# Knot Surfaces

Junfeng Wang (website), Yuan Zhan

Harvard University Graduate School of Design

Seminar

Brief: Generative Geometry Modeling

Faculty: Andrew Witt

2012

Apart from the control of fundamental curves, the control and characterization of surfaces is one of the pivotal geometric constructions in architecture. Surface geometry includes both conditions of global geometry (for example, topological configuration) and local geometry (for example, curvature and componentized discretization of surfaces). This exercise considers the conditions of global geometry and the generative methods for its control.

Using knot surface method to create a surface or surfaces that exemplify a topologically intricate assembly. The assembly should not be easily describable with any one view. Although there may be corners, creases, or ruptures in the surface, these should reinforce an integral logical quality demonstrated through shared tangencies, symmetries, coincidences, or other geometric conditions. Tiling or patterning your topological surface may deepen its spatial nuance.

Particular thought should be given to the structural performance of the configuration, as well as the spaces of enclosure defined by the surface(s).

This final assignment integrates the ideas global topology, geometric control, and parametric detailing. The key aspect of this assignment is designing an effect that plays out at both local and global scales. A related set of large-scale, medium-scale, and small-scale geometries are designed to achieve in intricate, unified, designed effect. The large-scale geometry is a topologically complex surface or complex or surfaces that forms the basis which defines a building volume. The medium-scale geometry will be some subset of the large-scale geometry, with a particular surface pattern. This medium-scale geometry becomes an armature for the small-scale geometry, which is a detailed powercopy achieving the designed effect. The small-scale geometry will be a detail, which should exhibit some parametric behavior and variation.