BEYOND FLAT SURFACES PARAMETRIC DERIVATIONS OF HISTORICAL ISLAMIC GEOMETRIC DESIGNS

Abstract

Abstract This paper sets out to identify a guiding methodology and define algorithms to extend the existence of Islamic geometric designs beyond flat surfaces. The paper discusses two computational approaches to deriving various non-flat geometric compositions: Euclidean Point Extrusion and Curved Surface Fitting. The paper examines historical precedents, conducts an in-depth analysis of patterns employed to generate those elements, then establishes a computational process to explore the potential of translating 2D Islamic Geometric Designs into 3D non-flat surfaces.