Ongoing development of digital modeling software allows design to depart from the Euclidean geometrical limits that paralleled architectural thinking for many years. Before digital technologies, curved surfaces and forms were the product of approximations using tangents to circular arcs and straight-line segments that were translated from drawings to the building site. In freeing the designer from the constraints of Cartesian space, digital modeling programs typically use the
topological geometry of continuous curves and surfaces.
Also known as “rubber sheet” geometry, topological geometry enables curvilinear surfaces to be described as NURBS. The curves and surfaces produced by NURBS provide a high degree of formal control via “control points,” “weights,” and “knots.” Extending the rubbersheet analogy, it is easier to imagine how if we fixed certain points of it, added weights to others, and affected it from other positions we would be able to see the resultant deformations as we varied our actions. NURBS provide the mathematical underpinning for this very simplified description of the process, and allow the user to develop complex geometrical designs computationally and transfer this data using digital machinery as CNC.
The key advantage of NURBS is their role in the production of a wide range of geometric forms, ranging from simple volumetric solids to extensively detailed, complex surfaces. NURBS offer a very efficient way of representing data by using comparatively few steps for shape computation, which is why many digital modeling software packages use them. If this all sounds rather abstract, then it may help to think about them as Branko Kolarevic suggests: “NURBS are a digital equivalent of the drafting splines used to draw the complex curves in the cross-sections of ship hulls and airplane fuselages. Those splines were flexible strips made of plastic, wood or metal that would be bent to achieve a desired smooth curve, with weights attached to them in order to maintain the given shape.”
Source:
Digital Fabrication in Architecture. By Nick Dunn