  The task of finding an extension to a given partial drawing of a graph while
adhering to constraints on the representation has been extensively studied in
the literature, with well-known results providing efficient algorithms for
fundamental representations such as planar and beyond-planar topological
drawings. In this paper, we consider the extension problem for bend-minimal
orthogonal drawings of planar connected graphs, which is among the most
fundamental geometric graph drawing representations. While the problem was
known to be \NP-hard, it is natural to consider the case where only a small
part of the graph is still to be drawn. Here, we establish the fixed-parameter
tractability of the problem when parameterized by the size of the missing
subgraph. Our algorithm is based on multiple novel ingredients which intertwine
geometric and combinatorial arguments. These include the identification of a
new graph representation of bend-equivalent regions for vertex placement in the
plane, establishing a bound on the treewidth of this auxiliary graph, and a
global point-grid that allows us to discretize the possible placement of bends
and vertices into locally bounded subgrids for each of the above regions.
