POLYHEDRAL TESSELLATIONS:

Workshop on 2D and 3D Pattern Transformations

escher

M.C.Escher, “Reptiles”, 1943

The translation of a three-dimensional geometry onto the two-dimensional plane requires certain mathematical calculations, which vary based on different mapping methods.

These methods and techniques create rule based relations between the diverse dimensions of mathematical space and consequently, the same solid is readable on plane surfaces through projective geometry. Architects and designers acknowledge such relations and tempt to imagine and realize physical forms from their two-dimensional transitions. Therefore, the conversation of the solid geometry between different dimensions play an ambivalent role in design.

The computational era provided new methods and techniques that made challenging forms more applicable and reproducible. Consequently, reading the relation among different dimensions has become more crucial than ever. The comprehension of the spatial relations of complex geometries stand therefore as one of the main Future trajectories of design computation.

This workshop session aims to highlight such relations by providing participants with an understanding of a different kind of transition. At the beginning, participants will be provided with various pattern designs on a plane geometry. They will explore the symmetry notations and explore the visual rules behind these patterns.   Secondly, participants will be introduced to three-dimensional polyhedral geometries both as digital models in Rhinoceros and paper models. The design process will consist of developing and manipulating three-dimensional models by placing patterns onto three-dimensional geometries. Participants are welcome to use analog and/or digital tools such as paper cutter, Rhinoceros, and Grasshopper to explore innovative geometries. The final models will be produced with 3D printer or laser cutter at the end.  By doing so, participants will inevitably rethink the relations between the solid geometry and the plane geometry. Furthermore, they will gain an intuitive understanding of basic notions such as symmetry rules and groups, and visual computation of transitions between different dimensions and therefore, projective geometry.

This workshop will be held at the CAADFutures 2017 organized by Istanbul Technical University, Institute of Science, Engineering and Technology, Department of Informatics, Architectural Design Computing Graduate Program.

 

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