ECE4893A/CS4803MPG: Multicore and GPU Programming for Video Games
Homework #1: “Roll Your Own” 3-D Rendering
Due: Monday, Sept. 24 at 23:59:59 (via T-square)
Late policy: The homework will be graded out of 100 points. We will
accept late submissions up to Thursday, Sept. 27 at 23:59:59; however,
for every day that is it is overdue,
we will subtract 20 points from the total. For
instance, it you turn it in late but turn it in by Tuesday, Sept. 25,
at 23:59:59, we will take off 20 points.
(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.)
[I’ve gotten some good questions on this homework; I’ve included some
clarifications and modifications in the writeup below in boldface.]
Using a high-level scripting language of your choice, write a program that
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,”
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 and OpenGL 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 or 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
and specular components arising from a single light source.
At the top of your program, you should set variables that determine:
- The position and RGB color of the light source. Clarification:
This line originally included the direction; that’s only relevant if
you’re using a spotlight effect. Coding a spotlight effect is
optional, so if you’re not trying for one, you don’t need to
specify a light direction.
- The RGB color of the ambient light.
- The position and orientation of the camera
- The position and orientation of the object.
- The “near” and “far” distances of the viewing frustum.
- The field of view.
When we run your code, we should be able to change the variables at the top
different scenes. The variables should be given easily understandable names.
You will need to find a 3-D model on the web, and figure out how to get that
model in a
format that you can read into your scripting language. We recommend choosing
a relatively simple
model that consists of a small number of facets. You can often find programs to
convert strange formats into easy-to-read ASCII formats. (If you get into 3-D
wrangling the dozens of different formats is something you will have to
wrestle with sooner
or later, so you might as well start wrestling with it now.) No two
students should be
using the same model.
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 (maybe based on information from your 3D object
file), you are welcome to do so, but it is not required for full credit.
For this assignment, use a “flat shading” model; throw away whatever normal information is
in the file you downloaded, and 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!) Clarification: It seems that a lot of models
out there are not consistent in following either a right hand or left
hand rule. We want to see the line(s) in your code that perform(s) this
operation, but if you see that half your facets randomly disappear when
you turn this on because the modeler was sloppy, feel free to comment it
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
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
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. MATLAB’s vectorization features let you write compact,
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])
If you don’t want to use MATLAB, you might try Python, Ruby, or
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’re
willing to lose the interactivity of use of an interpreted language.
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
work better with coordinates stores along the columns; hence, you may find
to use some transposition operations (indicated using a single quote) to flip
between row and column representations as needed. Your mileage may vary.
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.
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 “HW1” and as much as possible of your full name
in the filename, e.g., HW1_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 firstname.lastname@example.org, with “MPG HW #1” 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.
- Don’t get the ideas of “spotlight” and “specular” confused. They give
similar kind of effects but are quite different things.
- A few folks have tried writing programs that use CAD files with
polygons with variable numbers of sides within the same file.
That way lies madness. You can
do the assignment with a file with, say, quadralaterals iinstead of triangles
– everything will still work (after all, the Sega Saturn GPU rasterized
quadrilaterals and not triangles) – but you can’t easily write code that will
mix and match. You want a CAD file where all the polygons have the same
number of sides. Triangles are probably the easiest to code up.
- Once you transfer everything to screen coordinates, specifying
the x,y axis limits on your plot is sufficient to specify the “field of view.”
- A good way to think about the camera transformation is to work
“backwards” – you’re essentially translating the your universe of
objects, including the
camera, so the camera sits at the origin, and then rotating your universe
including the camera, around the origin,
so that the camera lines up along with your axes. Another way to think
about it is to imagine creating the transformation of your camera as if
it were an object, and then taking the inverse of the resulting matrix. If
what I wrote here makes no sense, ignore it; it’s the way I think about it,
but you’ve probably figured out my brain is a bit strange.