Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of $n$ vertices and $h$ holes. We introduce a \emph{graph of oriented distances} to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in $\min \{\,O(n^\omega), O(n^2 + nh \log h + \chi^2)\,\}$ time, where $\omega<2.373$ denotes the matrix multiplication exponent and $\chi\in \Omega(n)\cap O(n^2)$ is the number of edges of the graph of oriented distances. We also provide a faster algorithm for computing the diameter that runs in $O(n^2 \log n)$ time

A new approach to tolerance analysis

Journal ArticleTolerance analysis is seen as part of a more general problem, namely handling data with uncertainty. Uncertain geometric data arises when interpreting measured data, but also in solid modeling where floating point approximations are common, when representing design tolerances, or when dealing with limited manufacturing precision. The common question is whether parts with uncertain shape fulfill certain functional specification. The question is expressed as geometrical relationship between toleranced objects. Unfortunately, tolerance based relations are often inconsistent, unlike relations between exactly represented objects. In this paper we survey current tolerance representation and analysis methods. We then derive our method of intuitionistic tolerance handling from a method developed for robust solid modeling. A new representational framework is proposed, which serves as the basis for robust geometric modeling and tolerance analysis. We illustrate the framework with examples of assembly design

Robust boolean set operations for manifold solids bounded by planar and natural quadric surfaces

Journal ArticleThis paper describes our latest effort in robust solid modeling. An algorithm for set operations on solids bounded by planar and natural quadric surfaces, that handles all geometrically degenerate cases robustly, is described. We identify as the main reason for the lack of robustness in geometric modeling, that dependent relations are handled inconsistently by disregarding the dependencies. Instead of using explicit reasoning to make dependent decisions consistent, we show that redundant computation can be avoided by correctly ordering the operations, and redundant data can be eliminated in the set operation algorithm, so that the result is guaranteed to be a valid two-manifold solid

Visual Techniques for Geological Fieldwork Using Mobile Devices

Visual techniques in general and 3D visualisation in particular have seen considerable adoption within the last 30 years in the geosciences and geology. Techniques such as volume visualisation, for analysing subsurface processes, and photo-coloured LiDAR point-based rendering, to digitally explore rock exposures at the earth&rsquo;s surface, were applied within geology as one of the first adopting branches of science. A large amount of digital, geological surface- and volume data is nowadays available to desktop-based workflows for geological applications such as hydrocarbon reservoir exploration, groundwater modelling, CO2 sequestration and, in the future, geothermal energy planning. On the other hand, the analysis and data collection during fieldwork has yet to embrace this &rdquo;digital revolution&rdquo;: sedimentary logs, geological maps and stratigraphic sketches are still captured in each geologist&rsquo;s individual fieldbook, and physical rocks samples are still transported to the lab for subsequent analysis. Is this still necessary, or are there extended digital means of data collection and exploration in the field ? Are modern digital interpretation techniques accurate and intuitive enough to relevantly support fieldwork in geology and other geoscience disciplines ? This dissertation aims to address these questions and, by doing so, close the technological gap between geological fieldwork and office workflows in geology. The emergence of mobile devices and their vast array of physical sensors, combined with touch-based user interfaces, high-resolution screens and digital cameras provide a possible digital platform that can be used by field geologists. Their ubiquitous availability increases the chances to adopt digital workflows in the field without additional, expensive equipment. The use of 3D data on mobile devices in the field is furthered by the availability of 3D digital outcrop models and the increasing ease of their acquisition. This dissertation assesses the prospects of adopting 3D visual techniques and mobile devices within field geology. The research of this dissertation uses previously acquired and processed digital outcrop models in the form of textured surfaces from optical remote sensing and photogrammetry. The scientific papers in this thesis present visual techniques and algorithms to map outcrop photographs in the field directly onto the surface models. Automatic mapping allows the projection of photo interpretations of stratigraphy and sedimentary facies on the 3D textured surface while providing the domain expert with simple-touse, intuitive tools for the photo interpretation itself. The developed visual approach, combining insight from all across the computer sciences dealing with visual information, merits into the mobile device Geological Registration and Interpretation Toolset (GRIT) app, which is assessed on an outcrop analogue study of the Saltwick Formation exposed at Whitby, North Yorkshire, UK. Although being applicable to a diversity of study scenarios within petroleum geology and the geosciences, the particular target application of the visual techniques is to easily provide field-based outcrop interpretations for subsequent construction of training images for multiple point statistics reservoir modelling, as envisaged within the VOM2MPS project. Despite the success and applicability of the visual approach, numerous drawbacks and probable future extensions are discussed in the thesis based on the conducted studies. Apart from elaborating on more obvious limitations originating from the use of mobile devices and their limited computing capabilities and sensor accuracies, a major contribution of this thesis is the careful analysis of conceptual drawbacks of established procedures in modelling, representing, constructing and disseminating the available surface geometry. A more mathematically-accurate geometric description of the underlying algebraic surfaces yields improvements and future applications unaddressed within the literature of geology and the computational geosciences to this date. Also, future extensions to the visual techniques proposed in this thesis allow for expanded analysis, 3D exploration and improved geological subsurface modelling in general.publishedVersio

3D Modelling from Real Data

The genesis of a 3D model has basically two definitely different paths. Firstly we can consider the CAD generated models, where the shape is defined according to a user drawing action, operating with different mathematical “bricks” like B-Splines, NURBS or subdivision surfaces (mathematical CAD modelling), or directly drawing small polygonal planar facets in space, approximating with them complex free form shapes (polygonal CAD modelling). This approach can be used for both ideal elements (a project, a fantasy shape in the mind of a designer, a 3D cartoon, etc.) or for real objects. In the latter case the object has to be first surveyed in order to generate a drawing coherent with the real stuff. If the surveying process is not only a rough acquisition of simple distances with a substantial amount of manual drawing, a scene can be modelled in 3D by capturing with a digital instrument many points of its geometrical features and connecting them by polygons to produce a 3D result similar to a polygonal CAD model, with the difference that the shape generated is in this case an accurate 3D acquisition of a real object (reality-based polygonal modelling). Considering only device operating on the ground, 3D capturing techniques for the generation of reality-based 3D models may span from passive sensors and image data (Remondino and El-Hakim, 2006), optical active sensors and range data (Blais, 2004; Shan & Toth, 2008; Vosselman and Maas, 2010), classical surveying (e.g. total stations or Global Navigation Satellite System - GNSS), 2D maps (Yin et al., 2009) or an integration of the aforementioned methods (Stumpfel et al., 2003; Guidi et al., 2003; Beraldin, 2004; Stamos et al., 2008; Guidi et al., 2009a; Remondino et al., 2009; Callieri et al., 2011). The choice depends on the required resolution and accuracy, object dimensions, location constraints, instrument’s portability and usability, surface characteristics, working team experience, project’s budget, final goal, etc. Although aware of the potentialities of the image-based approach and its recent developments in automated and dense image matching for non-expert the easy usability and reliability of optical active sensors in acquiring 3D data is generally a good motivation to decline image-based approaches. Moreover the great advantage of active sensors is the fact that they deliver immediately dense and detailed 3D point clouds, whose coordinate are metrically defined. On the other hand image data require some processing and a mathematical formulation to transform the two-dimensional image measurements into metric three-dimensional coordinates. Image-based modelling techniques (mainly photogrammetry and computer vision) are generally preferred in cases of monuments or architectures with regular geometric shapes, low budget projects, good experience of the working team, time or location constraints for the data acquisition and processing. This chapter is intended as an updated review of reality-based 3D modelling in terrestrial applications, with the different categories of 3D sensing devices and the related data processing pipelines

Book of Abstracts 15th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering and 3rd Conference on Imaging and Visualization

In this edition, the two events will run together as a single conference, highlighting the strong connection with the Taylor & Francis journals: Computer Methods in Biomechanics and Biomedical Engineering (John Middleton and Christopher Jacobs, Eds.) and Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualization (JoãoManuel R.S. Tavares, Ed.). The conference has become a major international meeting on computational biomechanics, imaging andvisualization. In this edition, the main program includes 212 presentations. In addition, sixteen renowned researchers will give plenary keynotes, addressing current challenges in computational biomechanics and biomedical imaging. In Lisbon, for the first time, a session dedicated to award the winner of the Best Paper in CMBBE Journal will take place. We believe that CMBBE2018 will have a strong impact on the development of computational biomechanics and biomedical imaging and visualization, identifying emerging areas of research and promoting the collaboration and networking between participants. This impact is evidenced through the well-known research groups, commercial companies and scientific organizations, who continue to support and sponsor the CMBBE meeting series. In fact, the conference is enriched with five workshops on specific scientific topics and commercial software.info:eu-repo/semantics/draf

Design Transactions

Design Transactions presents the outcome of new research to emerge from ‘Innochain’, a consortium of six leading European architectural and engineering-focused institutions and their industry partners. The book presents new advances in digital design tooling that challenge established building cultures and systems. It offers new sustainable and materially smart design solutions with a strong focus on changing the way the industry thinks, designs, and builds our physical environment. Divided into sections exploring communication, simulation and materialisation, Design Transactions explores digital and physical prototyping and testing that challenges the traditional linear construction methods of incremental refinement. This novel research investigates ‘the digital chain’ between phases as an opportunity for extended interdisciplinary design collaboration. The highly illustrated book features work from 15 early-stage researchers alongside chapters from world-leading industry collaborators and academics

Design Transactions: Rethinking Information for a New Material Age

Design Transactions presents the outcome of new research to emerge from ‘Innochain’, a consortium of six leading European architectural and engineering-focused institutions and their industry partners. The book presents new advances in digital design tooling that challenge established building cultures and systems. It offers new sustainable and materially smart design solutions with a strong focus on changing the way the industry thinks, designs, and builds our physical environment. Divided into sections exploring communication, simulation and materialisation, Design Transactions explores digital and physical prototyping and testing that challenges the traditional linear construction methods of incremental refinement. This novel research investigates ‘the digital chain’ between phases as an opportunity for extended interdisciplinary design collaboration. The highly illustrated book features work from 15 early-stage researchers alongside chapters from world-leading industry collaborators and academics