This paper extends previous work on the interpretation of line drawing
s of curved objects to include objects with tangential edges and surfa
ces. We present a catalogue of labelled junctions and show that the ex
istence of a legal global labelling can be determined in linear time.
However, minimising the number of invisible vertices necessary to prod
uce a legal global labelling is shown to be NP-hard. The potential com
binatorial ambiguity inherent in the drawings can be mitigated by usin
g information from the intensity image to identify points at which the
object surface is tangential to the viewing direction.