The three-dimensional printing is a manufacturing method involving the addition of materials by using certain principles valid in printing techniques. There are various techniques of a three-dimensional printing method and the most of them could be applied inclusively to generate objects of polymers. The objective of the research presented in this paper was to analyze the capabilities of 3D printing process or equipment of generating fine details and to identify a way of evaluating these capabilities when using polyester PLA as filament material. The systemic analysis of the printing techniques which use a fused polymer filament deposition showed that there are some groups of factors able to affect the obtaining of fine details. An experimental research was designed in order to highlight the influence exerted by the diameter of the nozzle orifice and by the values of sharp angles of isosceles triangles on the heights of these triangles, thus obtaining an image concerning the possibilities of generating sharp edges by three-dimensional printing. To evaluate the capacity of the 3D printing process of obtaining thin walls, a spiral including linear segments with a decreasing thickness from 1 mm was also achieved on the test piece. By mathematical processing of the experimental results using a specialized software, empirical mathematical models were determined to evaluate the intensity of influences exerted by the two process input factors on the heights corresponding to isosceles triangles characterized by sharp angles.