- Gauss-Seidel Relaxation for unstructured mesh
- Deadline: June 3rd (Thursday) at 15:00
Pleae look at the following document for environment setup, creating branch, and making pull request.
Additionally, you need the library DelFEM2 installed and updated in pba-<username>/3rd_party
$ 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).
Build the main.cpp using cmake. Run the program and take a screenshot image of the window. You will probably see some highly distorted mesh and that's OK. Paste the screenshot image below by editing this mark down document:
=== paste screenshot here ===
Consider each edge of the mesh is a spring with zero rest length. In other words the spring's elastic potential energy is E_i=1/2l_i^2, where l_i is the distance between two end points of i-th spring. Write a program to minimize the sum of elastic potential energy E=∑E_i.
The optimization has to be done using the Gauss-Seidel(GS) method. The GS method updates the coordinate of the point one-by-one. Let us denote ip is the point to be moved, and jp is the point surrounding ip. For each updates of GS method, the coordinate of ip is optimized and coordinates for jp is fixed. Use the fact the sum of squared distance between ip and jp is minimized when the ip is moved to the gravity center of jp.
The one-ring neighbourhood of vertices are stored inside Psup_Ind and Psup in the format of jagged array. See the slides below for the detail of the format.
Write some code around line #31 in the main.cpp. Once the implementation is successful, the energy should steadly decrease. Paste the resulting screenshot image below.
=== paste screenshot image here ===