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Recycled/Pre-Cycled
Published in Christopher Beorkrem, Material Strategies in Digital Fabrication, 2017
Packed is a design/build project defined by parameters of efficiency. These parameters are necessitated by the project needing to be fabricated in Switzerland and constructed in Shanghai. The installation was assembled for the Shanghai Museum of Arts and Crafts as part of the exhibition 3D Paper Art. The form of the installation is inconsequential to some of the material parameters and highly consequential to others. The cones are organized to construct a perfect spherical dome; as such, each of the cones taper uniformly toward a point at the centre of the dome's base. This system, however, could also be adapted to other shapes, with tapers in (and out) to accommodate undulations in a surface. The patterning of each of the cones on the sphere can be derived as a sort of circle-packing. Circle-packing is the basis for a myriad of tessellation types, attempting to maximize the density of circles in a given area.
Finetuning Discrete Architectural Surfaces by use of Circle Packing
Published in Journal of Asian Architecture and Building Engineering, 2023
In the previous section, we summarised how various properties of the surface are determined as functions of other properties. A mesh defines the topology, the number of triangles and how they are connected, and serves as a container of geometric structures. A metric is a function specifying the edge lengths , which determines the shape of each triangle. An embedding is a function specifying the vertex coordinates , that is, how each triangle is placed in the space. The Gaussian curvatures are solely determined by the metric (the triangle shape) independent of an embedding. To obtain a surface with prescribed Gaussian curvatures, we have to find the appropriate metric. Instead of handling the edge lengths directly, we can consider proxy variables. A circle packing is a function specifying the radius of a circle centred at each vertex. A conformal structure together with a circle packing determines a metric. Table 1 summarises the relations among various structures on a mesh. This may sound complicated but it allows us flexibility in choosing design variables when the problem of finding a desired surface is formulated in terms of an optimisation problem.