title: Algorithmic Computer Reconstructions of Stalactite Vaults - Muqarnas - in Islamic Architecture
creator: Harmsen, Silvia
subject: ddc-510
subject: 510 Mathematics
description: Muqarnas, or stalactite vaults, are three--dimensional ornaments, common in the Islamic architecture.  They are used in vaults, domes, niches, arches, and as an almost flat decorative frieze. It is the function of a muqarnas to guarantee a smooth transition between straight walls and more curved parts.  A muqarnas vault is built from different niche--like elements, arranged in horizontal tiers.  One of the main characteristics of muqarnas is its form as a three--dimensional unit that can be represented as a two--dimensional outline. In this study, we focus on the question whether this two--dimensional projection contains all structure information of the three--dimensional muqarnas  vault.   Explicit definitions are given to create a framework in which we are able to describe the muqarnas structure. Each muqarnas element is described by means of parameters representing its type and measurements together with parameters that describe the position of the element in the muqarnas vault. A graph theoretical approach makes it possible to include the structure information of the three--dimensional muqarnas in the two--dimensional outline.  This is done by constructing a directed subgraph from the muqarnas design.  The main task is then to find all directed subgraphs corresponding to a muqarnas design for which a three--dimensional muqarnas representation is possible. We can construct three--dimensional computer reconstructions directly from the directed subgraphs.  An algorithm is developed  for constructing the directed subgraphs  and reconstructing the three--dimensional muqarnas. Two software tools are designed to execute this process. The program plantograph finds the directed subgraphs corresponding to a muqarnas structure from a muqarnas design. The program graphtomuq converts a subgraph into a three--dimensional computer reconstruction of the muqarnas. The various subgraphs result in different muqarnas reconstructions with the same plane projection. Some interaction is necessary to select the required reconstruction, for this art historical expertise is essential. The differences between muqarnas with the same plane projection can be local or global. Local means that by exchanging several elements the muqarnas are equal.  Muqarnas are globally different if more elements are involved and the shape, or number of tiers, of the muqarnas differ.  We can restrict the number of reconstructions if we know the proportions of the vault into which the muqarnas needs to fit. This gives  a restriction on the amount of tiers that can be used.    This work focuses on the muqarnas vaults fitting into domes or niches from the Seljuk and Ilkhanid periods. Different tests of such muqarnas from Anatolia and Iran are given. Additionally a new interpretation for the oldest known design which is found at Takht-i Sulayman is presented.
date: 2006
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/7047/1/diss.pdf
identifier: DOI:10.11588/heidok.00007047
identifier: urn:nbn:de:bsz:16-opus-70471
identifier:   Harmsen, Silvia  (2006) Algorithmic Computer Reconstructions of Stalactite Vaults - Muqarnas - in Islamic Architecture.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/7047/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng