Design principles of hardware-based phong shading and bump-mapping

The VISA+ hardware architecture is the first of a new generation of graphics accelerators designed primarily to render bump-, texture-, environment- and environment-bump-mapped polygons. This paper presents examples of the main graphical capabilities and discusses methods and simplifications used to create high quality images. One of the key concepts in the VISA+ design, the use of reflectance cubes, is predestined for environment mapping. In combination with bump- and texture-mapping it shows the strength of our new architecture. Furthermore it justifies some of the decisions made during simulation and development of the complex VISA+ architecture

A Skyrme lattice with hexagonal symmetry

Recently it has been found that the structure of Skyrmions has a close analogy to that of fullerene shells in carbon chemistry. In this letter we show that this analogy continues further, by presenting a Skyrme field that describes a lattice of Skyrmions with hexagonal symmetry. This configuration, a novel `domain wall' in the Skyrme model, has low energy per baryon (about 6% above the Faddeev-Bogomolny bound) and in many ways is analogous to graphite. By comparison to the energy per baryon of other known Skyrmions and also the Skyrme crystal, we discuss the possibility of finding Skyrmion shells of higher charge.Comment: 12 pages, 1 figure. To appear in Phys. Lett.

Exploiting low-cost 3D imagery for the purposes of detecting and analyzing pavement distresses

Road pavement conditions have significant impacts on safety, travel times, costs, and environmental effects. It is the responsibility of road agencies to ensure these conditions are kept in an acceptable state. To this end, agencies are tasked with implementing pavement management systems (PMSs) which effectively allocate resources towards maintenance and rehabilitation. These systems, however, require accurate data. Currently, most agencies rely on manual distress surveys and as a result, there is significant research into quick and low-cost pavement distress identification methods. Recent proposals have included the use of structure-from-motion techniques based on datasets from unmanned aerial vehicles (UAVs) and cameras, producing accurate 3D models and associated point clouds. The challenge with these datasets is then identifying and describing distresses. This paper focuses on utilizing images of pavement distresses in the city of Palermo, Italy produced by mobile phone cameras. The work aims at assessing the accuracy of using mobile phones for these surveys and also identifying strategies to segment generated 3D imagery by considering the use of algorithms for 3D Image segmentation to detect shapes from point clouds to enable measurement of physical parameters and severity assessment. Case studies are considered for pavement distresses defined by the measurement of the area affected such as different types of cracking and depressions. The use of mobile phones and the identification of these patterns on the 3D models provide further steps towards low-cost data acquisition and analysis for a PMS

Fast algorithms for computing defects and their derivatives in the Regge calculus

Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson like scheme. In such cases it is essential that efficient algorithms be used when computing the defect angles and their derivatives with respect to the leg-lengths. The purpose of this paper is to present details of such an algorithm.Comment: 38 pages, 10 figure

Surface cubications mod flips

Let $\Sigma$ be a compact surface. We prove that the set of surface cubications modulo flips, up to isotopy, is in one-to-one correspondence with $\Z/2\Z\oplus H_1(\Sigma,\Z/2\Z)$.Comment: revised version, 18

Scaling limits of random planar maps with large faces

We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index $\alpha\in(1,2)$. When the number $n$ of vertices of the map tends to infinity, the asymptotic behavior of distances from a distinguished vertex is described by a random process called the continuous distance process, which can be constructed from a centered stable process with no negative jumps and index $\alpha$. In particular, the profile of distances in the map, rescaled by the factor $n^{-1/2\alpha}$, converges to a random measure defined in terms of the distance process. With the same rescaling of distances, the vertex set viewed as a metric space converges in distribution as $n\to\infty$, at least along suitable subsequences, toward a limiting random compact metric space whose Hausdorff dimension is equal to $2\alpha$.Comment: Published in at http://dx.doi.org/10.1214/10-AOP549 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org