CDS/CIMMS Lunchtime Seminar: Discrete Laplacians in Graphics

Mathieu Desbrun

In this talk, we will present a series of concrete applications in graphical modeling and meshing where a discrete Laplacian is not only helpful, but crucial in getting good results. Harmonic forms and eigenfunctions of the Laplacian will be shown useful in applications ranging from quadrangle meshing to mesh puppeteering, and from tangent vector field design to 2-manifold point cloud reconstruction. While we will not focus on the actual discretization of the Laplacian, we will show that the Hodge star (present in the exterior calculus expression of the Laplace operator) can be altered to accommodate arbitrary metrics, allowing us to easily tweak the results to our liking.