PS 3 - Mesh Parameterization and Graph Drawing

(Maks Ovsjanikov)

The goal of this practical session is to implement the basic version of
Tutte's graph drawing algorithm, which is also used for mesh parameterization.

   
        Example of a 3D surface mesh and its 2D parameterization.

0. Getting started

Files to download today

Instructions

The zip package includes the following 3 directories:

Exercise 1

In today's practical session, there will only be one exercise and this will be to implement and test the basic version of Tutte's graph drawing (parameterization) algorithm. Use the basic structure of the given file draw_planar_mesh.m to to compute the x and y coordinates of all of the graph vertices, by using the coordinates of the boundary vertices.
A few points which may be useful: The final implementation should be quite short and should take a few (approx. 1-3) seconds for both the bunny graph (where the boundary is a single triangle) and the face graph (where the boundary is a full loop).
You should verify that you get a planar embedding as a result. In other words, you should get a planar graph embedding whose edges do not self-intersect.