinder, BeadTracker, and Avogadro.

BlobFinder. The assignment page shows the output from running BlobFinder with run_1/frame00001.jpg. Here are the results for run_1/frame00000.jpg:

% java BlobFinder 25 180.0 run_1/frame00000.jpg
13 Blobs:
 37 (220.0270, 122.8919)
  1 (254.0000, 223.0000)
 17 (255.4118, 233.8824)
 23 (265.8261, 316.4348)
 36 (297.8333, 394.5000)
 39 (312.3077, 215.8205)
 23 (373.0000, 357.1739)
 19 (390.8421, 144.8421)
 31 (433.7742, 375.4839)
 32 (475.5000,  44.5000)
 31 (525.2903, 443.2903)
 24 (591.0000, 399.5000)
 35 (632.7714, 154.5714)

7 Beads:
 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)

The file beads-run_1.txt lists all of the beads in each frame (using tau = 180.0 and P = 25). and was generated by a different client program using BlobFinder: for convenience it lists the reference frame for each set of beads.

BeadTracker. For reference, displacements-run_1.txt and displacements-run_2.txt contain a list of all of the displacements (using tau = 180.0 and P = 25) for run_1 and run_2, respectively. They were obtained by running

% java BeadTracker 25 180.0 25.0 run_1/*.jpg   % java BeadTracker 25 180.0 25.0 run_2/*.jpg
 7.1833                                        5.1818
 4.7932                                        7.6884
 2.1693                                        6.7860
 5.5287                                        6.4907
 5.4292                                        4.2102
 4.3962                                        1.1412
 ...                                           4.4724
                                               7.5191
                                               3.0659
                                               4.4238
                                               5.0600
                                               1.7280
                                               ...

Avogadro. The assignments gives the output for run_1. Below is the output for run_2.

% java BeadTracker 25 180.0 25.0 run_2/*.jpg | java Avogadro
Boltzmann = 1.4200e-23
Avogadro  = 5.8552e+23

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, Luminance.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. The file beads-run_1.txt lists the beads found in each frame of run_1 using tau = 180.0 and P = 25. The files displacements-run_1.txt and displacements-run_2.txt are the output of BeadTracker for those runs.
Blob data type. Implement the Blob data type. You do not need to store all of the individual pixels that comprise a blob; instead, store three numbers:
- (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.
Be sure to thoroughly test your data type before proceeding.
BlobFinder data type. Implement the BlobFinder 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 blob 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 private nonrecursive helper method findBlobs() 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.
- Next, implement the method countBeads() that counts the number of beads (blobs of sufficient size).
- Implement a main() method that takes as command-line arguments P, tau, and the name of a JPEG file. The main() method should print out the number of blobs and the number of beads with at least P pixels.
- Next, implement the method getBeads() that searches through the blobs and stores all of the beads (blobs of sufficient size) in a Blob array. The length of the array should be equal to the number of beads.
- Modify main() to print out the blobs and beads.
BeadTracker client. The main() method in BeadTracker takes an arbitrary number of command-line arguments, args[0], args[1], and so forth. You only need to consider two frames at a time, so don't try to store them all in memory at one time.
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.

Enrichment

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 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.

Where can I learn more about Brownian motion? Here's the Wikipedia entry. You can learn about the theory in ORF 309 - it's likely the first subject you'll be asked about if you interview on Wall Street.