In this lecture we’ll attempt to translate several smooth characterizations of conformal maps into the discrete setting. We’ll also see how each of these attempts leads to a different class of computational algorithms, with different trade offs. Although conformal maps are often associated with angle preservation, we’ll see that preserving angles at the discrete level results in a theory that is far to *rigid*: i.e., it does not capture any of the interesting structure of smooth conformal geometry. Instead, we’ll see how less-obvious starting points (such as patterns of circles, or preservation of *length cross ratios*) lead to some deep and beautiful connections between the classic smooth picture, and the discrete, combinatorial picture.

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Another set of slides, with additional stuff, can be found here: http://geometry.cs.cmu.edu/ddgshortcourse/