Surface triangulations based-on 3D arbitrary point-sets are widely applied in CAGD/CAD and reverse-engineering

etc. In the first place

this paper reviews two main methods in surface triangulations

named as plane-projection and direct triangulation. For the former

Delaunay triangulations are mainly enunciated. For the later

algorithm developed by B. K. Choi is particularized. Some typical algorithms are introduced in detail

as well as various data-structures built in these algorithms. Next

since the final result of triangulation is determined by the optimal criterion

some proverbial optimal criteria are specified and analyzed in this paper

and they are thoroughly compared with each other here through anatomizing an example. It is pointed that

in practical engineering

it is necessary to develop new algorithms with new criteria for triangulations of scattered points sampled from complicated surfaces so as to maintain the properties such as better smoothness and shape preserving. Finally the time and space complexities of various algorithms are briefly and concisely discussed

also the research trend of surface triangulations based-on 3D arbitrary point-sets.