How to compute and represent the Gaussian approximations of planar curved objects is described. Also considered are various applications of the Gaussian approximation to various primitive geometric operations on monotone curve segments. The exact solutions for these problems can be computed by solving simultaneous polynomial equations; however, this requires an intensive computation time. Efficient heuristic approximation algorithms using simple binary subdivisions on the original geometric components are suggested. It is shown that simple data structures such as arrays and circular lists can be used to represent the Gaussian approximations of planar curved objects.