In an effort to advance discrete element aggregation using the Grasshopper3D plugin WASP (and Andrea building new features into it along the way), we are exploring a ‘sequence-based design’ approach and identified Peter Pearce’s Curved Space Diamond Structure as an ideal foundation.
Digital model of Peter Pearce’s Curved Space Diamond StructureContinue reading →
Applying a clustering algorithm to an inventory of irregular unique objects can help to reduce the complexity involved in designing with such parts significantly. By dividing the inventory items into groups with similar characteristics, each group can then be represented by one “proto-part” instead, therefore reducing the amount of unique elements to be handled in setting up aggregation logics and the aggregation processes. The decision about the number of different groups (Fig. 1) can be completely left to an algorithm (depending on various predefined – by the programmer – conditions) or be manually determined by the user/designer.
Fig. 1: clustering of inventory with different amounts of groups (“proto-parts”)
Based on the Sommerville tetrahedron, part systems using multiple compatible types can be created that produce more differentiated complex aggregations.
Fig. 1: Chart from Michael Goldberg, “Three Infinite Families of Tetrahedral Space-Fillers,” Journal of Combinatorial Theory A, 16, pp. 348–354, 1974.Fig. 2: Construction of a Sommervile No. 1 tetrahdron
The particularity here is, that the No. 1 tetrahedron consist of two “brackets” of each 2 triangles with two edges the length of the square root of 3 and one edge length of 2, connected at an right angle at their edges of the length 2.