  This paper presents a comprehensive review of geometric constraint solving in
parametric computer-aided design (CAD), with the major focus on its advances in
the last 15 years. Geometric constraint solving can date back to the very first
CAD prototype, Sketchpad, in the 1960s, but serious research studies were
carried out only after parametric CAD was introduced in the late 1980s. In the
following 30-year history of GCS research, two development stages may be
identified: (1) the first 15 years (late 1980s - mid 2000s) were primarily
devoted to geometric constraint decomposition for well-constrained systems or
those with only structural constraint dependencies; and (2) the second 15 years
(late 2000s - now) have seen research efforts shifted towards classification
criteria and decomposition algorithms for general constraint systems (with and
without non-structural constraint dependencies). Most existing reviews focused
on the first 15 years. The problem researched in the second 15 years is,
however, equally important, considering that a manually specified constraint
system usually contains under- and over-constrained parts, and that such parts
must be correctly detected and resolved before numerical solving can work. In
this regard, this review paper covers both stages and will discusses what has
already been made possible for handling general constraint systems, what
developments can be expected in the near future, and which areas remain
problematic.
