In this paper we present a method to create textures on smooth surfaces of arbitrary topology using ReactionDiffusion systems in a graphics processing unit (GPU). To do this we use a parametrization of Catmull-Clark subdivision surfaces and obtain the metric information of the distortion caused by this parametrization, so we can calculate differential operators of functions defined on this surf...

In this paper, a novel technique of parametrization of supply rates is developed for establishing Input-to-State Stability(ISS) and dissipative properties of nonlinear interconnected systems. In the application of the ISS small-gain theorem, selecting supply rates to establish stability properties is not a straightforward task. This paper proposes useful tools for selecting supply rates by allo...

We study the concept of stabilization with internal loop for infinite-dimensional discrete timevarying systems in the framework of nest algebra. We originally give a parametrization of all stabilizing controllers with internal loop, and it covers the parametrization of canonical or dual canonical controllers with internal loop obtained before. We show that, in practical application, the control...

Cartan’s method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group G. The contact geometry of curves in low dimensional equi-affine geometry is then made explicit. This delivers the complete set of invariant data which solves the G-equivalence problem via a straightforward procedure, and which is, in some sense a supplement to the equi...

We consider a new state-space parametrization for linear time series models: data driven coordinates (DDC), which provides an atlas for the manifold of (stable) p×m transfer functions of fixed McMillan degree n. Hence, DDC has similar desirable properties as more traditional overlapping parametrizations and better than classical canonical forms. Moreover, the choice of charts can be done in a d...

In this paper we show how a simple parametrization, built from the definition of cubic splines, can aid in the implementation and interpretation of penalized spline models, whatever configuration of knots we choose to use. We call this parametrization value-first derivative parametrization. We perform Bayesian inference by exploring the natural link between quadratic penalties and Gaussian prio...