Most general purpose Computer Algebra (CA) systems include more and more sophisticated 2D and 3D plotting facilities. Axiom, Macsyma, Maple, and Mathematica, for example, all include options to change graphical parameters such as colors, labels, viewpoint, or painting style. In addition several of them allow interactive rotating, choice of lighting model, or recording of frames for later replay and animation.
     Clearly, improved visual appearance makes graphics always more appealing to the user who might (wrongly) assume that these graphics are not only beautiful but also reliable. In fact, improved visual appearance was usually added as part of successive releases of these systems without changing the underlying approach, which remains nearly identical in all major systems: first, points are computed on the CA side; then the data produced are translated into an intermediate representation and sent to the graphical part of the application (which is sometimes a separate process); finally the intermediate representation is rendered either in a separate window or inside a notebook-style document. The whole approach is uni-directional (CA system to graphical part), limiting the possibilities of interacting with the mathematical object behind the image.
     Recently, several CA systems have included links with commercial high-quality volume rendering packages including AVS [UFK+89] and IRIS Explorer [Edw92]. However, communications between these packages and the CA system is still based on a one-way commonication (from the CA system to the graphics side) which does not allow back requests such as computation of additional points when inteacting with the graphics.
     In this paper we will present a number of techniques which are aimed towards making plotters mmore intelligent. By intelligent plotting we mean taking advantage of the symbolic and/or numerical capabilities available from a mathematical engine in order to transparently improve reliability, speed, and usability.
     The experiences presented in this paper were made using two packages: the Graphing Calculator [Avi95] and IZIC [FKM93]. In short, the Graphung Calculator is a small Mmmacintosh program designed as a successor to the usual desktop calculator. It includes an expression editor and a graphical window were expressions can be plotted (see figure 9). The whole program is very much direct manipulation oriented both in terms of formula editing and interaction with the graphics. It is also extremely simple to use in the spirit of the Macintosh desktop accesory series. Among its characteristics, one may notice that the set of available functions is predefined and relatively small.
     IZIC is a stand-alone 3D graphic tool allowing visualization of mathematical objects such as curves and surface under Unix/X11 [FKM93]. In short, IZIC capabilities include management of the illumination model, shading, transparency, etc. The architecture consists of ZICLIB - a hardware-independent C library providing a large collection of graphical operations - which is linked with a Tcl interpreter [Ous94]. At runtime, IZIC can be driven both through its graphic control panel and via TCL scripts which can be sent remotely from one or more CA systems. Currently, there are four interfaces ro IZIC: from maple, Mathematica, Reduce, and Macsyma.