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Task01: Implicit Time Integration

preview

Deadline: Apr. 20th (Thu) at 15:00pm

Before Doing Assignment

If you have not done the task00, do it first to set up the C++ graphics development environment.

Follow this document to submit the assignment, In a nutshell, before doing the assignment,

  • install eigen library following this document
  • make sure you synchronized the main branch of your local repository to that of remote repository.
  • make sure you created branch task01 from main branch.
  • make sure you are currently in the task01 branch (use git branch -a command).

Now you are ready to go!

Problem 1

  1. Build the code using cmake
  2. Run the code
  3. Take a screenshot image (looks like image at the top)
  4. Save the screenshot image overwriting task01/problem1.png

problem1

This program solves the equation of motion ${d^2 r}/{d t^2} = - {1}/{r^2}$ and visualize it in the polar coordinate, simulating the motion of small objects under gravity. The points bounce at the surface $r=0.5$. The movement of blue object is integrated using the Forward Time Integration. Observe the energy gain artifact.

Problem 2

Modify the code at line #43 and line #44 in main.cpp to integrate the equation of motion using the Backward(Implicit) Euler Method scheme for the movement of Red object.

Save the screenshot image overwriting task01/problem2.png

problem2

After Doing the Assignment

After modifying the code, push the code and submit a pull request.

Notes

  • Do not submit multiple pull requests. Only the first pull request is graded
  • Do not close the pull request by yourself. The instructor will close the pull request
  • If you mistakenly merge the pull request, it's OK, but be careful not to merge next time.