  We consider the problem of approximating a two-dimensional shape contour (or
curve segment) using discrete assembly systems, which allow to build geometric
structures based on limited sets of node and edge types subject to edge length
and orientation restrictions. We show that already deciding feasibility of such
approximation problems is NP-hard, and remains intractable even for very simple
setups. We then devise an algorithmic framework that combines shape sampling
with exact cardinality-minimization to obtain good approximations using few
components. As a particular application and showcase example, we discuss
approximating shape contours using the classical Zometool construction kit and
provide promising computational results, demonstrating that our algorithm is
capable of obtaining good shape representations within reasonable time, in
spite of the problem's general intractability. We conclude the paper with an
outlook on possible extensions of the developed methodology, in particular
regarding 3D shape approximation tasks.
