11th EAEA Envisioning Architecture: Design, Evaluation, Communication Conference in 2013

Track 3 | Conceptual Representation | Exploring the layout of the built environment

Visibility polygon traversal algorithm

ABSTRACT

The determination of visibility relations within polygonal environments has applications in many different fields; In the current context it is primarily investigated as a basis for spatial architectural analysis, and as a design driver for architectural design from a user and occupant perspective, but it is equally applicable to a wide range of engineering problems and it’s a well-established topic in computational geometry. We introduce a new query-based algorithm for traversing over the visible convex regions of a polygon with holes from any point inside the polygon or from any of its vertices, where each query runs in O(f’ h’ + log n) for a polygon with n vertices, f’ visible convex partitions, and h’ visible holes, with a preprocessing stage that runs in O(n log* n) with O(n) space. The log n component of the query only applies to internal points. The visibility polygon traversal algorithm is applicable to a varied set of visibility problems, including the construction of visibility polygons (isovists), and visibility graphs of polygon vertices and/or points inside the polygon. The algorithmic findings are linked to spatial architectural analysis by representing the regions of architectural or urban plans that are permeable or visually open as polygons with holes. Two applications of the algorithm are presented, which have enabled more responsive and dynamic user interactions with architectural plans. These consist of an interactive isovist tool and a tool for calculating shortest paths, flows and distances within a multi-storey layout.

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AUTHORS

Åsmund Izaki

Computational Design & Research, R&D, Aedas, London, United Kingdom

Åsmund Izaki is a senior designer and researcher at Aedas R&D where he joined the Computational Design and Research group in 2007. During his time with Aedas he has been researching and implementing new forms of furniture design, architecture and urban planning through code. This takes the form of interactive tools and methods that have been applied in projects both internally and as an external service or in collaboration with industry or academic partners. Åsmund holds an MArch from NTNU, Norway and is regularly invited to lead courses and workshops on interdisciplinary topics related to design and technology.

Christian Derix

Computational Design & Research, R&D, Aedas, London, United Kingdom

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