| 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 2005a, 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 kinds 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 kind is a local boundary, which specifies how a discrete element is formed—namely, the pattern of a face, e.g. triangle or quadrilateral. By looking at given surface boundary conditions and tessellation patterns, this research presents an algorithmic approach to pattern-based surface tessellation and develops strategies to resolve issues that stem from the juxtaposition of computational geometry and freeform architectural design.;The contributions includes the technical implementation of boundary-driven mesh generation, which demonstrates the potential of utilizing featured boundaries for customizable polygon-based tessellation in comparison to conventional iso-parametric subdivision. This is described through examples by extending the optimized mesh network for various pattern generations. In addition, pedagogical implications are exemplified by solving the geometric constraints for surface tessellation within the parametric modeling paradigm. These contributions are expected to support future sustainable development in the field of freeform architectural design.;Keywords: Pattern-based surface tessellations, irregular boundary conditions, meshing. |
