Soley Ersoy

Abstract This study examines the topological properties of architectural decorations from the Anatolian Seljuk period, with a focus on the Malatya Grand Mosque (1224), the Kubadabad Palace (1227), and the Konya Karatay Madrasa (1251). By employing knot theory and two-structures, the research delves into the intricate interlaced motifs found in tile work and other decorative elements.

1. Introduction Sweeping is a widely used technique in geometric modeling to define the geometry of three-dimensional objects. The geometric and computational properties of this technique have been examined via various approaches where planar curves sweep along the trajectories called the spine curves. For instance, in the process of generating sweeping surfaces, the superiority of using the rotation minimizing frame (RMF) with the Frenet frame was compared in [1,2].

1. Introduction In 1843, William Rowan Hamilton, an Irish mathematician, first introduced the concept of quaternions [1]. Quaternions have since found numerous applications across a wide range of disciplines, including computer graphics, vision device development, animation representations, control theory, molecular dynamics, quantum theory, robot kinematics, and navigation devices.