Exploring Symmetry as a Modeling Tool Project Report

The word symmetry originates from the Greek word sum metria (’to measure together’ ) and has two primary definitions; the harmony of the parts with each other and the whole and the condition of being well-balanced and well-proportioned. Both of these definitions imply a strong relationship between symmetry and beauty. Essentially, many objects in nature which human beings find exceptionally appealing, such as a snowflake or the shell of a snail, are highly symmetrical. Furthermore, studies show that infants prefer to look at symmetric patterns rather than unsymmetric ones [2]. In addition to this strong link between symmetry and attractiveness, existence of symmetry, either as perfect symmetry or partial or approximate symmetry, almost in every object we see around us has an intense influence on the use of symmetry in many different fields, such as engineering, art, and architecture. Besides satisfying aesthetic concerns, impact of symmetry on economical and functional considerations reinforces the use of symmetry in man-made structures. To illustrate, symmetry is used as an organizing principle in architecture and use of repeated structures in objects eases the manifacturing process. To conclude, this ubiquitous nature of symmetry makes it important to explore this notion to have a better understanding of the world. Therefore, many studies focus on exploring symmetry in application areas diversing from biology to architecture. Shape analysis is one of these application fields. Related work in this field include shape matching, completion of occluded parts, mesh segmentation, and compression.