Copyright © 2011 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions Dept, ACM Inc., fax +1 (212) 869-0481 or e-mail permissions@acm.org . CAe 2011, Vancouver, British Columbia, Canada, August 5 – 7, 2011. © 2011 ACM 978-1-4503-0908-0/11/0008 $10.00 Computational Aesthetics in Graphics, Visualization, and Imaging (2011) D. Cunningham and T. Isenberg (Editors) Interactive Modeling of Muqarnas N. Hamekasi 1 , F.F. Samavati 1 and A. Nasri 2 1 Department of Computer Science, University of Calgary, Canada 2 Department of Computer Science, American University of Beirut Figure 1: Model of an existing building. Abstract Muqarnas is a mesmerizing 3D feature of Islamic architecture that exhibit intricate geometry. Such designs are composed of several basic structures combined in successive layers, producing complicated 3D surfaces. In this paper we propose a new approach for interactive modelling of muqarnas based on their layered structure. As a guidance for the modeling workflow, floor plans are used. We also discuss how to edit the resulting models and how to automatically generate new forms. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Modeling packages 1. Introduction Mathematics and art, these two seemingly diverse aspects of humanity, have influenced each other from the early days. Over thousands of years, the use of geometric patterns as decorations is well established. Art has evolved and devel- oped along with humankind, changing not only with time but also with cultural and geographical conditions, result- ing in a diversity of styles. For instance, traditional western art exhibits figurative art which is derived from real object sources. In contrast, use of abstract geometrical patterns be- came a popular and principal characteristic of Islamic art simply because Islam does not encourage figure represen- tations in artistic expression. Consequently, Islamic art has a rich mathematical foundation. Islamic geometric decorations can be categorized into two major categories: two dimensional and three dimensional patterns. The first group is the type of ornament used to dec- orate flat or curved surfaces, such as domes or walls. A well- known example of this category is star pattern. The other category is Muqarnas, a type of 3D ornamental structure. Muqarnas is the Arabic word for stalactite vault; a capti- vating structure based on replicating units arranged in tiers, each one supporting another corbel on top of it. The early purpose of these structures was to create an architectural transition between a circular dome and its square supporting 129 DOI: 10.2312/COMPAESTH/COMPAESTH11/129-136