# PhD Proposal Presentation - Tsung-Hsien Wang -School of Architecture - Carnegie Mellon University

Wednesday, May 19, 2010

# PhD Proposal Presentation - Tsung-Hsien Wang

## May 26, 2010, 12:00pm, MMC Intelligent Workplace

ABSTRACT

A growing trend in contemporary architectural practice, pioneered by such avant-garde architects as Frank Gehry, Zaha Hadid and others, exploits NURBS (Non-Uniform Rational Basis Spline) surfaces to design and model intricate geometries for projects which otherwise would be impossible to realize. In doing so, they have liberally borrowed digital fabrication techniques developed in the automobile and aerospace industries (Kolevaric 2005, 2008; Pottmann 2008). A NURBS surface is a mathematical model for freeform shapes. To manifest a NURBS surface, a discrete model, namely, mesh, is utilized.

Transforming a NURBS surface into a mesh appropriate for application is computationally intensive, and generally, it is not an easy task for architects or designers who have no formal geometry training.

In order to design, model, and, subsequently, fabricate intriguing, sometimes intricate, freeform shapes, this research looks at the surface tessellation problem, which is an extension of the problem of meshing a NURBS surface, with an added consideration of incorporating constructible building components. There are close relationships and analogies between the elements of a mesh and the components of a freeform design, e.g., face to panel, edge to structural frame, etc.

Initially, features of a NURBS surface and contemporary tessellation methods are examined.

Mathematically, a NURBS surface is regulated by a set of control points and edges. The control points are used mainly to interpolate a continuous shape using a higher order equation, in most cases, usually cubic.  The edges delineate the appearance of the freeform shape. For a surface, edges  (also called boundaries) indicate where the surface analysis starts and where it ends, and thus, plays a significant
role in the meshing process.

Two types of boundaries are examined in this research. The first are global boundaries, which form the overall appearance, e.g. exterior edges, or interior trimming edges. The second type is a local boundary, which specifies how a discrete element is formed˜namely, the pattern on a face, e.g. triangle or quadrilateral. By looking at given surface boundary conditions and tessellation patterns, this research aims to present a parametric modeling framework for pattern generation, and to develop strategies to resolve issues that stem from the juxtaposition of computational geometry and freeform architectural design.