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Constructed geometric diagrams capture a dynamic relationship
between text and image that played a central role in ancient science and
mathematics. Euclid, Theodosius, Ptolemy, Archimedes and others constructed
diagrams to geometrically model optics, astronomy, cartography, and
hydrostatics. Each derived geometric properties from their models and
interpreted their results with respect to the model's underlying semantics. Although
diagram construction is a dynamic process, the media in which these works were
published (manuscripts and books) forced scholars to either view a snapshot
of that process (a static image) or manually perform the entire construction. Mainstream
approaches to digitization represent constructed diagrams as they appear in print,
as static images. Such representations fail to capture the dynamic nature of constructed
diagrams and so we designed and implemented a computational framework for
dynamically interacting with them. Our architecture for representing, retrieving, and
interacting with diagrams has already been used to produce a publicly-available, archival-quality
digital corpus of diagrams for the Archimedes Palimpsest Project, establishing our
approach's viability in the real world. After using our system to study diagrams in
Archimedes, we discuss the generality of our approach and its application to other domains
including circuit design, software engineering, and patent databases.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
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Gabriel A. Weaver, "Semantic and Visual Encoding of Diagrams." Dartmouth Computer Science Technical Report TR2009-654, August 2009.
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