Symbolic computations in applied differential geometry

Symbolic Computations in Applied Differential Geometry

The main aim of this paper is to contribute to the automatic calculations in differential geometry and its applications, with emphasis on the prolongation theory of Estabrook and Wahlquist, and the calculation of invariance groups of exterior differential systems. A large number of worked examples have been included in the text to demonstrate the concrete manipulations in practice. In the appen...

Symbolic computations in differential geometry

We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this approach with explicit examples. In particular, we describe a short program to determine whether a given linear exterior differential system is involutive.

Applied Differential Geometry

My main research goal is to develop robust, predictive, and multi-purpose computation tools by leveraging differential geometric concepts and foundations. In particular, I wish to contribute a number of practical applications in computer graphics and related areas, such as medical imaging, biometrics, medical simulation, and visualization, by focusing on the geometrical foundations common to co...

Discrete Differential Geometry: an Applied Introduction

domain M parameterization immersed surface Remember that, like the cartographers of yore, our goal is to parameterize a given surface over the plane. In particular, we want to find a map that preserves angles. How can we express this condition more explicitly? Well, we know how to express 90-degree rotations on the surface, using the complex structure J . And we know how to express 90-degree ro...

System Theory as Applied Differential Geometry