Intersection test and blossoming perturbation for disk parametric curves and ball parametric surfaces

Errors in curve and surface representation due to inaccuracies in the data are considered and accounted for by introducing disk parametric curves and ball parametric surfaces. Intersection test algorithms and interval extensions using blossoming are discussed for each of the three cases of Bézier curves, tensor product surfaces, and triangular patches. A stability analysis is also performed for each of the three cases. It is shown that under certain restrictions disk Bézier curves and triangular ball Bézier patches are stable with respect to perturbations of the control disks (balls); whereas tensor product ball Bézier surfaces are in general not

Rendering PostScript^TM fonts on FPGAs

This paper describes how custom computing machines can be used to implement a simple outline font processor. An FPGA based co-processor is used to accelerate the compute intensive portions of font rendering. The font processor builds on several PostScript components previously presented by the authors to produce a system that can rapidly render fonts. A prototype implementation is described followed by an explanation of how this could be extended to build a complete system

Parameter selection in the design of displacement and motion functions by means of B-splines

This work analyses the incidence of the parameter selection of B-spline curves, used in the design of displacement and motion functions, on its degree of freedom and shape. A complete design process based on the use of non-parametric B-spline curves and the convenience of selecting the curve parameters from the point of view of its practical application is shown. In order to make easy the design and use of the displacement function, the algorithms for derivation and integration of the B-splines used are presented. Three case studies validate the proposed design process and the selection of the adequate parameters. The first case presents the design of a displacement function of a roller follower driven by a disk cam; the corresponding cam profile and its prototype are shown. The second case presents the design of the motion function corresponding to the cutting unit of a manufacturing cardboard tube machine. The third case exposes the design of the displacement function of the bar feeding mechanism in a single-spindle automatic lathe, to produce a partial thread screw of hexagonal head.Postprint (author's final draft

CuBe: parametric modeling of 3D foveal shape using cubic Bézier

Optical coherence tomography (OCT) allows three-dimensional (3D) imaging of the retina, and is commonly used for assessing pathological changes of fovea and macula in many diseases. Many neuroinflammatory conditions are known to cause modifications to the fovea shape. In this paper, we propose a method for parametric modeling of the foveal shape. Our method exploits invariant features of the macula from OCT data and applies a cubic Bézier polynomial along with a least square optimization to produce a best fit parametric model of the fovea. Additionally, we provide several parameters of the foveal shape based on the proposed 3D parametric modeling. Our quantitative and visual results show that the proposed model is not only able to reconstruct important features from the foveal shape, but also produces less error compared to the state-of-the-art methods. Finally, we apply the model in a comparison of healthy control eyes and eyes from patients with neuroinflammatory central nervous system disorders and optic neuritis, and show that several derived model parameters show significant differences between the two groups

Infinite Procedural Infrastructured World Generation

Käesolev magistritöö kirjeldab uudset algoritmi lõpmatu deterministliku maailma genereerimiseks koos üldlevinud tehislike ja looduslike struktuuridega, mis leiduvad parasvöötme asustatud piirkondades. Kuna lõpmatuid maailmu tuleb genereerida jupikaupa ning ilma ühegi naabruses oleva tüki olemasoluta, on genereeritavate struktuuride järjepidev ja deterministlik genereerimine keeruline. Kirjeldatav algoritm kasutab eksponentsiaalse genereerimise metoodikat, mis võimaldab genereerida erineva suurusega struktuure alates liiklusmärkidest kuni pikkade jõgedeni. Algoritm genereerib erinevat tüüpi lõpmatuid teede võrgustikke, nimedega linnu ja külasid, elektriliine ja levinumaid liiklusmärke nagu kiiruspiirangud ja suunamärgid. Asulatest väljaspool olev maastik genereeritakse kolme üldlevinud maakasutuse kategooria vahel – metsandus, viljakasvatus ning looduskaitsealad. Lisaks kirjeldatavale algoritmile antakse ülevaade eelnevast teadustööst lõpmatu protseduurilise maailma genereerimise valdkonnas ning kirjeldatakse edasiarendusvõimalusi lõpmatute asustatud maailmade genereerimiseks.This Master's thesis describes and provides an implementation of a novel algorithm for generating infinite deterministic worlds with both man-made and natural features commonly found in the civilized regions of the temperate climate zone. Considering that infinite worlds have to be generated in a piecewise manner without any of the neighbouring pieces necessarily existing, ensuring continuity and deterministic results for the generation of such features can be challenging. The algorithm uses an exponential generation technique, which enables the generation of varying sized features from traffic signs to rivers. The algorithm generates infinite road networks of different tiers, named cities and villages, power lines between them and common traffic signs like speed limits and navigation signs. Rural areas are generated based on three types of land usage – forestry, cultivation of crops and untouched nature reserves. The thesis also gives an overview of the previous work in the field of procedural world generation and proposes multiple new ideas for further expansion of infinite infrastructured terrain generation

Robomaths: Robotics to Learn Matematics in a Architecture Degree

The abstract part of mathematics is a difficult matter included in many subjects in university degrees. Specifically, in architecture degrees students lack interest in this topic if they don’t experience its immediate application. In addition, technological skills are required at every educational level and the students of these degrees are usually more interested in art than in technology. With the aim of encouraging architecture students' interest in mathematics and technology, a methodology is presented here that includes the use of robotics in maths lectures. The key idea is to make the abstract part of mathematics understandable by means of robots

Segmentation of nerve bundles and ganglia in spine MRI using particle filters

14th International Conference, Toronto, Canada, September 18-22, 2011, Proceedings, Part IIIAutomatic segmentation of spinal nerve bundles that originate within the dural sac and exit the spinal canal is important for diagnosis and surgical planning. The variability in intensity, contrast, shape and direction of nerves seen in high resolution myelographic MR images makes segmentation a challenging task. In this paper, we present an automatic tracking method for nerve segmentation based on particle filters. We develop a novel approach to particle representation and dynamics, based on Bézier splines. Moreover, we introduce a robust image likelihood model that enables delineation of nerve bundles and ganglia from the surrounding anatomical structures. We demonstrate accurate and fast nerve tracking and compare it to expert manual segmentation.National Institutes of Health (U.S.) (NAMIC award U54-EB005149)National Science Foundation (U.S.) (CAREER grant 0642971

ROBAST: Development of a ROOT-Based Ray-Tracing Library for Cosmic-Ray Telescopes and its Applications in the Cherenkov Telescope Array

We have developed a non-sequential ray-tracing simulation library, ROOT-based simulator for ray tracing (ROBAST), which is aimed to be widely used in optical simulations of cosmic-ray (CR) and gamma-ray telescopes. The library is written in C++, and fully utilizes the geometry library of the ROOT framework. Despite the importance of optics simulations in CR experiments, no open-source software for ray-tracing simulations that can be widely used in the community has existed. To reduce the dispensable effort needed to develop multiple ray-tracing simulators by different research groups, we have successfully used ROBAST for many years to perform optics simulations for the Cherenkov Telescope Array (CTA). Among the six proposed telescope designs for CTA, ROBAST is currently used for three telescopes: a Schwarzschild-Couder (SC) medium-sized telescope, one of SC small-sized telescopes, and a large-sized telescope (LST). ROBAST is also used for the simulation and development of hexagonal light concentrators proposed for the LST focal plane. Making full use of the ROOT geometry library with additional ROBAST classes, we are able to build the complex optics geometries typically used in CR experiments and ground-based gamma-ray telescopes. We introduce ROBAST and its features developed for CR experiments, and show several successful applications for CTA.Comment: Accepted for publication in Astroparticle Physics. 11 pages, 10 figures, 4 table