Reinterpreting Rasmi Domes With Geometric Constraints: A Case Of Goal-Seeking In Parametric Systems

Geometry has long been a generator of architecture. In traditional Persian architecture, Rasmi domes project a drawing onto a predefined 3D geometry. In fact, the word 'rasmi' and the verb for drawing in Persian have the same linguistic root. Projection is readily done in manual drawings or conventional CAD programs. From a constraint perspective, the dome is constrained by the drawing and the 3D geometry. If the latter constraint is replaced by invariance of distance on the original drawing, a class of domes results, but members of this class cannot be computed conventionally. Class members are developable from a planar layout of triangles, which is, in turn, generated by a simple drawing rule. This yields a parametric structure of four parameters. Three determine the initial planar diagram. One determines configuration. Further, domes in the class are mechanisms: they are not fully specified by the constraints and parameters. We develop the geometric constraints representing the location of the defining points of a dome and present a goal-seeking algorithm to solve the constraints within a propagation-based parametric modeling system.