Orderly Spanning Trees with Applications

We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an {\em orderly pair} for any connected planar graph $G$, consisting of a plane graph $H$ of $G$, and an orderly spanning tree of $H$. We also present several applications of orderly spanning trees: (1) a new constructive proof for Schnyder's Realizer Theorem, (2) the first area-optimal 2-visibility drawing of $G$, and (3) the best known encodings of $G$ with O(1)-time query support. All algorithms in this paper run in linear time.Comment: 25 pages, 7 figures, A preliminary version appeared in Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), Washington D.C., USA, January 7-9, 2001, pp. 506-51

Area, perimeter, height, and width of rectangle visibility graphs

A rectangle visibility graph (RVG) is represented by assigning to each vertex a rectangle in the plane with horizontal and vertical sides in such a way that edges in the graph correspond to unobstructed horizontal and vertical lines of sight between their corresponding rectangles. To discretize, we consider only rectangles whose corners have integer coordinates. For any given RVG, we seek a representation with smallest bounding box as measured by its area, perimeter, height, or width (height is assumed not to exceed width)

Efficient abstractions for visualization and interaction

Abstractions, such as functions and methods, are an essential tool for any programmer. Abstractions encapsulate the details of a computation: the programmer only needs to know what the abstraction achieves, not how it achieves it. However, using abstractions can come at a cost: the resulting program may be inefficient. This can lead to programmers not using some abstractions, instead writing the entire functionality from the ground up. In this thesis, we present several results that make this situation less likely when programming interactive visualizations. We present results that make abstractions more efficient in the areas of graphics, layout and events

Animating the evolution of software

The use and development of open source software has increased significantly in the last decade. The high frequency of changes and releases across a distributed environment requires good project management tools in order to control the process adequately. However, even with these tools in place, the nature of the development and the fact that developers will often work on many other projects simultaneously, means that the developers are unlikely to have a clear picture of the current state of the project at any time. Furthermore, the poor documentation associated with many projects has a detrimental effect when encouraging new developers to contribute to the software. A typical version control repository contains a mine of information that is not always obvious and not easy to comprehend in its raw form. However, presenting this historical data in a suitable format by using software visualisation techniques allows the evolution of the software over a number of releases to be shown. This allows the changes that have been made to the software to be identified clearly, thus ensuring that the effect of those changes will also be emphasised. This then enables both managers and developers to gain a more detailed view of the current state of the project. The visualisation of evolving software introduces a number of new issues. This thesis investigates some of these issues in detail, and recommends a number of solutions in order to alleviate the problems that may otherwise arise. The solutions are then demonstrated in the definition of two new visualisations. These use historical data contained within version control repositories to show the evolution of the software at a number of levels of granularity. Additionally, animation is used as an integral part of both visualisations - not only to show the evolution by representing the progression of time, but also to highlight the changes that have occurred. Previously, the use of animation within software visualisation has been primarily restricted to small-scale, hand generated visualisations. However, this thesis shows the viability of using animation within software visualisation with automated visualisations on a large scale. In addition, evaluation of the visualisations has shown that they are suitable for showing the changes that have occurred in the software over a period of time, and subsequently how the software has evolved. These visualisations are therefore suitable for use by developers and managers involved with open source software. In addition, they also provide a basis for future research in evolutionary visualisations, software evolution and open source development

Discrete Geometry

[no abstract available

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Graph-level operations: A high-level interface for graph visualization technique specification

More and more the world is being described as graphs---as connections between people, places, and ideas---since they provide a richer model than simply understanding each item in isolation. In order to help analysts understand these graphs, researchers have developed and studied a large number of graph visualization techniques. This variety of techniques presents solutions to a breadth of graph analysis tasks, but it introduces a new issue: complexity. The variety introduces both the complexity of comparing techniques in an objective way and the engineering complexity of implementing so many techniques. In this thesis, I present graph-level operations models (or GLO models) as an elegant solution to these challenges. A GLO model consists of a model of visual elements and a set of functions (GLOs) that manipulate those elements. I introduce GLOv1 and GLOv2, GLO models derived from six hand-picked graph visualization techniques and twenty-nine techniques derived from a review of 430 graph visualization publications, respectively. I show how to use GLOs to define graph visualization techniques, including a model's original seed techniques as well as novel techniques. I demonstrate the analysis potential of the GLO model by clustering the twenty-nine seed techniques using two different GLO-based schemes. Finally, I demonstrate the practical engineering potential of the model through an open-source Javascript implementation (GLO.js) and two applications built atop the implementation for exploring a graph and discovering novel techniques using GLOs (GLO-STIX and GLO-CLI).Ph.D

Room layout estimation on mobile devices

Room layout generation is the problem of generating a drawing or a digital model of an existing room from a set of measurements such as laser data or images. The generation of floor plans can find application in the building industry to assess the quality and the correctness of an ongoing construction w.r.t. the initial model, or to quickly sketch the renovation of an apartment. Real estate industry can rely on automatic generation of floor plans to ease the process of checking the livable surface and to propose virtual visits to prospective customers. As for the general public, the room layout can be integrated into mixed reality games to provide a better immersiveness experience, or used in other related augmented reality applications such room redecoration. The goal of this industrial thesis (CIFRE) is to investigate and take advantage of the state-of-the art mobile devices in order to automate the process of generating room layouts. Nowadays, modern mobile devices usually come a wide range of sensors, such as inertial motion unit (IMU), RGB cameras and, more recently, depth cameras. Moreover, tactile touchscreens offer a natural and simple way to interact with the user, thus favoring the development of interactive applications, in which the user can be part of the processing loop. This work aims at exploiting the richness of such devices to address the room layout generation problem. The thesis has three major contributions. We first show how the classic problem of detecting vanishing points in an image can benefit from an a-priori given by the IMU sensor. We propose a simple and effective algorithm for detecting vanishing points relying on the gravity vector estimated by the IMU. A new public dataset containing images and the relevant IMU data is introduced to help assessing vanishing point algorithms and foster further studies in the field. As a second contribution, we explored the state of-the-art of real-time localization and map optimization algorithms for RGB-D sensors. Real-time localization is a fundamental task to enable augmented reality applications, and thus it is a critical component when designing interactive applications. We propose an evaluation of existing algorithms for the common desktop set-up in order to be employed on a mobile device. For each considered method, we assess the accuracy of the localization as well as the computational performances when ported on a mobile device. Finally, we present a proof of concept of application able to generate the room layout relying on a Project Tango tablet equipped with an RGB-D sensor. In particular, we propose an algorithm that incrementally processes and fuses the 3D data provided by the sensor in order to obtain the layout of the room. We show how our algorithm can rely on the user interactions in order to correct the generated 3D model during the acquisition process