Classical assembly of micelles, cylinders, gyroids, and other structures usually takes place in three dimensions or on a rigid planar support. This program aims to assemble and reconfigure complex dynamic patterns of objects on shape-changing contoured surfaces. We employ fluid membranes, only nanometers thick, as a support for rigid plate-like building blocks, and employ tension and curvature to accomplish assembly. Regulating tension and curvature controls pairwise and non-additive multi-body interactions enabling precise positioning of features on length scales of microns and many tens of microns, at least an order of magnitude greater than the building blocks themselves.