Preface

The intended audience of this book is threefold. We wrote it as a textbook

on discrete differential geometry and integrable systems. A one semester

graduate course in discrete differential geometry based on this book was held

at TU Berlin and TU M¨ unchen several times. At the end of each chapter

we included numerous exercises which we recommend for the classes. For

some of them (marked with asterisks) solutions are supplied. The standard

undergraduate background, i.e., calculus and linear algebra, is required. In

particular, no knowledge of differential geometry is expected, although some

familiarity with curves and surfaces can be helpful.

On the other hand, this book is also written for specialists in geometry

and mathematical physics. It is the first monograph on discrete differential

geometry which reflects the progress in this field during the last decade,

and it contains many original results. The bibliographical notes at the end

of each chapter are intended to provide the reader with an overview of the

relevant research literature.

The third group at which this book is targeted are specialists in geometry

processing, computer graphics, architectural design, numerical simulations

and animation. There is a growing evidence of the importance of intelli-

gent geometric discretizations in these fields. Talking with researchers in

these fields, we were asked many questions regarding the discretization of

differential geometry. We hope to have answered some of them in this book.

All the readers are encouraged to read or at least to skim the Introduc-

tion (some parts of it assume a broader knowledge than the minimum) to

see the words and pictures and to get a sense of how the ideas fit together

and what does the book cover.

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