Locked and unlocked smooth embeddings of surfaces

We study the continuous motion of smooth isometric embeddings of a planar surface in three-dimensional Euclidean space, and two related discrete analogues of these embeddings, polygonal embeddings and flat foldings without interior vertices, under continuous changes of the embedding or folding. We show that every star-shaped or spiral-shaped domain is unlocked: a continuous motion unfolds it to a flat embedding. However, disks with two holes can have locked embeddings that are topologically equivalent to a flat embedding but cannot reach a flat embedding by continuous motion.Comment: 8 pages, 8 figures. To appear in 34th Canadian Conference on Computational Geometr

Quality Assessment of the Canadian OpenStreetMap Road Networks

Volunteered geographic information (VGI) has been applied in many fields such as participatory planning, humanitarian relief and crisis management because of its cost-effectiveness. However, coverage and accuracy of VGI cannot be guaranteed. OpenStreetMap (OSM) is a popular VGI platform that allows users to create or edit maps using GPS-enabled devices or aerial imageries. The issue of geospatial data quality in OSM has become a trending research topic because of the large size of the dataset and the multiple channels of data access. The objective of this study is to examine the overall reliability of the Canadian OSM data. A systematic review is first presented to provide details on the quality evaluation process of OSM. A case study of London, Ontario is followed as an experimental analysis of completeness, positional accuracy and attribute accuracy of the OSM street networks. Next, a national study of the Canadian OSM data assesses the overall semantic accuracy and lineage in addition to the quality measures mentioned above. Results of the quality evaluation are compared with associated OSM provenance metadata to examine potential correlations. The Canadian OSM road networks were found to have comparable accuracy with the tested commercial database (DMTI). Although statistical analysis suggests that there are no significant relations between OSM accuracy and its editing history, the study presents the complex processes behind OSM contributions possibly influenced by data import and remote mapping. The findings of this thesis can potentially guide cartographic product selection for interested parties and offer a better understanding of future quality improvement in OSM

Creep crack-growth: A new path-independent T sub o and computational studies

Two path independent integral parameters which show some degree of promise as fracture criteria are the C* and delta T sub c integrals. The mathematical aspects of these parameters are reviewed. This is accomplished by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects and large deformations. Two principal conclusions are that delta T sub c is a valid crack tip parameter during nonsteady as well as steady state creep and that delta T sub c has an energy rate interpretation whereas C* does not. An efficient, small displacement, infinitestimal strain, displacement based finite element model is developed for general elastic/plastic material behavior. For the numerical studies, this model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations

Point Line Cover: The Easy Kernel is Essentially Tight

The input to the NP-hard Point Line Cover problem (PLC) consists of a set $P$ of $n$ points on the plane and a positive integer $k$, and the question is whether there exists a set of at most $k$ lines which pass through all points in $P$. A simple polynomial-time reduction reduces any input to one with at most $k^2$ points. We show that this is essentially tight under standard assumptions. More precisely, unless the polynomial hierarchy collapses to its third level, there is no polynomial-time algorithm that reduces every instance $(P,k)$ of PLC to an equivalent instance with $O(k^{2-\epsilon})$ points, for any $\epsilon>0$. This answers, in the negative, an open problem posed by Lokshtanov (PhD Thesis, 2009). Our proof uses the machinery for deriving lower bounds on the size of kernels developed by Dell and van Melkebeek (STOC 2010). It has two main ingredients: We first show, by reduction from Vertex Cover, that PLC---conditionally---has no kernel of total size $O(k^{2-\epsilon})$ bits. This does not directly imply the claimed lower bound on the number of points, since the best known polynomial-time encoding of a PLC instance with $n$ points requires $\omega(n^{2})$ bits. To get around this we build on work of Goodman et al. (STOC 1989) and devise an oracle communication protocol of cost $O(n\log n)$ for PLC; its main building block is a bound of $O(n^{O(n)})$ for the order types of $n$ points that are not necessarily in general position, and an explicit algorithm that enumerates all possible order types of n points. This protocol and the lower bound on total size together yield the stated lower bound on the number of points. While a number of essentially tight polynomial lower bounds on total sizes of kernels are known, our result is---to the best of our knowledge---the first to show a nontrivial lower bound for structural/secondary parameters

Introducing Diversion Graph for Real-Time Spatial Data Analysis with Location Based Social Networks

Neighbourhood graphs are useful for inferring the travel network between locations posted in the Location Based Social Networks (LBSNs). Existing neighbourhood graphs, such as the Stepping Stone Graph lack the ability to process a high volume of LBSN data in real time. We propose a neighbourhood graph named Diversion Graph, which uses an efficient edge filtering method from the Delaunay triangulation mechanism for fast processing of LBSN data. This mechanism enables Diversion Graph to achieve a similar accuracy level as Stepping Stone Graph for inferring travel networks, but with a reduction of the execution time of over 90%. Using LBSN data collected from Twitter and Flickr, we show that Diversion Graph is suitable for travel network processing in real time

The convex hull in a new model of computation

We present a new model of geometric computation which supports the design of robust algorithms for exact real number input as well as for input with uncertainty, i.e. partial input. In this framework, we show that the convex hull of N computable real points in R^d is indeed computable. We provide a robust algorithm which, given any set of N partial inputs, i.e. N dyadic or rational rectangles, approximating these points, computes the partial convex hull in time O(N log N) in 2d and 3d. As the rectangles are refined to the N points, the sequence of partial convex hulls converges effectively both in the Hausdorff metric and the Lebesgue measure to the convex hull of the N points

Modelling and Optimization of an Airflow Window with Between-the-Panes Shading Device

Abstract This thesis deals with the numerical investigation of the upper section of a building-integrated photovoltaic/thermal double-façade. The upper section consists of an airflow window with a between-the-panes roller blind. The purpose of this thesis is to develop and validate a numerical model in order to optimize the design of the system. The lower section, which consists of building-integrated photovoltaics, has already been modelled at Concordia University. The results from the lower section will be used as inputs to the upper section. The validation of the model was carried out in three stages. In the first stage, the model was validated for forced convection between parallel plates using analytical data as benchmarks. In the second stage, a radiation analysis was performed for single, double and triple-glazed closed system with natural convection only. In the third and final validation stage, experimental data gathered from the Solar Lab at Concordia University was compared to the numerical model. The model included the effects of radiation for an open system with forced convection and a between-the-panes roller blind. For all three stages of validation, the results from the model were in excellent agreement with the benchmarking data. Once the model was validated, a parametric analysis was used to determine the effects of varying key model parameters. The outlet temperature, the useful energy gain, and the net energy gain of the system were plotted as a function of inlet velocity. It was concluded that as the flow rate through the cavity was increased, the air temperature at the outlet approached that of the outdoor ambient air. By computing the heat generated from advection as well as the total losses from the system, including the heat lost from the indoor environment as well as the power consumed by the fan, the net useful heat gain of the system was calculated as a function of insolation level. Operating points (of the fan) for the upper section were therefore determined as functions of insolation level. A second order polynomial equation provided an excellent fit to the data and could therefore be used to determine the ideal operating point of the upper section for any insolation level