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||2. Scene, Camera, Lights!|
||3. Buffers, Textures, Shaders|
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EECS 487 PA1: Rasterization
EECS 487 PA1: Rasterization
This assignment is due on Saturday,
Oct. 3rd, 2015 at 12 noon.
We can help debug until Thu, 10/1, 7 pm.
Review the grading policy
page on the course website. Remember that to incorporate publicly available
code in your solution is considered cheating in this course.
To pass off the implementation of an algorithm as that
of another is also considered cheating. For example, if the
assignment asks you to implement sort using heap sort and you turn in
a working program that uses insertion sort in place of the heap sort,
it will be considered cheating. If you can not implement a required
algorithm, you must inform the teaching staff when turning in
your assignment by documenting it in your writeup.
In this assignment you will implement the midpoint line drawing
algorithm to rasterize line segments, scan conversion of triangles,
line clipping and line anti-aliasing. You will use barycentric
coordinates to interpolate colors and provide anti-aliasing for
lines and triangles.
Graded Tasks (100 points total)
- Implement the midpoint algorithm for line
segments. 5 pts
- Implement triangle rasterization. 5 pts
- Implement line clipping. 25 pts
- Implement anti-aliased rendering/filtering for lines. 25 pts
- Implement anti-aliased rendering/filtering for triangles. 25 pts
- Create a fun and interesting scene. 10 pts
- Writeup. 5pts
Support Code: Vcanvas
Download and extract the support code gzipped tarball.
The support code should compile under Linux, Mac OS X, and Windows.
We provide a Makefile to build the application on the command line.
We do not provide any IDE (Eclipse, Visual Studio, or XCode) project
files. If you're going to use an IDE, please take a look at the
Makefile to find out which source files, header files, and
libraries must be included in your project.
For this assignment, the Makefile builds two applications.
The first one, called vcanvas, depends only on the
files vcanvas.cpp, rasterizer.cpp, rasterizer.h,
and xvec.h. The second one, called draw, requires
all the .cpp and .h files provided, except
To use an IDE you must create two separate projects, one to build
vcanvas, the other to build draw.
If you include both draw.cpp and vcanvas.cpp
in either project, your IDE will complain and you won't be able
to build either program.
It may also be helpful to read the details on setting up IDE
projects in the Building OpenGL/GLUT Programs course note.
Once you've built vcanvas and run it, you should see
a window similar to the one from Labs 1 and 2. The
program displays a coarse grid of virtual pixels and allows you to
draw one line or one triangle at a time. Two clicks on different
virtual pixels give you a line. A third click on a pixel different
from the first two gives you a triangle. The program is very simple
and doesn't check for degenerate, e.g., colinear, triangles. Either
of the following actions clears the grid, ready for another line or
triangle to be drawn:
In addition, the program offers the following functionalities, listed
with their keyboard shortcuts:
- Clicking on either end points of a line
- Clicking anywhere on the grid after a triangle is drawn
- Pressing the SPACEBAR or ESC key on the keyboard
|a ||Toggles anti-aliasing
on and off. |
|c ||Toggles clipping
on and off. When clipping is on, a clipping window is drawn on
the grid. Only line clipping is currently supported; triangle
clipping is not supported.
||Turns the first (red) vertex of the line or triangle transparent, cycling
through alpha values of 0.75, 0.5, 0.25, 0.0, and back to 1.0 on each press
of the keyboard shortcut. (The size of alpha decrement is controlled by
the ALPHA_DEC macro in vcanvas.cpp.)
||Quits the program.
rasterizer.cpp for /*YOUR CODE HERE*/ to find where
you can put your implementation. All your modifications must be
rasterizer.h if necessary).
Do NOT use any OpenGL state or call any OpenGL function. You are writing a
software rasterizer; to use OpenGL's rasterizer would be considered cheating.
Besides, the support code will malfunction if you use OpenGL in your code.
The vector class
is used heavily throughout this course. Be comfortably familiar with it.
The assignment uses two graphical primitives. The first is the line.
rasterizer.cpp implement the following function using the
midpoint line rasterization algorithm:
void Line::drawInRect(XVec4i& clipWin);
clipWin is described in the
Line Clipping section below.
The lines drawn should be 1-pixel thick, that means every row
(or every column, or both) contains at most one pixel.
You can draw a solid red line first to test your line drawing code.
You may, and are expected to, simply adapt your Lab1 code for this
task (which is why it is not worth that many points).
Once your line drawing code is correctly implemented, incorporate color
interpolation across the line using the parametric equation of a line segment;
do not forget to interpolate the alpha values also.
To set pixels use the function:
void drawPoint(XVec2f& p, XVec4f& color);
To test your line drawing code, build and run the vcanvas application.
Click in the virtual canvas to set the first end point of the line.
Then move the mouse and click on another virtual pixel to set the second
end point, release the mouse button and click again (double click) on the
same virtual pixel to draw a line. Moving the mouse before that third
click produces a triangle.
The second graphical primitive is the triangle.
rasterizer.cpp implement the function:
bool Triangle::containsPoint(XVec2f& p, XVec4f& pointColor);
It returns a boolean denoting whether the point
within the triangle; if it is, the function returns
pointColor to be the interpolated color of the
vertices' colors, using barycentric coordinates. You may, and are
expected to, adapt your Lab2 code for this task. To test your
triangle drawing code, you may want to return only the color blue
initially. Once your triangle drawing code is correctly implemented,
incorporate color interpolation using barycentric coordinates; again,
do not forget to interpolate the alpha values.
Next implement the function:
void Triangle::drawInRect(XVec4f& clipWin);
It should draw a triangle using scan conversion; be sure to have it
use the function
containsPoint() above! Build and run
the vcanvas application to test your triangle rasterization code.
You are to implement the Cohen-Sutherland trivial accept/reject and
Cyrus-Beck line clipping alogrithms.
The goal is to discard any line segment that lies entirely outside the
clipping window, and trim line segments that lie partially outside the
clipping window, leaving only parts that are inside the window. Thus
line clipping must be done at the start of the
clipWin of function
Line::drawInRect(XVec4f& clipWin) is a 4-vector
containing, in order, the x-coordinate of the lower left corner,
the y-coordinate of the lower left corner, the width, and the
height of the clipping window.
function before drawing. When clipping, do not modify the vertices
of the given line segment, instead use local variables to store the
clipped endpoints. If you have written your line rasterization code
above to use the vertices of the given line segment, you would need
to modify it to use the clipped endpoints instead. When a line is clipped,
its color interpolation must be clipped accordingly. For example, if
one vertex is red and the other is green and the line is clipped
three quarters of the way towards green, the clipped line should
show only gradations of green.
Note: the triangle clipping provided in draw.cpp is a brute
force rejection test of every pixel. Do not use the brute
force method for your line clipping. You are required to
implement both the Cohen-Sutherland and the Cyrus-Beck algorithm. Use
Cohen-Sutherland to trivially accept/reject a line. Then clip those
lines that Cohen-Sutherland cannot trivially accept/reject using the
Cyrus-Beck algorithm. If you cannot implement either algorithm, you
must say so in your writeup. To pass off another algorithm as the one
required is considered cheating.
To test your line clipping code, first draw a clipping window by
c', then draw a line with one or both end points outside the
clipping window. Pressing '
c' repeatedly toggles the clipping window
on and off. The clipping window is of fixed size and location. The
lower left corner of the clipping window is currently set at (4,4) in
virtual pixel coordinates (controlled by macros CMINX and
CMINY in vcanvas.cpp). The size of the clipping
window is (screen_width/2, screen_height/2). Note that a
virtual pixel at coordinate (x, y) is centered at (x+0.5,
y+0.5). So when drawing pixels be aware when you need to use
rintf(), floorf(), or ceilf() to convert
from float to int. When clipping is on,
portion(s) of the displayed line outside the clipping window is shown
in shades of grey and the portion inside the clipping window is shown
in color. Your clipping code should not change the rasterization of a
line (which pixels are turned on to draw the line). However, due to
precision error, you may find some pixels inside the clipping window
near its boundaries to be grayed out. This is ok.
What to Test
Here are some of the cases we will test for:
- Lines entering the clip window from 8 directions are properly clipped.
- Lines leaving the clip window to 8 directions are properly clipped.
- Lines straddling the clip window are properly clipped.
- Horizontal and vertical lines are properly treated.
- Cases where Cohen-Sutherland trivial accept/reject test fails
are properly clipped.
- Clipped lines should lie exactly on the original unclipped lines.
- Color is properly clipped; lines completely outside the
clipping window should be grayed out. Some pixels inside the
clipping window near its boundary may be grayed
out due to precision error. This is ok.
The Line object has a member variable denoting whether it
should be drawn anti-aliased. If this variable is set to true, draw
your line anti-aliased using an area-sampling based algorithm briefly
described as follows.
Considering only lines with slope
0 ≤ m ≤ 1,
the midpoint algorithm begins by drawing a point, then it moves right,
and perhaps up, and repeats. Every time the algorithm draws the point
(x,y), it also draws the point above or below the point.
Doing this will create a
two-pixel thick line. Now just set the alpha values of those two pixels
"appropriately" and the line will appear smoother. It is part of the
assignment for you to determine how to set the alphas appropriately.
(Hint: between what values is
fmid/dx in the midpoint algorithm?)
Further, if the alphas of the line's two endpoints are not the same,
for each point on the line, the alphas of the two pixels should add
up to the interpolated alpha at that point. This is a form of anti-aliasing
by area sampling, also known as pre-sample filtering. See Lecture 8
for further discussion on the algorithm.
Press the '
a' key to toggle anti-aliasing on and off.
The figure below shows an anti-aliased line clipped to the clipping
window. (The color of the anti-aliased line becomes darker
when clipping is turned on. This is due to our drawing a greyed-out
unclipped line under the clipped line. The color of each pixel is
blended with the greyed-out pixel, darkening the color. This is okay
as long as your pixels do not turn completely grey.)
The Triangle object has a member variable denoting whether it should be drawn
anti-aliased. If this variable is set, draw the triangle anti-aliased using
multi-sampling with at least four samples. That is, for every pixel, compute
and average the colors of at least four subpixels. Recall that we differentiate
multi-sampling from super-sampling. Whereas super-sampling draws into a large
buffer and then average down and re-draw to a smaller buffer, multi-sampling
averages the color of
multiple sub-pixels of a pixel in a single buffer. It does not use
multiple buffers of different sizes. You can treat a given pair of pixel coordinates
as specifying the lower left corner of the unit area covered by a pixel.
Press the '
The figure below shows an anti-aliased triangle:
Draw an interesting scene using the provided drawing application (described in
the next section). Do not simply throw down 42 triangles and call it a
Put some time into it and play! Try to convey lighting or make a happy clown.
Graphics is part programming, part math, and part art, so use your imagination!
See samples from previous terms in the
Before having fun with this part, read the following section on how to use the
The support code comes with a simple drawing application that utilizes
your rasterizer. To build the drawing program, type "make
draw" and run the draw executable binary file.
You should see the application running
and showing its window. By default, the application is set up to use your
sofware renderer. Until you have your software renderer implemented, you
would want to toggle the application to use the hardware renderer, as
described below, to see how it is supposed to behave.
It is highly recommended that you skim through the code to understand how this
application works (it actually has a lot less code than you might imagine).
The application provides two panels, the canvas on the left, the
picker on the right. The picker is fixed size and contains a few
"sliders" and "buttons"---even if it ducks back to a 1980s UI (such is life
To draw a triangle in the canvas, click on the canvas with the left
mouse button and do not release. Drag the mouse and then
release. This sets the first two vertices of the triangle. Then move
the mouse and watch a triangle grow. Click again to set the third
vertex to complete the triangle. Repeat to create multiple
triangles. To draw a line, do not move the mouse after specifying the
second vertex, instead click it at the same location one more
a' key to toggle anti-aliasing on and off.
Remember that if you cannot implement an algorithm, you must disclose
it in your writeup. This applies to the anti-aliasing algorithms also.
Clicking on an existing triangle selects it. Selection of triangles
uses the function
The above explanation is enough to create wonderful scenes.
The application does offer a little more functionality for ease of use.
Right-click in the application window and a popup menu appears. Each
menu item is listed with its keyboard shortcut.
containsPoint(). Make sure to test
this function with "hardware rendering" turned on. When a line or
triangle is selected, its vertices have boxes drawn on them and a thin
edge surrounds it. One vertex will have a yellow box; this is the
selected vertex. The picker on the right can be used to modify the
color of the selected vertex (which is always displayed at the top of
the picker). Try playing with the sliders (the diamond-shape outlines
on the "Opacity", "Hue", and "Saturation+Value" boxes) to change the
hue, saturation, value (color spaces such as this, HSV, will be
discussed later in the course), and alpha (opacity) of the vertex.
User can select any already drawn line or triangle or its vertices and
change the color accordingly. The picker will not function if no
vertex is selected.
||Toggles a grid on and off to help alignment of vertices.
||Toggles snapping on and off. With it enabled, vertices will
automatically snap to the grid (even if it is not visible).
||Deletes the currently selected object.
||Toggles anti-aliasing of the currently selected object. Polygon
anti-aliasing in the hardware renderer is not implemented, so
do not expect to compare your results against those produced
by the hardware renderer.
||Toggles between hardware and software rendering. Toggle on
hardware rendering to see how the application is supposed to
behave in terms of color interpolation and clipping using
OpenGL instead of your code. Note that without your
Triangle::containsPoint(), triangle selection
||Enables the user to draw a clipping window on the screen: press
c', then press the mouse button to mark one corner
of the clipping window, without releasing the mouse button, drag
the mouse to the opposing corner of the clipping window and
release the mouse button.
||Toggles clipping on and off toggle clipping off and on (when drawing
a clipping window, clipping is automatically toggled on). When
clipping is toggled on, lines and triangles will be clipped to the
clipping window; visually, the portions inside the clipping window
will be shown in color, while those outside will be shown in grayscale.
Toggle on "hardware rendering" to see how clipping is supposed to work.
You only need to implement the line clipping function, the
draw program provides the triangle clipping function.
||Brings the currently selected object forward. There may be no
visual change if the object "above" it does not overlap. The
user may have to tap 'f' a few times to move an object forward
||Brings the currently selected object to the front.
||Sends the currently selected object backward. There may be no
visual change if the object "below" it does not overlap. The
user may have to tap 'b' a few times to move an object backward enough.
||Sends the currently selected object to the back.
||Clears the canvas and creates a new scene. It does not save the current
canvas or re-confirm canvas clearing, so be careful!
||Type in the name of a file to open in the input area above the canvas.
||Saves the scene. It also saves a tga image of the scene. If this is the
first time you try to save and the file is untitled, CTRL+s behaves the
same as CTRL+SHIFT+s below. In Mac OS X, choosing "Save" under the "File"
menu or hitting CMD+S will store a screen shot of the application as a
tiff file instead (which is not what you should turn in).
||Type in the input area above the canvas the name of a file for saving.
It also saves a tga image of the scene under the same name, appended
with a ".tga " extension, as shown in the screen shot below. Note that
in Mac OS X, choosing "Save As" under the "File" menu or hitting CMD+SHIFT+s
will create a screen shot of the application as a tiff file instead.
||Cancel the current operation. It applies to line drawing, triangle drawing,
clip area drawing, and file name input.
The application does not feature undo/redo nor cut/copy/paste. When the grid is on,
it is visible; when snapping is on a magnet is shown in the upper left corner; whether
rendering is currently done in hardware or software is displayed in the lower right
corner. Play, fidget, and have fun!
WARNING: The program reads and writes a simple file format. Modify the files
created at your own peril.
After completing this project take a moment to understand why hardware and software
rendering differ so greatly in speed. Think about how the graphical components on
screen interact; this is UI stuff but still heavily graphics-related. Imagine some
simple additions to the application and how they may be accomplished. Hopefully those
who use Photoshop or Gimp now appreciate their true power.
Test your compilation!
Your submission must compile without errors and warnings
(on Visual Studio, warnings of "PBO file not found" is ok).
Code that does not compile
will be heavily penalized.
Create a writeup in text format that discusses:
Save an image file from the draw application (using CTRL+s,
not by capturing a screen shot!) and post the image (one or more)
to the course's Image Gallery
by logging in (using ssh) to an ITD/CAEN Linux machine and run
- Your platform -
Linux, Mac OS X, or Windows, and which version and flavor of each.
- Anything about your implementation that is noteworthy. Be sure to
explain how you determine the "appropriate" alpha values in line
anti-aliasing and how corner cases were implemented.
- The name of the scene you created and a brief description.
- Feedback on the assignment.
- Name the file writeup-uniqname.txt.
For example, the person with uniqname
tarukmakto would create
On Windows, you can use MobaXterm Personal/Home Edition to login to an ITD/CAEN Linux machine.
Do not include the rendered image in your PA1 files below.
Your PA1 files then consists of your
% cd <to where your image.tga file is located>
% /afs/umich.edu/class/eecs487/scripts/postimg <image.tga> [<image2.tga ...>]
rasterizer.cpp, and, if modified,
Your code must not require other external libraries
or include files other than the ones listed in the Makefile.
To turn in your PA1, upload a zipped or gzipped tarball of your
PA1 files to the CTools Drop Box.
Keep your own backup copy!
The timestamp on your uploaded file will be your time of submission.
If this is past the deadline, your submission will be considered late.
You are allowed multiple "submissions" without late-policy implications
as long as you respect the deadline.
Turn in ONLY the files you have modified.
Do not turn in support code we provided that you haven't modified.
Your code must not require other external libraries or include files
other than the ones listed in the Makefile.
For this assignment, you should turn in only your
Do not turn in any binary files (object, executable, or image)
with your assignment. Post your image(s) to the course's Image
Gallery using the
postimg script as explained above.
Do remove all printf()'s or
cout's and cerr's you've added for debugging
It is part of the Honor Code of this course that the overall design and final
details and implementation of your programming assignments must be your own.
If you're stuck in either the design, implementation, or debugging of the
assignment, you're allowed and encouraged to consult with your classmates.
However, the original design and final implementation details must
all be your own. So you cannot come up with the original design
together with your classmates. You can consult your classmates
only after you've come up with your own design but ran
into some specific problems. Similarly for the implementation, you
cannot consult your classmates prior to writing your own
implementation. And in all cases, you're not allowed to look at
any of your classmates' source code, not even in order to help them
to debug. The same applies to design and implementation from
Unreadable code can cost you up to
- Use a reasonable organization for your overall program:
- Design a fairly reasonable class structure. On the one hand,
don't stick everything into one class/struct. On the other hand, don't be
bureaucratic and require the reader to follow one class definition
after another to find a single line of code wrapped in n layers of
methods, with each method doing nothing but calling the next one.
If the way you design your code feels sloppy to you, it
probably is. Utilize multiple files in a way that is consistent with
the general use of C/C++. Don't use more files than necessary, you don't
have to put each class/struct in a separate file of its own.
Don't use literals!
- Use either
to give your literals meaningful names. We do deduct points for each
occurrence of literals, even if it is the same one. The only
exceptions will be for loop counter, command-line options, NULL(0) and
TRUE/FALSE(1/0) testing/setting, help and error messages printed
out to user, and mathematically well-defined uses
such as (1-probability) or (1-interpolating_factor) or to test for
negativite values (< 0), etc. The intent here is to ensure that
should the literal value need to be changed in the future, it only
needs to be changed at one place. Thus defining '0' as "ZERO" does not
serve this purpose because should the value '0' needs to be changed in
the future, the macro "ZERO" becomes totally misleading. We will thus deduct
points for such semantically meaningless names also.
Use reasonable comments:
- Explain what each class does and what each data member is used
for. A one or two line description of most member functions is also
desirable. Where you use non-standard coding techniques, document them.
List your name and the date last modified for each file.
- Remember that a useless comment is worse than no comment at all.
int temp; // declare temp. variable
would be an example of a useless comment which just makes code harder
Use reasonable formatting:
- From indentation alone, it should be obvious where a given code
block ends. Avoid lines that wrap in an 80 column display wherever
possible. Your code should be tight, compact, and visually tidy. Don't
let bits and pieces fly off every which way. Your code is not abstract
- Use reasonable and informative variable names, but limit name
size to a reasonable length. A 40-character name better has a very good
reason to exist. Variable names like 'i' and 'j' can be reasonable, but
you should not use such variables to store meaningful long-term data.
Other than LCV (loop control variables) you should use descriptive
names for your variables, functions, classes, methods, structures, etc.
Reduce, Reuse, and Recycle your code, algorithms, and structures:
- Try using inheritance, templating, polymorphism (virtual
function), or similar methods to reduce the size of your code. Do not
unnecessarily duplicate code. Less code leads to less debugging. If you
find yourself rewriting basically the same code more than once, stop
and try to see if you can somehow reuse the code by making it a
function call or implementing a polymorphic function.
We will check for empirical efficiency both by measuring the memory
usage and running time of your code and by reading the code. We will
focus on whether you use unnecessary temporary variables, whether you
copy data when a simply reference to it will do, whether you use an
O(n) algorithm or an O(n^2) algorithm,
but not whether you use
Nor whether your ADTs
have the cleanest interfaces. In general, if the tradeoff is between
illegible and fast code vs. pleasant to read code that is unnoticeably
less efficient, we will prefer the latter. (Of course pleasant to read
code that is also efficient would be best.) However, take heed what you
put in your code. You should be able to account for every class, method,
function, statement, down to every character you put in your code.
Why is it there? Is it necessary to be there? Can you do without?
Perfection is reached not when there is nothing more to add, but when
there is nothing more that can be taken away, someone once said.
Okay, that may be a bit extreme, but do try to mind how you express
yourself in code.
Hints and advice
Testing Your Code
We will be grading for correctness primarily by running your program on
a number of test cases.
If you have a single silly bug that causes most of the test cases to
fail, you will get a very low score on that part of the programming
assignment even though you completed 95% of the work.
Most of your grade will come from correctness testing.
Therefore, it is imperative that you test your code thoroughly.
Each testcase should test only one particular feature of your
If any part of this document is unclear, ambiguous,
contradictory, or just plain wrong, please let one of the teaching staff know. Have fun coding!