PARALLEL √3-SUBDIVISION with ANIMATION in CONSIDERATION of GEOMETRIC COMPLEXITY

We look at the broader field of geometric subdivision and the emerging field of parallel computing for the purpose of creating higher visual fidelity at an efficient pace. Primarily, we present a parallel algorithm for √3-Subdivision. When considering animation, we find that it is possible to do subdivision by providing only one variable input, with the rest being considered static. This reduces the amount of data transfer required to continually update a subdividing mesh. We can support recursive subdivision by applying the technique in passes. As a basis for analysis, we look at performance in an OpenCL implementation that utilizes a local graphics processing unit (GPU) and a parallel CPU. By overcoming current hardware limitations, we present an environment where general GPU computation of √3-Subdivision can be practical

A Comparison of GPU Tessellation Strategies for Multisided Patches

We propose an augmentation of the traditional tessellation pipeline with several different strategies that efficiently render multisided patches using generalised barycentric coordinates. The strategies involve different subdivision steps and the usage of textures. In addition, we show that adaptive tessellation techniques naturally extend to some of these strategies whereas others need a slight adjustment. The technique of Loop et al. [LSNC09], commonly known as ACC-2, is extended to multisided faces to illustrate the effectiveness of multisided techniques. A performance and quality comparison is made between the different strategies and remarks on the techniques and implementation details are provided

Smooth shading of specular surfaces in polygon-based high-definition CGH

High-definition computer-generated holograms (CGH) created by the polygon-based method feature reconstruction of very fine 3D image accompanied with strong sensation of depth. However, rendering technique for specular surfaces has not been established. We propose a novel technique for smooth shading of specular surfaces in the polygon-based method. This technique divides the surface function of polygons into some segments and controls the spectral envelopes.2011 3DTV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON 2011), 16-18 May 2011, Antalya, Turke

Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. The method distinguishes the hierarchy between singular set, Pareto critical set and stable Pareto critical set, and can handle the problem of superposition of local Pareto fronts, occurring in the general nonconvex case. Furthermore, a quadratic convergence result in a suitable set-wise sense is proven and tested in a number of numerical examples.Comment: 29 pages, 12 figure

Solving N=2 SYM by Reflection Symmetry of Quantum Vacua

The recently rigorously proved nonperturbative relation between u and the prepotential, underlying N=2 SYM with gauge group SU(2), implies both the reflection symmetry $\overline{u(\tau)}=u(-\bar\tau)$ and $u(\tau+1)=-u(\tau)$ which hold exactly. The relation also implies that $\tau$ is the inverse of the uniformizing coordinate u of the moduli space of quantum vacua. In this context, the above quantum symmetries are the key points to determine the structure of the moduli space. It turns out that the functions a(u) and a_D(u), which we derive from first principles, actually coincide with the solution proposed by Seiberg and Witten. We also consider some relevant generalizations.Comment: 12 pg. LaTex, Discussion of the generalization to higher rank groups added. To be published in Phys. Rev.

Geometric effects on critical behaviours of the Ising model

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic susceptibility and the correlation length deviate from those for the Ising lattice model on a flat plane. Furthermore, when reducing the effects of boundary spins, the values of the critical exponents tend to those derived from the mean field theory. These findings evidence that the underlying geometric character is responsible for the critical properties the Ising model when the lattice is embedded on negatively curved surfaces.Comment: 16 pages, 6 figures, to appear in J. Phys. A: Math. Ge

High-Level GPU Programming: Domain-Specific Optimization and Inference

When writing computer software one is often forced to balance the need for high run-time performance with high programmer productivity. By using a high-level language it is often possible to cut development times, but this typically comes at the cost of reduced run-time performance. Using a lower-level language, programs can be made very efficient but at the cost of increased development time. Real-time computer graphics is an area where there are very high demands on both performance and visual quality. Typically, large portions of such applications are written in lower-level languages and also rely on dedicated hardware, in the form of programmable graphics processing units (GPUs), for handling computationally demanding rendering algorithms. These GPUs are parallel stream processors, specialized towards computer graphics, that have computational performance more than a magnitude higher than corresponding CPUs. This has revolutionized computer graphics and also led to GPUs being used to solve more general numerical problems, such as fluid and physics simulation, protein folding, image processing, and databases. Unfortunately, the highly specialized nature of GPUs has also made them difficult to program. In this dissertation we show that GPUs can be programmed at a higher level, while maintaining performance, compared to current lower-level languages. By constructing a domain-specific language (DSL), which provides appropriate domain-specific abstractions and user-annotations, it is possible to write programs in a more abstract and modular manner. Using knowledge of the domain it is possible for the DSL compiler to generate very efficient code. We show that, by experiment, the performance of our DSLs is equal to that of GPU programs written by hand using current low-level languages. Also, control over the trade-offs between visual quality and performance is retained. In the papers included in this dissertation, we present domain-specific languages targeted at numerical processing and computer graphics, respectively. These DSL have been implemented as embedded languages in Python, a dynamic programming language that provide a rich set of high-level features. In this dissertation we show how these features can be used to facilitate the construction of embedded languages