Late policy: The homework will be graded out of 100 points. We will accept late submissions up to Sunday, Sept. 28 at 23:59:59; however, for every day that is it is overdue, we will subtract 20 points from the total. We understand thst sometimes multiple assignments hit at once, or other life events intervene, and hence you have to make some tough choices. We'd rather let you turn something in late, with some points off, than have a "no late assignments accepted at all" policy, since the former encourages you to still do the assignment and learn something from it, while the latter just grinds down your soul. The somewhat aggressive late penalty is not intended to be harsh - it's intended to encourage you to get things in relatively on time (or just punt if you have to and not leave it hanging over you all semester) so that you can move on to assignments for your other classes.
Using a high-level scripting language of your choice, write a program that implements the geometry transformations and lighting calculations Prof. Lee discussed in lecture to render an image of a scene consisting of a single 3-D object. For this assignment, you shouldn't worry too much about "modularity," "reuse," "extensibility," "good taste," etc., and you shouldn't worry at all about speed. This is a "quick and dirty" assignment that is primarily intended to make you review the material Prof. Lee has covered and make sure that you understand it. Direct3D, OpenGL, and XNA (using BasicEffect) handles most of this "behind the scenes," but we want to make sure you understand what is going on behind the scenes. Also, you wind up coding much of this "behind the scenes" work explicitly when you write vertex shaders in languages such as HLSL/Cg; hence, there is value in first testing your understanding of these basic computer graphics concepts using a simple language like MATLAB before we add the additional complexities of shader languages on top of it.
Your lighting model should include ambient and emissive components, as well as diffuse and specular components arising from a single light source.
At the top of your program, you should set variables that determine:
When we run your code, we should be able to change the variables at the top to render different scenes. The variables should be given easily understandable names.
In last year's version of this assignment, the students were required to find their own 3-D model and figure out how to read it in. This turned out to be pretty challenging. So, this year, we are going to let you benefit from the labors of last year's class. Here is a gzipped tarfile of some of the 3-D models used by last year's class. To give credit where it is due, I have added the names of the students who used the models to the filename. In some cases, the students could use the files as they found them; in other cases, they wrote conversion programs to turn some complex format into a simpler format, which I am giving you here. Some of the files consist of rows of 9 numbers, which are just the x,y,z coordinates of the three vertices of the triangles. Others consist of a list of vertices (again in x,y,z), followed by a list of triangles given as indexes into that set of vertices, or vice versa; some such files have a couple of numbers at the start giving the number of facets and vertices. Some such files have little other indicators such as "v" on the vertex lines and "f" on the facet lines. You will have to inspect the files to see what file is using what format and write your code accordingly. You may use one of these model for your assignment, or if you are feeling ambitious, you may find and use a model not given here (This won't be worth more points, but if you're a Halo fan, for instance, and find a model of the Master Chief - go for it! It could be fun.) Warning: some of the models in the given tarfile may have problems with correct triangle orientation. If you find that some of your triangles are mysteriously disappearing when you implement backface culling, try another file.
In the interest of simplicity, you should feel free to use the same emissive color for all the facets, the same specular color for all the facets, etc. If you feel like doing something more sophisticated, where different facets have different properties, you are welcome to do so, but it is not required for full credit.
For this assignment, use a "flat shading" model; have your program compute its own normal for each flat-faced triangle based on the vertex information for that triangle.
At an appropriate point in your processing chain, you should perform "backface culling" and remove those facets that are facing away from the camera. (Be careful to make sure the model you are using is following the conventions you are expecting it to!)
One you get things into "screen coordinates," you only need to worry about "clipping in z," i.e. delete all facets whose z-values all fall outside the viewingfrustum in the z-dimension. (If only some of the vertices fall outside the z-dimension, go ahead and render it.) We'll let the scripting languages native triangle drawing features worry about clipping in x and y.
Instead of using a z-buffer to handle the fact that some facets will obscure other facets, use "z-sorting." Z-sorting was popular when memory was expensive; for instance, the Playstation 1 uses z-sorting. Real-time implementations typically use some sophisticated data structures to do the sorting; here, you can just use the "sort" command built into whatever scripting language you use. For each facet, compute the average of the z-values of its vertices, and then sort the facets in order of these z-value averages. Then, render the facets in order of farthest to closest.
Again, don't worry about efficiency when doing the culling and sorting. It doesn't matter at this stage if your program runs more slowly with culling than without it. All we care about is that you understand the core operations.
Implementation language: You should choose a scripting language that has built-in matrix and vector operations, as well as a mechanism to draw filled 2-D triangles on the screen - we will let the language handle the rasterization process for you. (The language you choose may have built in 3-D graphics operations, but you should not use them for this assignment.)
We recommend using MATLAB; it has all the operations you need "out of the box," including dot and cross products; you can compute many dot and cross products at once with a single line of code. It should be available on most campus lab machines, such as the library and CoC and ECE computing labs. (You also may be able to get some use out of octave, which is an open-source MATLAB equivalent, although I haven't tried its graphics features so I'm not sure about that part.) MATLAB's vectorization features let you write compact, expressive code. MATLAB is now used in the intro CS class for engineers, and is also extensively used throughout the ECE curriculum, particularly in ECE2025: Introduction to Signal Processing. CS students will have been less likely to be exposed to it; however, an advanced CS undergraduate, who has had exposure to many different kinds of programming languages, will have little difficulty picking it up. In any case, if you are CS major, you will find MATLAB to be a worthy weapon to add to your arsenal, as it lets you try out a variety of numerical algorithms with a minimal amount of fuss. Here is an examples session at a MATLAB prompt that illustrates various features. ECE students will find this familiar; CS students should be able to quickly get a "feel" for the language.
>> % MATLAB comments start with a % sign
>> % type 'help command' into MATLAB to get help on a particular command
>> % 'ones(rows,columns)' generates a rows-by-columns matrix of 1s
>> % * by itself is matrix multiplication, but .* will do elementwise multiplication
>> % a semicolon at the end of a command suppresses output
>> a = ones(3,1) * (9:-2:1)
a =
9 7 5 3 1
9 7 5 3 1
9 7 5 3 1
>> b = (11:-2:7)' * ones(1,5)
b =
11 11 11 11 11
9 9 9 9 9
7 7 7 7 7
>> c = a + b
c =
20 18 16 14 12
18 16 14 12 10
16 14 12 10 8
>> d = a * b
??? Error using ==> mtimes
Inner matrix dimensions must agree.
>> d = a .* b
d =
99 77 55 33 11
81 63 45 27 9
63 49 35 21 7
>> % compute columnwise cross product
>> cross(a,b)
ans =
-18 -14 -10 -6 -2
36 28 20 12 4
-18 -14 -10 -6 -2
>> % compute columnwise dot product
>> dot(a,b)
ans =
243 189 135 81 27
>> 1 / (c + 3)
??? Error using ==> mrdivide
Matrix dimensions must agree.
>> 1 ./ (c + 3)
ans =
0.0435 0.0476 0.0526 0.0588 0.0667
0.0476 0.0526 0.0588 0.0667 0.0769
0.0526 0.0588 0.0667 0.0769 0.0909
>> dude = [1 2 3; 5 6 7; 11 12 29]
dude =
1 2 3
5 6 7
11 12 29
>> inv(dude)
ans =
-1.4062 0.3437 0.0625
1.0625 0.0625 -0.1250
0.0937 -0.1562 0.0625
>> dude(:,2) = [99 100 101]'
dude =
1 99 3
5 100 7
11 101 29
>> dude(1:2,:)
ans =
1 99 3
5 100 7
>> % most importantly for this assignment, MATLAB will also draw triangles for you!
>> the image below was created via these commands:
>> axis([-10 10 -10 10])
>> axis square
>> % the first argument to patch consists of x coordinates, the second consists of y
>> coordinates, and the third consists of an RGB triple
>> patch([3 4 6],[-4 -3 -6],[1 0 0])
>> patch([1 5 9],[10 13 14],[0 1 0])
>> patch([-3 -6 -9],[1 2 5],[0 0 1])
>> patch([-1 -3 -5],[-4 -6 -7],[0.25 0.5 0.3])
You can tell MATLAB to not draw edges on the patches via set(0,'DefaultPatchEdgeColor','none') - thanks to Michael Cook for the tip.
If you don't want to use MATLAB, you might try Python, Ruby, Visual Basic, TCL, or Perl with one of their numeric/scientific/graphical extensions; Mathematica or Maple might also be useful. You can even use Scheme or Lisp, if you can find one that will draw triangles. (If you insist, you can use a compiled language Java or C++ or something if you can find an appropriate matrix-manipulation library and are willing to lose the interactivity of use of an interpreted language. However, you will find that the assignment will take much longer than necessary if you take that route.)
The main reason we are asking you to use a flat shading model instead of Gourard shading is that MATLAB, as far as we can tell, will only do Gourard shading in a "colormap" sort of mode instead of a full RGB sort of mode.
Homogeneous coordinates in computer graphics are usually represented as rows vectors,
with operations conducted by doing row .* matrix
type operations. However, some of the "vectorized"
commands in MATLAB, such as cross and dot,
work better with coordinates stores along the columns; hence, you may find
it useful
to use some transposition operations (indicated using a single quote) to flip
between row and column representations as needed. Your mileage may vary.
Philosophy: The instructions to this assignment are deliberately a little bit vague - you should feel free to experiment a bit and come up with your own choices of parameters and implementation techniques. For instance, how exactly should you parameterize orientations, or the field of view? It's up to you! Here, you're not stuck with whatever choices an API designer made.
Deliverables: Package everything needed to run your script (3D data file, program, etc.), as well as three example scenes (in any common image format you'd like) created with your program with different parameters, and upload them to T-square as a zip file, StuffIt file, or gzipped tar file. Include "HW2" and as much as possible of your full name in the filename, e.g., HW2_Aaron_Lanterman.zip. (The upload procedure should be reasonably self explanatory once you log in to T-square.) Be sure to finish sufficiently in advance of the deadline that you will be able to work around any troubles T-square gives you to successfully submit before the deadline. If you have trouble getting T-square to work, please e-mail your compressed file to lanterma@ece.gatech.edu, with "MPG HW #2" and your full name in the header line; please only use this e-mail submission as a last resort if T-square isn't working.
The midnight due date is intended to discourage people from pulling all-nighters, which are not healthy.
Ground rules: You are welcome to discuss high-level implementation issues with your fellow students, but you should avoid actually looking at one another student's code as whole, and under no circumstances should you be copying any portion of another student's code. However, asking another student to focus on a few lines of your code discuss why a you are getting a particular kind of error is reasonable. Basically, these "ground rules" are intended to prevent a student from "freeloading" off another student, even accidentally, since they won't get the full yummy nutritional educational goodness out of the assignment if they do.
Assorted notes: