June, 2006
This tutorial introduces the concept of surface Ricci flow, the major theorems on the convergence of Ricci flow. Practical algorithms are explained in details, some experiemental results are demonstrated. [PDF]
This tutorial introduces the concept and theorems of Riemann surfaces. Practical algorithms on computing conformal structure are explained in details, some experiemental results are demonstrated.
Major algorithms inlcude spherical harmonic maps, Riemann mapping algorithm, computing harmonic 1-forms and holomorphic 1-forms etc. [PDF]
This tutorial introduces the concept and theorems of surface topology. Practical algorithms on computing topology are explained in details, some experiemental results are demonstrated.
Major algorithms inlcude computing homology, cohomology, fundamental domain, universial covering space, shortest loops, cut graph etc. [PDF]
This is the lecture notes given in my seminar "computational conformal geometry". It covers the major concepts in topology, differential geometry, Riemann surface theories related to conformal geometry, and many major algorithms for computing conformal structures. Most directly related applications are demonstrated. [PDF]
This is an early version of the tutorial introducing Euclidean Ricci flow. It includes some examples for computing flat metrics on surfaces with a single cone singularity, in other words, all curvature is concentred on a single point. [PDF]