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Task02: Rasterization of Parametric Curves

Deadline: April 25st (Thu) at 15:00pm

This is the blurred preview of the expected result:

preview

When you execute the program, it will output an PNG image file (output.png) replacing the image below. Try making the image below and the image above look similar after doing the assignment.

preview

Instruction

Please follow this instruction to prepare the environment to do the assignment

If you did not do the task01 assignment, you need to prepare git, cmake, and C++ compiler in your computer to complete this assignment. Read the following document to install these.

How to Set Up C++ Programming Environment

If you had some trouble with git in the local repository in the previous assignment, clone your remote repository again to avoid trouble.

$ git clone https://github.com/ACG-2024S/acg-<username>.git

Go to the top of the local repository

$ cd acg-<username>     # go to the local repository

Update Local Repository

Update the local repository on your computer

$ git checkout main   # set main branch as the current branch
$ git fetch origin main    # download the main branch from remote repository
$ git reset --hard origin/main  # reset the local main branch same as remote repository

After this command, you will see the local repository is synced with the remote repository at https://github.com/ACG-2024S/acg-<username>

Create a Branch

To do this assignment, you need to be in the branch task02.
You can always check your the current branch by

$ git branch -a   # list all branches, showing the current branch

You are probably in the main branch. Let's create the task02 branch and set it as the current branch.

$ git branch task02   # create task0 branch
$ git checkout task02  # switch into the task02 branch
$ git branch -a   # make sure you are in the task02 branch

The environment is ready.

Problem1

Install eigen under acg-<username>/external by the following command

$ pwd # make sure you are in acg-<username> directory 
$ git submodule update --init external/eigen # clone the "eigen" repository (this may take one or two minutes)

Make sure you have a header file Dense at

acg-<username>/external/eigen/Eigen/Dense

Eigen can be used as a header-only library. You do not need to compile it to do this task.

Next, compile the code with out-of-source build by making a new directory for build task02/build and compile inside that directory

$ cd task02  # you are in "acg-<username>/task02" directory
$ mkdir build
$ cd build
$ cmake -DCMAKE_BUILD_TYPE=Release .. # configure Release mode for fast execution
$ cmake --build .

Now you will see the output.png is updated. The output.png will show an angular shape of the letter R. Now let's write a program to make the font shape smooth as the original one.

Problem2

The code you compiled above uses the *Jordan's curve theorem to find whether the center of a pixel is inside or outside the character.The code counts the number of intersections of a ray against the boundary. The boundary of the letter is represented by sequences of line segments and quadratic Bézier curves. The Problem1's output was angular because the Bézier curve was approximated as a line segment.

Modify the code main.cpp around line #65 to compute the number of intersections of a ray against the Bézier curve. The output will be the letter R with smooth boundary.

Submit

Finally, you submit the document by pushing to the task02 branch of the remote repository.

cd acg-<username>    # go to the top of the repository
git status  # check the changes
git add .   # stage the changes
git status  # check the staged changes
git commit -m "task02 finished"   # the comment can be anything
git push --set-upstream origin task02  # update the task02 branch of the remote repository

got to the GitHub webpage https://github.com/ACG-2024S/acg-<username>. If everything looks good on this page, make a pull request.

Trouble Shooting

If you have trouble with #include <filesystem>, your C++ compilar is very old. Try update one. Following command may work tos specify which compilar to use on linux & Mac

export CC=/usr/local/bin/gcc-8
export CXX=/usr/local/bin/g++-8
cmake ..

Reference