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.
Description of the Design Studio
Premise
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.
Precedent
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.
CAD/CAM
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.
