Many applications in physics, biology or chemistry exhibit complex geometrical shapes. Often these models feature partial differential equations (PDEs) on the complex shaped domain and its surface. At the same time the domain might be time-dependent, e.g. in cell biology the shape of a cell depends on its internal state and couples back to the cell metabolism, cf. [12]. Modern imaging technique...

In a general setting, the transfinite interpolation problem requires constructing a single function´Üµ that takes on the prescribed values and/or derivatives on some collection of point sets. The sets of points may contain isolated points, bounded or unbounded curves, as well as surfaces and regions of arbitrary topology. All such closed semi-analytic sets may be represented implicitly by real ...

Many applications require the minimization of a smooth function f : R nu → R whose evaluation requires the solution of a system of nonlinear equations. This system represents a numerical simulation that must be run to evaluate f. This system of nonlinear equations is referred to as an implicit constraint. In principle f can be minimized using the steepest descent method or Newton-type methods f...

Enabling intuitive interaction in system design remains an art more than a science. This difficulty is exacerbated when the diversity of device and end user group is considered. In this paper, it is argued that conventional interaction modalities are unsuitable in many circumstances and that alternative modalities need be considered. Specifically the case of implicit interaction is considered, ...

The dominant theory of what people can learn implicitly is that they learn chunks of adjacent elements in sequences. A type of musical grammar that goes beyond specifying allowable chunks is provided by serialist or 12-tone music. The rules constitute operations over variables and could not be appreciated as such by a system that can only chunk elements together. A series of studies investigate...

It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In this paper we will investigate in more detail the case of canal surfaces that are often used in geometric modelling, Computer-Aided Design and technical practice (e.g. as blending surfaces smoothly joining two parts with circular ends). It is know...