On dinamic spiral patterns - polygonal frames inscribed in circular sections of quadric surfaces

Abstract

Spiral forms, nowadays actual, especially in the area of architecture and design, were the inspiration point for an creative geometrical research. Acquainted with different approaches, present in practical and theoretical sense, from empiric creations to parametric modeling, we chose to explore the dynamic patterns which appear in spiral shapes generating process. Since the term "spiral" is directly connected to circles we aimed our investigation to quadric surfaces with circular sections, where inscribed polygons obtain the spiral form by "twisting". We observed the series of inscribed polygons as dynamical spiral patterns of scaled frames, according to the geometry of the basic quadric surface. This investigation includes surfaces: cone, sphere, ellipsoid and elliptic hyperboloid. Three types of regular polygons are here included: triangle, square and pentagon. 3D model presentation of dynamic spiral patterns is performed in engineering software Auto-CAD. While considering the possibilities in application of such creations (models), some optimal intersecting surfaces are discussed.