We describe how some simple properties of discrete one-forms directly relate to some old and new results concerning the parameterization of 3D mesh data. Our first result is an easy proof of Tutte’s celebrated “springembedding” theorem for planar graphs, which is widely used for parameterizing meshes with the topology of a disk as a planar embedding with a convex boundary. Our second result gen...

We present a conjugate analysis of two different dark energy models, namely the Barboza–Alcaniz parameterization and the phenomenologically-motivated Hobbit model, investigating both their agreement with observational data and their thermodynamical properties. We successfully fit a wide dataset including the Hubble diagram of Type Ia Supernovae, the Hubble rate expansion parameter as measured f...

The introduction of methods from statistical physics for traffic flow modelling, such as cellular automata models, enabled the faster than real time simulation of large traffic networks. A key issue faced by such efforts is the expandability of the network model. This paper discusses the development of a cellular automata framework for micro-simulation of vehicle traffic flow in road networks a...

The motion of a plane can be described by a homography. We study how to parameterize homographies to maximize plane estimation performance. We compare the usual 3 × 3 matrix parameterization with a parameterization that combines 4 fixed points in one of the images with 4 variable points in the other image. We empirically show that this 4pt parameterization is far superior. We also compare both ...

Use qij to denote the (i; j)-entry of the matrix Q (i; j = 1; 2). Then (Q) reads as (Q) = 0(1 + p 05)r 0 2 0(2 0 p 05)r + (1 + p 05) 2r + (1 0 p 05) 0(1 + p 05)r 0 2 (2) where r = (01+ p 05)q 11 0(2+ p 05)q 12 +2q 21 + (01+ p 05)q 22 : (3) Because any stabilizing controller can be obtained from the (2, 1)-and (2, 2)-entries of (2), we are interested in the set of r's of (3), that is, the ideal ...

The differential operator of the monochromatic polarized radiative transfer equation is studied in case of statistically homogeneous turbid medium in Euclidean three-dimensional space, with arbitrary curvilinear coordinate system defined in it. An apparent rotation of the polarization plane along the light ray with respect to the chosen polarization reference plane generally takes place, due to...

Streamline-like, free-form features that “flow” on a base shape are often utilized in the design of products ranging from automobiles to everyday consumer products. Providing computational support for the design of such features is challenging, because of the open-endedness of the design explorations involved, and the necessity to rapidly and precisely capture the design intents expressed in ve...

We use results by Kirilin to show that in general relativity the nonleading terms in the energy-momentum tensor of a particle depends on the parameterization of the gravitational field. While the classical metric that is calculated from this source, used to define the leading long-distance corrections to the metric, also has a parameteriztion dependence, it can be removed by a coordinate change...

Low-distortion parameterization of 3D meshes is a fundamental problem in computer graphics. Several widely used approaches have been presented for triangular meshes. But no direct parameterization techniques are available for quadrilateral meshes yet. In this paper, we present a parameterization technique for non-closed quadrilateral meshes based on mesh simplification. The parameterization is ...

Parameterization extends higher-order processes with the capability of abstraction (akin to that in lambda-calculus), and is known to be able to enhance the expressiveness. This paper focuses on the parameterization of names, i.e. a construct that maps a name to a process, in the higher-order setting. We provide two results concerning its computation capacity. First, name parameterization bring...