Use of ImplicitPlot in Drawing Surfaces Embedded into LATEX Documents

KETpic is a macro package of computer algebra systems(CAS) that allows us to insert figures easily into LATEX documents. As such, KETpic can also be used to generate surfaces. But because surfaces appear flat both on the screen and in printed form, shading is often used to emphasize their inherent three-dimensional nature. Unfortunately, this solution is no longer valid in KETpic, as it generates figures in black-and-white only. In this paper, we outline some techniques to yield line drawing pictures of surfaces by using plot data obtained from implicit functions of two variables. The paper discusses some theoretical issues regarding the use of the ImplicitPlot command for drawing surfaces and describes the implementation of our results by means of several illustrative examples. As the reader will see, we obtain very nice figures that can readily be embedded into our LATEX documents in order to yield educational materials as well as professional printouts of scientific documents.