Assignment 3 [Written]: The Laplacian (Due 4/13)

These exercises will lead you through two different derivations for the cotan-Laplace operator. As we’ll discuss in class, this operator is basically the “Swiss army knife” of discrete differential geometry and digital geometry processing, opening the door to a huge number of interesting algorithms and applications. Note that this time the exercises all come from the course notes—you will need to read the accompanying notes in order to familiarize yourself with the necessary material (though actually we’ve covered much of this stuff in class already!)


 

2 thoughts on “Assignment 3 [Written]: The Laplacian (Due 4/13)”

  1. In Chapter 6.2 page 104, is the derivation near the bottom of the page, applying Green’s first identity, missing a negative sign? Should it be
    $\sum_{k} \langle \Delta u, \phi_j \rangle _{\sigma_k} = – \sum_{k} \langle \nabla u, \nabla \phi_j \rangle _{\sigma_k} + \sum_{k} \langle N \cdot\nabla u, \phi_j \rangle_{\partial \sigma_k}$?

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