Learning modules for geometric pattern identification and mathematical modeling of facade systems

Document Type

Conference Proceeding

Publication Date



Engineering Technology

Publication Title

ASEE Annual Conference and Exposition, Conference Proceedings


Over the past decade, responsive facade systems have emerged to improve user comfort, energy consumption, and cost efficiency as they are capable of responding and adapting to environmental stimuli. Design of a responsive facade system involves various fields such as engineering, architecture, robotics, material science, mathematics, physics, structure, fabrication, and geometry in the process of design. The geometry of facades as socio-cultural design parameters affects the visual performance of facade. However, existing responsive facades are socio-culturally inert. This paper presents a set of educational activities that can be used in facade design courses. The proposed hands-on activities consist of different modules on pattern identification, mathematical modeling, shading function development, and design of the mechanism and simulation of the designed facade system. The educational activities of each module are demonstrated by using a Persian pattern named “SHAMSEH” as a pattern of the facade system. Excel software was utilized to develop the mathematical model of the selected pattern. Grasshopper-for-Rhino software was used to create shading function, design a mechanism for motion, and simulate the facade system. The proposed hands-on activities assist students, educators, and architects in pattern identification and mathematical modeling, in mechanism and control design, and in simulation of a facade system.


A. Eydgahi is a faculty member in EMU's School of Engineering.

*N. H. Matin is an EMU student.