|Narcisse||Curve, Surface and Mesh Objects||Graph Objects||Plotter Class||narcissemodule||Examples|
Narcisse is a graphics package developed by our French colleagues at Centre d'Etudes de Limeil-Valenton of the Commissariat d'Energie Atomique. Narcisse is quite comprehensive; it can do two-, three-, and four-dimensional plots (the latter meaning that the surface is colored according to the values of an arbitrary function). One can open and send plots to a Narcisse window on a distant machine (handy if you want to show the boss a nice plot but you don't want to run over to her building with a hard copy).
Narcisse has a user-friendly graphical user interface (GUI) which, once a graph has appeared, allows the user to change its characteristics interactively. This enables one to find the best appearance for a particular plot without having to graph it repeatedly from the user program. Previously created files in various formats can also be imported directly into the Narcisse GUI and manipulated from there.
Unlike many graphics systems, whose functions are actually linked into one's program, Narcisse runs independently, as a graphics server. The user program communicates with Narcisse via Unix sockets. This communication is quite low level and very complex. The appearance of a plot is controlled by nearly 150 parameters for determining such things as the color palette, type of shading, axis scales, curve and surface labels, titles, angle and distance of view (for three- and four-dimensional graphs), hidden line removal, etc. Most end users do not wish to spend time learning the tedious details of such interfaces; they would just like to specify data and ask to have it plotted.
This paper describes a high level, easy to use graphics interface which hides (as much as possible) the low level details of whatever graphics system is actually being used, so that the low level can be essentially ``plug-and-play.'' Then, whenever a better system becomes available, it should only be necessary to change low level interface routines not normally accessed by ordinary users. Python, with its easy extendability, was ideally suited for this job.
Curve, Surface, and Mesh are three Python classes which abstract the geometric properties of the objects which we wish to graph. Each instantiation of one of these objects will contain the geometric specification of a single curve, surface, or mesh respectively (coordinates, and physical data in the case of Surfaces and Meshes), as well as information about appearance (color, graph type, plotting options, etc.). Each of these classes has two member functions: set, which allows one or more of its characteristics to be changed; and new, which reinitializes the object.
A Surface is essentially a two-dimensional object viewed in three-dimensional space, while a Mesh is really a three-dimensional object. However, plotted with hidden lines removed, a closed surface and a solid realized as a mesh whose boundary is that surface may look exactly the same, and indeed, share many characteristics. The difference is that with a Surface, we are only interested in the outside, whereas with a Mesh, we may be interested in stripping away outside layers to see what is going on inside. In this way a Mesh can be considered a specialization of a Surface, and so in this implementation Mesh is a derived class of Surface.
The context in which a graph of a geometric object actually appears has been abstracted into a base class called Graph; its derived classes Graph2d and Graph3d contain information peculiar to two and three dimensional plots, respectively. Graphs know about such things as axes (whether they appear, what they look like, their scales, etc.), titles and other text which may appear on the graph, and (for three dimensional plots) the angle and distance of the view point. A Graph is aware that a graphics engine is out there and knows how to interface with it via a class instance of a Plotter (see the next section for more details on Plotters).
The interface to a Plotter is generic; it is only at the Plotter level of this interface, and the lower C interface level, that actual details of the graphics engine are known. A Graph can be asked to plot itself. If at this point the application program has not somehow been informed of the existence of a Plotter to use to plot itself, then it creates a generic Plotter which somehow connects to a graphics engine. In the case of Narcisse, a connection can easily be made if Narcisse is running on the same platform. The Plotter is able to communicate with this Narcisse via a socket, whose number it obtains from an environment variable PORT_SERVEUR. If Narcisse is running on a remote platform, the connection can be made if the DISPLAY variable is set for that platform and the environment variable DEST_SP3 is set to a string which encodes the platform name, Narcisse¹s socket number there, and the userid. Other graphics engines will work differently, but could still be fired up by the same generic call at the Graph level.
The application program (or the user at the command line) can also specify one or more connections to graphics. This can be done by passing encoded strings (called ³filenames²) or identifiers of open Plotters to the Graph object. In the case of Narcisse, a ³filename² is encoded as described above; with other graphics engines, it might be a real filename, or a differently encoded set of directions to a remote graphics process. Since a Graph may be aware of more than one Plotter, it is capable of plotting itself ³simultaneously² on more than one platform.
One of the design decisions was exactly how to apportion the 150-some Narcisse parameters among geometric objects and the Graph objects. Generally I tried to keep all information intrinsic to a geometric abstraction (coordinates, color, appearance) with the geometric objects, and extrinsic information about the context of the plot (presence or absence of axes, point of view, size, particular Narcisse connection, etc.) within Graph objects. Such a clean division was not always possible. For example, two dimensional plots in Narcisse can have their colors chosen from exactly one palette. However, three and four dimensional objects can be linked in such a way that each can have a separate palette. Thus in the former case, a palette could be considered a Graph characteristic, while in the latter, it can be treated as a characteristic of an individual Surface.
Nar.py, which embodies the definition of the Plotter class, is the low-level Python interface with the graphics engine, and as such is therefore acquainted with the graphics details. In our case a Plotter instantiation is aware of a connection to Narcisse, which is either handed to it by a Graph object or is created by default when it is instantiated. A Plotter has numerous somewhat higher level member functions which communicate with the lower level ones in the graphics interface. A Plotter object has two functionalities, namely:
The settings of the most common of the low level Narcisse parameters are controlled by functions with self-explanatory names, such as set_3d_grid_type, set_3d_options, set_axis_labels, set_curve_color, set_mask, and even set_language (the GUI can appear either in French or in English). Since most graphics packages offer similar functionality, I hope that these names are sufficiently generic to be usable regardless of the underlying graphics. Curve plotting and surface plotting are each controlled by a single function (plot_curve and plot_surface, respectively). This is possible because of the ability of Python to determine the number of arguments with which a function is called, and their types, sizes, and shapes. With this information, a Plotter can decide which of the several Narcisse functions is the appropriate one to call. Again, I hope that this will carry over to Plotter-type interfaces with other graphics packages.
This module, written in C and callable (of course) from Python, is really a low-level set of wrappers for the functions in Narcisse. It accepts Python argument lists, parses them (if possible) into data acceptable to Narcisse, and passes it on. There is a local data structure for storing up Narcisse keywords and their values (which are used mainly to control the appearance of the graph) until they are to be shipped to Narcisse. Normally a whole series of keywords will be specified and then accumulated to configure a graph, but not sent to Narcisse until it is actually ready to do a plot. (If keywords were sent to Narcisse as they were defined, then whatever data that had been last sent would be replotted using the new values, which is usually not the desired outcome.) Finally, there is a local translation table: since Narcisse recognizes only French keywords, we have supplied a table of English equivalents to make things easier for the low-level user (mainly us, to be sure).
Thus there are very few surprises in this module. It contains routines to open and close a connection to Narcisse, to query whether one exists, and to synchronize. There are routines to add keyword values to the local table, and one to send the final list to Narcisse. Two dimensional routines can plot one or several curves simultaneously. The curves can be colored and labeled, and drawn in various ways (continuously, as step functions, or just as points marked by various symbols).
Surface plotting routines are where Narcisse excels. It supports both three dimensional plots, where the surface is colored according to the value of the z coordinate, and four-dimensional plots, where the coloring is determined by a function defined at each of the plotted points. There are various coloring options, including wire grid, flat or face coloring, contour lines, and contour shading. The surface can be transparent, or there are three masking options of increasing complexity to remove hidden portions from the graph.
Finally, there are routines for doing three dimensional solids which have been decomposed into cells by means of both structured and nonstructured grids. These plots can be most enlightening when a portion of the surface is removed so that one can see the interior cells.
No paper on graphics is complete without a few sample graphs.
For more information, contact:
Zane C. Motteler