# Assignment 11: Mass-spring System solution

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In this assignment, you will implement a simple mass-spring system to animate a piece of cloth. The template
include implementing the simulation step using semi-implicit Euler integration (Excercise 1), adding external
forces to get an interesting animation (Excercise 2), as well as recomputing the normal vectors of the cloth to
get a nicer rendering (Excercise 3).
Template
The new template implements for you the rendering of the cloth and the cloth geometry definition. The
rendering does not update at this point the normal vectors, which is the goal of the Exercise 3. Important
information regarding the template:
• geometry.js file includes now of the definition cloth geometry, i.e., vertices and triangles. You are free
to analyze the code, but what is important for the assignment is the order and the number of vertices.
The cloth is defined as a grid of vertices. One row and one column consists of cloth size vertices.
This gives the total number of vertices (also particles for the simulation) cloth size×cloth size.
The vertices of the cloth are ordered row by row starting from the top-left corner. Hint: the first and the
last vertices of the top row have indices 0 and cloth size-1.
• The whole rendering pipeline is defined for you. In this assignment, you do not have to code anything
related to WebGL. In particular, we have already defined for you the GPU buffers, which store positions
and normals, that can be updated every frame. We also added the code which does the update based
on the content of cloth vertices and cloth normals arrays.
• The template contains a well-documented skeleton of the simulation. Please check the main files starting at line 180. The functions you should modify in the assignments are: updateCloth, updateNormals.
Of course, you are encouraged to play around with the other parts, especially parameters of the springs
and time step.
Exercise 1 [9 points]
To solve this exercise, you need to modify the updateCloth function to implement one step of the simulation. Follow the comments and the skeleton, which should make your task easier. Remember about including
both the forces coming from Hooke’s spring model and damping. Remember to constrain some of the particles, so they do not move. Otherwise, your cloth will not hang but fall under gravity.
Exercise 2 [3 points]
Use the simulation to animate the cloth in an exciting way. To this end, add time-depended external forces
acting on each particle. You can use for this purpose time variable, which is already defined in the template
and contains the time elapsed from the beginning of the simulation counted in milliseconds. Like that, you
can, for example, simulate the cloth moving on a wind. Additionally, you can release at some point the cloth
such that it flies away.
Exercise 3 [3 points]
If you solved exercise 2, you probably realized that something is wrong with the illumination of your cloth. In
particular, you do not see it nicely folding. This is because the normal vectors of the cloth are not recomputed
during the simulation. To fix this, implement the function updateNormals, which should updated the
cloth normals array based on cloth vertices array.
Submitting the assignment
Submit an archive file (ZIP) with all the files required for running your application. The additional readme
file should contain information about the authors of the solution as well as explanation of any encountered
problems.
Solutions must be returned on December 30, 2022 via iCorsi3