ESC203: Spring 2023: Monday Lecture: 10:15-11:00 in Y27-H-35/36 with Joachim, Exercises: 11:15-12:00 in Y27-H-35/36 with Sebastian

TA: Sebastian Schulz

20. Feb. 2023:

1. Simulating light - First Steps to Ray Tracing
2. Introduction to ray tracing book

27. Feb. 2023

1. Ray Tracing - Material Properties

6. Mar. 2023:

1. Ray Tracing - Triangulations
2. The famous UTAH Teapot triangultion (source: Stanford media lab)

13. Mar. 2023:

1. Fast Fourier Transform

20. Mar. 2023:

1. Fast Fourier Transform, part 2

27. Mar. 2023:

1. Solving PDEs, different methods compared

3. Apr. 2023:

1. Multigrid Method

17. Apr. 2023:

1. MacCormack's Method

Assignments should be individual and should be in python and, if you are using non-standard python libraries, provide a correct virtual environment!

For help getting started with virtual environments, please read carefully Python Virtual Environments for Pip and Python Virtual Environments for Conda.

You should email 3 things to Sebastian (sebastian.schulz@uzh.ch):

1. The working python source code
2. The requirements.txt file for your virtual environment
3. A .pdf or .png image or animation of the output of your program

Template: template.zip

Instructions:

Please add the names of the people you work together (if you do) to the comment section of your python scripts.

Create a virtual environment using

Pip

- run virtualenv yourenv_name to create a virtual environment

- run source yourenv_name/bin/activate to activate yourenv_name

- install necessary libraries that you want using pip install package_name

- work in that directory, get your outputs (*.pdf, *.png, *jpeg, *.mp4, etc…)

- run pip freeze > requirements.txt to get your list of libraries

Conda

- run conda create -n yourenvname python=x.x anaconda to create a virtual environment

- run source activate yourenvname to activate yourenv_name

- install necessary libraries that you want using conda install -n yourenv_name package_name

- work in that directory, get your outputs (*.pdf, *.png, *jpeg, *.mp4, etc…)

- run conda list –export > requirements.txt to get your list of libraries

Raytracing:

1. Write a basic ray tracing algorithm for spheres illuminated by a single light source (hand in by Monday, February 27th, 2023).
2. Implement the Phong model described in the lecture. Once you are done, you can implement reflection and refraction for transmissive materials (glasses, coatings) into your model. Optional: try out the approximations that make the code run faster (Blinn-Phong model, Schlick's approximation, replacing the power alpha with gamma, assuming beta is small) (hand in by Monday, March 6th 2023).
3. Ray trace the triangulated Utah tea pot. You can start by implementing the bounding volume hierarchy treewalk algorithm to quickly find the intersection points on the triangles. You can then interpolate the surface normals using the barycentric coordinate system on the triangle (hand in by Monday, March 13th, 2023).

Fourier transforms:

1. Implement the Cooley-Tuckey method for the FFT algorithm by splitting the W matrix into even and odd parts iteratively until you reach W_2 (hand in by Monday, March 20th, 2023).
2. Use the 2D-FFT to calculate the potential of a particle distribution on a 2D grid. Start by assigning the masses of the particles to the cells using a mass-assignment scheme of your choice (i.e. nearest grid point, cloud in cell, etc.), which will give you a density grid. Then you can Fourier transform the density grid in two dimensions, from which you can easily calculate the potential in Fourier space, according to the Poisson equation written in the lecture notes. You can then get the real-space potential by inverse Fourier transformation of the Fourier space potential (hand in by Monday, April 3rd, 2023).

Muligrid method:

1. Implement a 1-step v-cycle of the multi-grid approach and compare the result to SOR. After this, you can try out different cycles, e.g. the deep v-cycle, or the w-cycle (hand in by Monday, April 17th, 2023).

MacCormack's method:

1. Otional bonus task: Implement MacCormack's method for solving the 1D-Burgers' Equation and compare to the results obtained using the Lax-Wendroff method.