Geometric Modelling of Statically and Dynamically Symmetric Patterns: Theory, Generation and Applications

Designing is a task which requires a combination of technical knowledge, skill, training, patience and artistic imagination. Most of the designs made by man or available in nature have inherent symmetry in them. Considerable mathematical analysis is required to discover an order in such designs and encode them in mathematical descriptions. Moreover, such analysis is usually specific to a particular design (or a class of designs) and is difficult to generalize. Geometric modelling can be used as a design tool to avoid unnecessarily tedious or repetitive tasks. This allows the artist to work on the design idea rather than its implementation. The work presents a unified modelling scheme for artists, craftsmen and common users to facilitate user-defined and automatic generation of designs starting with the simple geometric primitives at the lowest level and creation, storage and retrieval of statically and dynamically symmetric patterns that can be used to generate design layouts. It has direct applications in the domain of art, metal engraving, designer furniture, textiles, jewelry, woodcarvings, wallpapers, tiles, flower vases, etc.