Conformal Geometry Processing

Symposium on Geometry Processing
2017 Graduate School Lecture by Keenan Crane
www.cs.cmu.edu...
geometry.cs.ucl...
Digital geometry processing is the natural extension of traditional signal processing to three-dimensional geometric data. In recent years, methods based on so-called conformal (i.e., angle-preserving) transformations have proven to be a powerful paradigm for geometry processing since (i) numerical problems are typically linear, providing scalability and guarantees of correctness and (ii) conformal descriptions of geometry are often dramatically simpler or lower-dimensional than traditional encodings. Conformal geometry is also linked to constitutive laws appearing in computational mechanics and 3D fabrication. This lecture will touch on both the mathematical foundations of conformal geometry, as well as recent numerical techniques and applications in 3D geometry processing.