Computer Science: Faculty Books

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  Reshaping Convex Polyhedra

  Joseph O'Rourke and Costin Vîlcu

  The focus of this monograph is converting—reshaping—one 3D convex polyhedron to another via an operation the authors call “tailoring.” A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a “vertex”) of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler’s “vertex truncation,” but differs in that the hole left by a truncated vertex is filled with new surface, whereas tailoring zips the hole closed. A powerful “gluing” theorem of A.D. Alexandrov from 1950 guarantees that, after closing the hole, the result is a new convex polyhedron. Given two convex polyhedra P, and Q inside P, repeated tailoring allows P to be reshaped to Q. Rescaling any Q to fit inside P, the result is universal: any P can be reshaped to any Q. This is one of the main theorems in Part I, with unexpected theoretical consequences.

  Part II carries out a systematic study of “vertex-merging,” a technique that can be viewed as a type of inverse operation to tailoring. Here the start is P which is gradually enlarged as much as possible, by inserting new surface along slits. In a sense, repeated vertex-merging reshapes P to be closer to planarity. One endpoint of such a process leads to P being cut up and “pasted” inside a cylinder. Then rolling the cylinder on a plane achieves an unfolding of P. The underlying subtext is a question posed by Geoffrey Shephard in 1975 and already implied by drawings by Albrecht Dürer in the 15th century: whether every convex polyhedron can be unfolded to a planar “net.” Toward this end, the authors initiate an exploration of convexity on convex polyhedra, a topic rarely studied in the literature but with considerable promise for future development.

  This monograph uncovers new research directions and reveals connections among several, apparently distant, topics in geometry: Alexandrov’s Gluing Theorem, shortest paths and cut loci, Cauchy’s Arm Lemma, domes, quasigeodesics, convexity, and algorithms throughout. The interplay between these topics and the way the main ideas develop throughout the book could make the “journey” worthwhile for students and researchers in geometry, even if not directly interested in specific topics. Parts of the material will be of interest and accessible even to undergraduates. Although the proof difficulty varies from simple to quite intricate, with some proofs spanning several chapters, many examples and 125 figures help ease the exposition and illustrate the concepts.

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  Real Life in Real Time: Live Streaming Culture

  Johanna Brewer, Bo Ruberg, Amanda L. L. Cullen, and Christopher J. Persaud

  The cultural ramifications of online live streaming, including its effects on identity and power in digital spaces. Some consider live streaming—the broadcasting of video and/or audio footage live online—simply an internet fad or source of entertainment, yet it is at the center of the digital mediation of our lives. In this edited volume, Johanna Brewer, Bo Ruberg, Amanda L. L. Cullen, and Christopher J. Persaud present a broad range of essays that explore the cultural implications of live streaming, paying special attention to how it is shifting notions of identity and power in digital spaces. The diverse set of international authors included represent a variety of perspectives, from digital media studies to queer studies, from human-computer interaction to anthropology, and more. While important foundational work has been carried out by game studies scholars, many other elements of streaming practices remain to be explored. To deepen engagement with diversity and social justice, the editors have included a variety of voices on such topics as access, gender, sexuality, race, disability, harassment, activism, and the cultural implications of design aesthetics. Live streaming affects a wide array of behaviors, norms, and patterns of communication. But above all, it lets participants observe and engage with real life as it unfolds in real time. Ultimately, these essays challenge us to look at both the possibilities for harm and the potential for radical change that live streaming presents. Source: Publisher

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  Bringing Stakeholders Along for the Ride: Towards Supporting Intentional Decisions in Software Evolution

  Alicia M. Grubb and Paola Spoletini

  Context and Motivation: During elicitation, in addition to collecting requirements, analysts also collect stakeholders’ goals and the present and historical interests that motivate their goals. This information can guide the resolution of requirements conflicts, support the evolution of requirements when changes occur (e.g., environmental constraints), and inform decisions in software design.

  Problem: Unfortunately, this information is rarely explicitly represented and maintained. When a stakeholder is modeled in the literature, the captured information is only part of that stakeholder’s intention (i.e., the goals and the present and historical interests that motivate those goals) and not other requirements documents. In addition, such representations of a stakeholder are not traced and kept aligned with the design and, thus, cannot be used during iterative development and in case of changes.

  Principal Idea: To support engineers in making informed decisions during the design, development, and evolution of a system, we propose a framework to collect and maintain intentionality in an efficient and effortless way.

  Contributions: To define intentionality, disambiguate it from its use in literature, and position it in relation to similar concepts (i.e., rationale and goals), we conduct a literature review. Based on our derived definition, we present our framework to appropriately include intentionality throughout the stages of a project and the research agenda to realize such a framework.

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  Pop-Up Geometry: The Mathematics Behind Pop-Up Cards

  Joseph O'Rourke

  Anyone browsing at the stationery store will see an incredible array of pop-up cards available for any occasion. The workings of pop-up cards and pop-up books can be remarkably intricate. Behind such designs lies beautiful geometry involving the intersection of circles, cones, and spheres, the movements of linkages, and other constructions. The geometry can be modelled by algebraic equations, whose solutions explain the dynamics. For example, several pop-up motions rely on the intersection of three spheres, a computation made every second for GPS location. Connecting the motions of the card structures with the algebra and geometry reveals abstract mathematics performing tangible calculations. Beginning with the nephroid in the 19th-century, the mathematics of pop-up design is now at the frontiers of rigid origami and algorithmic computational complexity. All topics are accessible to those familiar with high-school mathematics; no calculus required. Explanations are supplemented by 140+ figures and 20 animations. Source: Publisher