30,278 research outputs found

    On the expected size of the 2d visibility complex

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    We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the asymptotic expected number of free bitangents (which correspond to 0-faces of the visibility complex) among unit discs (or polygons of bounded aspect ratio and similar size) is linear and exhibit bounds in terms of the density of the objects. We also make an experimental assessment of the size of the visibility complex for disjoint random unit discs. We provide experimental estimates of the onset of the linear behavior and of the asymptotic slope and y-intercept of the number of free bitangents in terms of the density of discs. Finally, we analyze the quality of our estimates in terms of the density of discs.

    Assessing mobile mixed reality affordances as a comparative visualization pedagogy for design communication

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    Spatial visualisation skills and interpretation are critical in the design professions but are difficult for novice designers. There is growing evidence that mixed reality visualisation improves learner outcomes, but often these studies are focused on a single media representation and not on a comparison between media and the underpinning learning outcomes. Results from recent studies highlight the use of comparative visualisation pedagogy in design through learner reflective blogs and pilot studies with experts, but these studies are limited by expense and designs familiar to the learner. With increasing interest in mobile pedagogy, more assessment is required in understanding learner interpretation of comparative mobile mixed reality pedagogy. The aim of this study is to do this by evaluating insights from a first-year architectural design classroom through studying the impact and use of a range of mobile comparative visualisation technologies. Using a design-based research methodology and a usability framework for accessing comparative visualisation, this paper will study the complexities of spatial design in the built environment. Outcomes from the study highlight the positives of the approach but also the improvements required in the delivery of the visualisations to improve on the visibility and visual errors caused by the lack of mobile processing
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