Computation of bending forces on triangle meshes is required for numerous simulation and
geometry processing applications. In particular it is a key component in cloth simulation. A …

Discretization of curves is an ancient topic. Even discretization of curves with an eye toward
differential geometry is over a century old. However there is no general theory or …

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in
physics (super-fluidity, models for the onset of turbulence) as well as for numerical …

We investigate the discrete-time motions of planar discrete curves, and derive discrete
integrable equations on a two-dimensional nonuniform lattice. In particular, we obtain the …

This is an elementary introduction to a method for studying harmonic maps into symmetric
spaces, and in particular for studying constant mean curvature (CMC) surfaces, that was …

We propose a unified definition for discrete analogues of constant mean curvature surfaces
in spaces of constant curvature as a special case of discrete special isothermic nets. B\" …

In traditional product development, several iterations are usually necessary to obtain a
successful compromise between constraints emanating from engineering, manufacturing …

This thesis describes, how Bäcklund and Darboux transformations as well as soliton flows
can be defined for general conformal immersions of Riemann surfaces into the 4-sphere …

We connect certain continuous motions of discrete planar curves resulting in semi-discrete
potential Korteweg–de Vries (mKdV) equation with Darboux transformations of smooth …

This thesis concerns planar curvature lines of zero mean curvature surfaces in various
spaceforms. Using an analytic approach, we give the classification of maximal surfaces and …