Architecture and the Rhino Math Plug-In

Professor Andrew Saunders and Jess Maertterer educate architectual students at the Rensselaer Polytechnic Institute N.Y. In an advanced level design studio dealing with differential geometry they used the Math PlugIn to explore parametric surfaces with Rhinoceros 3D.

Adam LoGiudice


Description of the Design Studio

The studio will focus its investigation by exploring recent advancements of surface theory in mathematics, architecture's return to material practices, industrial shifts from mass standardization to mass customization, and new socio-economical programmatic relationships.

The studio will begin by understanding the role of surface, material and geometry in the practice of early 20th century reinforced concrete pioneer Luigi Nervi, and also other contemporaries such as Eduardo Torroja, Eugene Freyssinet, Robert Maillart and Felix Candela. In addition to these architect/engineers the studio will also look at other peripherally related designers such as Erwin Hauer and Naum Gabo. We will explore how their use of surface, material and geometry allowed them to negotiate between infrastructure and architecture. Due to the extreme costs of labor and exhaustion of the constructible geometries, in particular developable surfaces (those that have linear generating lines in order to construct traditional wood form work), these practices ceased to evolve giving way to new investigations of light weight membrane structures. Although lightweight membrane structures are interesting in themselves they never impacted infrastructural architecture in the same way.

Differential Surfaces
Particularly relevant to this studio, is the work of Alfred Gray who authored Modern Differential Geometry of Curves and Surfaces with Mathematica a complete manual used to visualize and construct surfaces based on differential equations. In the 19th century surface theory was a very important area of mathematics both in research and teaching. Earlier mathematicians made extensive use of models and drawings. Due to recent computational developments such as Stephen Wolfram's Mathematica, mathematical trends show an increased return to surface theory enabled by computational investigation. Students will learn how to construct and control these formula driven surface geometries in order to speculate on their value as architectural devices. Students will explore the flexibilities provided by the mathematical formulas in order to embed multiple parameters of architectural performance within the geometric logic as well as enabling them to synthesize with standard architectural devices. At this point thanks to Matthias Weber from Indiana Universtiy for his Mathematica files with minimal surfaces.

Computer Aided Drafting and Computer Aided Manufacturing have both drastically altered the industrial paradigm of mass standardization. Given these new computationally driven methods, architects have all too often quickly abandoned formal disciplines of geometry and instead turned to reductive principles for describing seemingly, complex form. In addition to totally weakening any integrity of formal logic that may have lead to the initial formation, this computationally aided process falsely assumes that as long as it is CAD/CAMed the resultant form will gain integrity. The studio will work with CAD/CAM technologies both inside the school of Architecture and the Advanced Manufacturing Lab to explore manufacturing techniques integral to the surface logics of differential geometry.


Ashley Hanrahan



Douglas Samuel



Emaan Farhoud



Joe Morin



John Davi



Justin Bosy



Kerstin Kraft



Lexie Sanford



Monzoor Tokhi



Patrick Conway



Sean Burns



Tori Means



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