Parameterization has lots of applications in computer graphics such as texture mapping, remeshing and morphing. Texture mapping a 2D image onto a 3D mesh would previously cost lots of efforts and time for an experienced modeler to tweak the u,v texture coordinates of the mesh. By parameterizing the mesh onto a rectangular 2D domain, this becomes an easy task of mapping a 2D image onto an rectan...

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...

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...

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, we study the implications for hedging Bermudan swaptions of the choice of the instantaneous volatility for the driving Markov process of the one-dimensional swap Markov-functional model. We find that there is a strong evidence in favour of what we term “parametrization by time” as opposed to “parametrization by expiry”. We further propose a new parametrization by time for the dri...

with a b 1. The shift dynamical system induced by a,b is measure theoretically isomorphic to an exchange of three domains on a compact tile Ta,b with fractal boundary. We prove that Ta,b is homeomorphic to the closed disk iff 2b a 3. This solves a conjecture of Shigeki Akiyama posed in 1997. To this effect, we construct a Hölder continuous parametrization Ca,b W S1 ! Ta,b of the boundary of Ta,...

A general parametrization for all three-dimensional crystal lattices is presented in this paper which guarantees that the three primitive vectors constructed by the parametrization are the three shortest possible, linearly independent lattice vectors existing in the whole lattice. The parameter space of this so-called minimum distance parametrization (MDP) can easily be confined to contain only...