task3

Task3: Mass-spring System

Deadline: May 27th (Thursday) at 15:00pm

Setting Up

Please take a look at the following document for environment setup, creating branch, and making pull request.

• How to Submit the Assignment

In this assignment, it is necessary to install Eigen library. Please follow the following document for setting up.

• How to set up the Eigen Library

Additionally, you need the newest versio of the library DelFEM2 in pba-<username>/3rd_party . Please keep this library installed and updated by.

$ cd pba-<username> # go to the top of local repository
$ git submodule update --init 3rd_party/delfem2

(DelFEM2 is a collection of useful C++ codes written by the instructer.)

Problem1

Build the program using cmake. Run the program and take a screenshot image of the window. (You will probably see some undesirable animation and that's OK). Paste the screenshot image below by editing this mark down document:

=== paste screenshot here ===

Problem 2

This program tries to solve the deformation of static mass-spring system by energy minimization using Netwon's method. However, unfortunately, the current implementation does not converge because the computation of the hessian of the spring's enegy is incomplete.

• The springs energy can be written as W=1/2(len-Len)*(len-Len) = 1/2C*C, where len is current and Len is rest length and C=(len-Len).
• Gradient can be written as dW=C*dC that is already implemented
• Hessian can be written as ddW=dC*dC+C*ddC. In the current code, ddCis not computed yes (set to zero) and thus the Newton's iteration does not converge.

Fill the code around line #56 to compute the correct hessian of the energy (about 6-8 lines of simple codes). If the optimization works well, the energy should steadily decrease and converges within 10 iterations.

Paste the screenshot image of converged deformation below:

== paste screenshot image here==