L_1 Shortest Path Queries among Polygonal Obstacles in the Plane

Given a point s and a set of h pairwise disjoint polygonal obstacles with a total of n vertices in the plane, after the free space is triangulated, we present an O(n+h log h) time and O(n) space algorithm for building a data structure (called shortest path map) of size O(n) such that for any query point t, the length of the L_1 shortest obstacle-avoiding path from s to t can be reported in O(log n) time and the actual path can be found in additional time proportional to the number of edges of the path. Previously, the best algorithm computes such a shortest path map in O(n log n) time and O(n) space. In addition, our techniques also yield an improved algorithm for computing the L_1 geodesic Voronoi diagram of m point sites among the obstacles

Shortest Path in a Polygon using Sublinear Space

\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\VorX}[1]{\mathcal{V} \pth{#1}} \newcommand{\Polygon}{\mathsf{P}} \newcommand{\Space}{\overline{\mathsf{m}}} \newcommand{\pth}[2][\!]{#1\left({#2}\right)} We resolve an open problem due to Tetsuo Asano, showing how to compute the shortest path in a polygon, given in a read only memory, using sublinear space and subquadratic time. Specifically, given a simple polygon \Polygon with $n$ vertices in a read only memory, and additional working memory of size \Space, the new algorithm computes the shortest path (in \Polygon) in O( n^2 /\, \Space ) expected time. This requires several new tools, which we believe to be of independent interest

Emergent Hybridity, Cyborgs in Architecture

This thesis examines architectural test-beds as an experimental and contemporary mode of creating architecture that realizes the potential of many of the connections and complexities found in living systems. It builds on the lineage of research from the Hylozoic Ground Environments and the notion of the chthonian, embodying the potent, hidden, and essential ingredients of life.1 From the notions of geotextiles and cyborgs, a new conception of architecture is uncovered at the scale of material compositions, wearables, and tensile structures in architecture. After a survey of precedents as well as their concepts, design processes, and cross-disciplinary inputs, the thesis concludes with the design of an interconnected human body that is, an expanded human physiology connecting body, site, and surrounding structure in the form of public space in the alleyways of the North Point Lowlands, Hong Kong. The design departs from the North Point Lowland’s reclaimed and constantly rehabilitating site features to generate a coherent public space. The design proposal utilizes bifurcative qualities found in living matter, solar energy, and physiological processes to inspire a physical structure and its inhabitants. The design proposal is a co-generated physical form arising from a moment of feeling peaceful and emergent while experiencing the hybrid qualities of life in the alleyways of Hong Kong, North Point. 1. Beesley, Philip, Rob Gorbet, Pernilla Ohrstedt, and Hayley Isaacs. “Introduction Liminal Responsive Architecture.” In Hylozoic Ground: Liminal Responsive Architecture, 12-42. Cambridge, Ont. Canada: Riverside Architectural Press, 2010