I am confused as to what the Laplacian exactly allows us to do and why the ability to map one scalar function to another linearly is so important. Is there a higher level explanation of all of this? Also, what does delta f show in this example?
@cupoftea It definitely takes a little while to really see why the Laplacian is so fundamental to so many applications. Here are some slides we put together on what the Laplacian is (with some additional intuition) and why it's so important for 3D geometry processing. Of course, it will show up in other ways in other areas of graphics as well (animation, imaging, etc.).