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+% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
+% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
+
+\texht{\setcounter{chapter}{6}}{} % Chapter 7
+
+\newcommand{\optArg}[1]{{{\tt [}{#1}{\tt ]}}}
+\newcommand{\argDef}[1]{{\tt ({#1})}}
+\newcommand{\funSyntax}[2]{\axiomFun{#1}{\tt ({\small\it{#2}})}}
+\newcommand{\funArgs}[1]{{\tt ({\small\it {#1}})}\newline}
+
+%
+\newcommand{\ugGraphTitle}{Graphics}
+\newcommand{\ugGraphNumber}{7.}
+%
+% =====================================================================
+\begin{page}{ugGraphPage}{7. Graphics}
+% =====================================================================
+\beginscroll
+
+%
+
+This chapter shows how to use the \Language{} graphics facilities
+%-% \HDindex{graphics}{ugGraphPage}{7.}{Graphics}
+under the X Window System.
+\Language{} has \twodim{} and \threedim{} drawing and rendering
+packages that allow the drawing, coloring, transforming, mapping,
+clipping, and combining of graphic output from \Language{}
+computations.
+This facility is particularly useful for investigating problems in
+areas such as topology.
+The graphics package is capable of plotting functions of one or
+more variables or plotting parametric surfaces and curves.
+Various coordinate systems are also available, such as polar and
+spherical.
+
+A graph is displayed in a viewport window and it has a
+%-% \HDindex{viewport}{ugGraphPage}{7.}{Graphics}
+control-panel that uses interactive mouse commands.
+PostScript and other output forms are available so that \Language{}
+%-% \HDindex{PostScript}{ugGraphPage}{7.}{Graphics}
+images can be printed or used by other programs.\footnote{PostScript
+is a trademark of Adobe Systems Incorporated, registered in the United
+States.}
+
+\beginmenu
+    \menudownlink{{7.1. Two-Dimensional Graphics}}{ugGraphTwoDPage}
+    \menudownlink{{7.2. Three-Dimensional Graphics}}{ugGraphThreeDPage}
+\endmenu
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphTwoDTitle}{Two-Dimensional Graphics}
+\newcommand{\ugGraphTwoDNumber}{7.1.}
+%
+% =====================================================================
+\begin{page}{ugGraphTwoDPage}{7.1. Two-Dimensional Graphics}
+% =====================================================================
+\beginscroll
+%
+The \Language{} \twodim{} graphics package provides the ability to
+%-% \HDindex{graphics!two-dimensional}{ugGraphTwoDPage}{7.1.}{Two-Dimensional Graphics}
+display
+%
+\indent{4}
+\beginitems
+%
+\item[-] curves defined by functions of a single real variable
+%
+\item[-] curves defined by parametric equations
+%
+\item[-] implicit non-singular curves defined by polynomial equations
+%
+\item[-] planar graphs generated from lists of point components.
+\enditems
+\indent{0}
+These graphs
+can be modified by specifying various options, such as
+calculating points in the polar
+coordinate system or changing the size of the graph viewport window.
+
+\beginmenu
+    \menudownlink{{7.1.1. Plotting Two-Dimensional Functions of One Variable}}{ugGraphTwoDPlotPage}
+    \menudownlink{{7.1.2. Plotting Two-Dimensional Parametric Plane Curves}}{ugGraphTwoDParPage}
+    \menudownlink{{7.1.3. Plotting Plane Algebraic Curves}}{ugGraphTwoDPlanePage}
+    \menudownlink{{7.1.4. Two-Dimensional Options}}{ugGraphTwoDOptionsPage}
+    \menudownlink{{7.1.5. Color}}{ugGraphColorPage}
+    \menudownlink{{7.1.6. Palette}}{ugGraphColorPalettePage}
+    \menudownlink{{7.1.7. Two-Dimensional Control-Panel}}{ugGraphTwoDControlPage}
+    \menudownlink{{7.1.8. Operations for Two-Dimensional Graphics}}{ugGraphTwoDopsPage}
+    \menudownlink{{7.1.9. Addendum: Building Two-Dimensional Graphs}}{ugGraphTwoDbuildPage}
+    \menudownlink{{7.1.10. Addendum: Appending a Graph to a Viewport Window Containing a Graph}}{ugGraphTwoDappendPage}
+\endmenu
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphTwoDPlotTitle}{Plotting Two-Dimensional Functions of One Variable}
+\newcommand{\ugGraphTwoDPlotNumber}{7.1.1.}
+%
+% =====================================================================
+\begin{page}{ugGraphTwoDPlotPage}{7.1.1. Plotting Two-Dimensional Functions of One Variable}
+% =====================================================================
+\beginscroll
+
+%-% \HDindex{curve!one variable function}{ugGraphTwoDPlotPage}{7.1.1.}{Plotting Two-Dimensional Functions of One Variable}
+The first kind of \twodim{} graph is that of a curve defined by a function
+\axiom{y = f(x)} over a finite interval of the \axiom{x} axis.
+
+%
+\beginImportant
+The general format for drawing a function defined by a formula
+\axiom{f(x)} is:
+%
+\centerline{{{\tt draw(f(x), x = a..b, {\it options})}}}
+where \axiom{a..b} defines the range of \axiom{x}, and where
+{\it options} prescribes zero or more options as described in
+\downlink{``\ugGraphTwoDOptionsTitle''}{ugGraphTwoDOptionsPage} in Section \ugGraphTwoDOptionsNumber\ignore{ugGraphTwoDOptions}.
+An example of an option is \axiom{curveColor == bright red().}
+An alternative format involving functions \axiom{f} and \axiom{g}
+is also available.
+\endImportant
+
+A simple way to plot a function is to use a formula.
+The first argument is the formula.
+For the second argument, write the name of the independent variable (here, \axiom{x}),
+followed by an \spadSyntax{=}, and the range of values.
+
+\psXtc{
+Display this formula over the range
+\texht{$0 \leq x \leq 6$}{0 <= x <= 6}.
+\Language{} converts your formula to a compiled
+function so that the results can be computed
+quickly and efficiently.
+}{
+\graphpaste{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)}
+}{
+\epsffile[0 0 295 295]{../ps/2D1VarA.ps}
+}
+
+Notice that \Language{} compiled the function before the graph was put
+on the screen.
+
+\psXtc{
+Here is the same graph on a different interval.
+This time we give the graph a title.
+}{
+\graphpaste{draw(sin(tan(x)) - tan(sin(x)),x = 10..16)}
+}{
+%window was 300 x 300
+\epsffile[0 0 295 295]{../ps/2D1VarB.ps}
+}
+%
+Once again the formula is converted to a compiled function before
+any points were computed.
+If you want to graph the same function on several intervals, it is
+a good idea to define the function first so that the function has
+to be compiled only once.
+\xtc{
+This time we first define the function.
+}{
+\spadpaste{f(x) == (x-1)*(x-2)*(x-3) \bound{f}}
+}
+\psXtc{
+To draw the function, the first argument is its name
+and the second is just the range with no independent variable.
+}{
+\graphpaste{draw(f, 0..4) \free{f}}
+}{
+\epsffile[0 0 295 295]{../ps/2D1VarD.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphTwoDParTitle}{Plotting Two-Dimensional Parametric Plane Curves}
+\newcommand{\ugGraphTwoDParNumber}{7.1.2.}
+%
+% =====================================================================
+\begin{page}{ugGraphTwoDParPage}{7.1.2. Plotting Two-Dimensional Parametric Plane Curves}
+% =====================================================================
+\beginscroll
+
+The second kind of \twodim{} graph is that of
+%-% \HDindex{parametric plane curve}{ugGraphTwoDParPage}{7.1.2.}{Plotting Two-Dimensional Parametric Plane Curves}
+curves produced by parametric equations.
+%-% \HDindex{curve!parametric plane}{ugGraphTwoDParPage}{7.1.2.}{Plotting Two-Dimensional Parametric Plane Curves}
+Let \axiom{x = f(t)} and \axiom{y = g(t)} be formulas or two
+functions \axiom{f} and \axiom{g} as the parameter \axiom{t} ranges
+over an interval \axiom{[a,b]}.
+The function \axiomFun{curve} takes the two functions \axiom{f} and
+\axiom{g} as its parameters.
+
+\beginImportant
+The general format for drawing a \twodim{} plane curve defined by
+parametric formulas \axiom{x = f(t)} and \axiom{y = g(t)} is:
+%
+\centerline{{{\tt draw(curve(f(t), g(t)), t = a..b, {\it options})}}}
+where \axiom{a..b} defines the range of the independent variable \axiom{t},
+and where {\it options} prescribes zero or more options as
+described in \downlink{``\ugGraphThreeDOptionsTitle''}{ugGraphThreeDOptionsPage} in Section \ugGraphThreeDOptionsNumber\ignore{ugGraphThreeDOptions}.
+An example of an option is \axiom{curveColor == bright red().}
+\endImportant
+
+Here's an example:
+
+\psXtc{
+Define a parametric curve using a range involving
+\axiom{\%pi}, \Language{}'s way of saying \texht{$\pi$}{``pi''}.
+For parametric curves, \Language{} compiles two
+functions, one for each of the functions \axiom{f} and \axiom{g}.
+}{
+\graphpaste{draw(curve(sin(t)*sin(2*t)*sin(3*t), sin(4*t)*sin(5*t)*sin(6*t)), t = 0..2*\%pi)}
+}{
+\epsffile[0 0 295 295]{../ps/2DppcA.ps}
+}
+%
+%
+\psXtc{
+The title may be an arbitrary string and is an
+optional argument to the \axiomFun{draw} command.
+}{
+\graphpaste{draw(curve(cos(t), sin(t)), t = 0..2*\%pi)}
+}{
+\epsffile[0 0 295 295]{../ps/2DppcB.ps}
+}
+%
+If you plan on plotting \axiom{x = f(t)}, \axiom{y = g(t)} as \axiom{t} ranges over
+several intervals, you may want to define functions \axiom{f} and \axiom{g} first, so
+that they need not be recompiled every time you create a new graph.
+Here's an example:
+\xtc{
+As before, you can first define the functions you wish to draw.
+}{
+\spadpaste{f(t:DFLOAT):DFLOAT == sin(3*t/4) \bound{f}}
+}
+\xtc{
+\Language{} compiles them to map \axiomType{DoubleFloat}
+values to \axiomType{DoubleFloat} values.
+}{
+\spadpaste{g(t:DFLOAT):DFLOAT == sin(t) \bound{g}}
+}
+
+\psXtc{
+Give to {\tt curve} the names of the functions,
+then write the range without the name of the
+independent variable.
+}{
+\graphpaste{draw(curve(f,g),0..\%pi) \free{f g}}
+}{
+\epsffile[0 0 295 295]{../ps/2DppcC.ps}
+}
+%
+%
+\psXtc{
+Here is another look at the same curve but over a different
+range. Notice that \axiom{f} and \axiom{g} are not recompiled.
+Also note that \Language{} provides a default title based on
+the first function specified in \axiomFun{curve}.
+}{
+\graphpaste{draw(curve(f,g),-4*\%pi..4*\%pi) \free{f g}}
+}{
+\epsffile[0 0 295 295]{../ps/2DppcE.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphTwoDPlaneTitle}{Plotting Plane Algebraic Curves}
+\newcommand{\ugGraphTwoDPlaneNumber}{7.1.3.}
+%
+% =====================================================================
+\begin{page}{ugGraphTwoDPlanePage}{7.1.3. Plotting Plane Algebraic Curves}
+% =====================================================================
+\beginscroll
+
+A third kind of \twodim{} graph is a non-singular ``solution curve''
+%-% \HDindex{curve!plane algebraic}{ugGraphTwoDPlanePage}{7.1.3.}{Plotting Plane Algebraic Curves}
+in a rectangular region of the plane.
+A solution curve is a curve defined by a polynomial equation
+\axiom{p(x,y) = 0}.
+%-% \HDindex{plane algebraic curve}{ugGraphTwoDPlanePage}{7.1.3.}{Plotting Plane Algebraic Curves}
+Non-singular means that the curve is ``smooth'' in that it does not
+cross itself or come to a point (cusp).
+Algebraically, this means that for any point \axiom{(x,y)} on the curve,
+that is, a point such that \axiom{p(x,y) = 0}, the partial derivatives
+\texht{${{\partial p}\over{\partial x}}(x,y)$ and
+${{\partial p}\over{\partial y}}(x,y)$}{\axiom{dp/dx(x,y)}
+and \axiom{dp/dy(a,b)}}
+are not both zero.
+%-% \HDindex{curve!smooth}{ugGraphTwoDPlanePage}{7.1.3.}{Plotting Plane Algebraic Curves}
+%-% \HDindex{curve!non-singular}{ugGraphTwoDPlanePage}{7.1.3.}{Plotting Plane Algebraic Curves}
+%-% \HDindex{smooth curve}{ugGraphTwoDPlanePage}{7.1.3.}{Plotting Plane Algebraic Curves}
+%-% \HDindex{non-singular curve}{ugGraphTwoDPlanePage}{7.1.3.}{Plotting Plane Algebraic Curves}
+
+%
+\beginImportant
+The general format for drawing a non-singular solution curve
+given by a polynomial of the form \axiom{p(x,y) = 0} is:
+%
+\centerline{{{\tt draw(p(x,y) = 0, x, y, range == [a..b, c..d], {\it options})}}}
+where the second and third arguments name the first and second
+independent variables of \axiom{p}.
+A {\tt range} option is always given to designate a bounding
+rectangular region of the plane \texht{$a \leq x \leq b, c \leq y
+\leq d$}{a <= x <= b, c <= y <= d}.
+Zero or more additional options as described in
+\downlink{``\ugGraphTwoDOptionsTitle''}{ugGraphTwoDOptionsPage} in Section \ugGraphTwoDOptionsNumber\ignore{ugGraphTwoDOptions} may be given.
+\endImportant
+
+\xtc{
+We require that the polynomial has rational or integral coefficients.
+Here is an algebraic curve example (``Cartesian ovals''):
+%-% \HDindex{Cartesian!ovals}{ugGraphTwoDPlanePage}{7.1.3.}{Plotting Plane Algebraic Curves}
+}{
+\spadpaste{p := ((x**2 + y**2 + 1) - 8*x)**2 - (8*(x**2 + y**2 + 1)-4*x-1) \bound{p}}
+}
+
+\psXtc{
+The first argument is always expressed as an equation of the form \axiom{p = 0}
+where \axiom{p} is a polynomial.
+}{
+\graphpaste{draw(p = 0, x, y, range == [-1..11, -7..7]) \free{p}}
+}{
+\epsffile[0 0 295 295]{../ps/2DpacA.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphTwoDOptionsTitle}{Two-Dimensional Options}
+\newcommand{\ugGraphTwoDOptionsNumber}{7.1.4.}
+%
+% =====================================================================
+\begin{page}{ugGraphTwoDOptionsPage}{7.1.4. Two-Dimensional Options}
+% =====================================================================
+\beginscroll
+
+The \axiomFun{draw} commands take an optional list of options,
+such as {\tt title} shown above.
+Each option is given by the syntax: {\it name} {\tt ==} {\it value}.
+Here is a list of the available options in the order that they are
+described below.
+
+\table{ {adaptive} {clip} {unit} {clip} {curveColor} {range}
+{toScale} {pointColor} {coordinates}}
+
+The \axiom{adaptive} option turns adaptive plotting on or off.
+%-% \HDindex{adaptive plotting}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+Adaptive plotting uses an algorithm that traverses a graph and computes
+more points for those parts of the graph with high curvature.
+The higher the curvature of a region is, the more points the algorithm
+computes.
+%-% \HDindex{graphics!2D options!adaptive}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+%
+%
+\psXtc{
+The {\tt adaptive} option is normally on.
+Here we turn it off.
+}{
+\graphpaste{draw(sin(1/x),x=-2*\%pi..2*\%pi, adaptive == false)}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptAd.ps}
+}
+%
+%
+\psXtc{
+The {\tt clip} option turns clipping on or off.
+%-% \HDindex{graphics!2D options!clipping}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+If on, large values are cut off according to
+\axiomFunFrom{clipPointsDefault}{GraphicsDefaults}.
+}{
+\graphpaste{draw(tan(x),x=-2*\%pi..2*\%pi, clip == true)}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptCp.ps}
+}
+%
+%
+\psXtc{
+Option {\tt toScale} does plotting to scale if {\tt true} or uses
+the entire viewport if {\tt false}.
+The default can be determined using
+\axiomFunFrom{drawToScale}{GraphicsDefaults}.
+%-% \HDindex{graphics!2D options!to scale}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+}{
+\graphpaste{draw(sin(x),x=-\%pi..\%pi, toScale == true, unit == [1.0,1.0])}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptSc.ps}
+}
+%
+%
+\psXtc{
+Option {\tt clip} with a range sets point clipping of a graph within the
+%-% \HDindex{graphics!2D options!clip in a range}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+ranges specified in the list \axiom{[x range,y range]}.
+%-% \HDindex{clipping}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+If only one range is specified, clipping applies to the y-axis.
+}{
+\graphpaste{draw(sec(x),x=-2*\%pi..2*\%pi, clip == [-2*\%pi..2*\%pi,-\%pi..\%pi], unit == [1.0,1.0])}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptCpR.ps}
+}
+%
+\psXtc{
+Option {\tt curveColor} sets the color of the graph curves or lines to be the
+%-% \HDindex{graphics!2D options!curve color}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+indicated palette color
+%-% \HDindex{curve!color}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+(see \downlink{``\ugGraphColorTitle''}{ugGraphColorPage} in Section \ugGraphColorNumber\ignore{ugGraphColor} and \downlink{``\ugGraphColorPaletteTitle''}{ugGraphColorPalettePage} in Section \ugGraphColorPaletteNumber\ignore{ugGraphColorPalette}).
+%-% \HDindex{color!curve}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+}{
+\graphpaste{draw(sin(x),x=-\%pi..\%pi, curveColor == bright red())}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptCvC.ps}
+}
+%
+\psXtc{
+Option {\tt pointColor}
+sets the color of the graph points to the indicated
+%-% \HDindex{graphics!2D options!point color}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+palette color
+(see \downlink{``\ugGraphColorTitle''}{ugGraphColorPage} in Section \ugGraphColorNumber\ignore{ugGraphColor} and \downlink{``\ugGraphColorPaletteTitle''}{ugGraphColorPalettePage} in Section \ugGraphColorPaletteNumber\ignore{ugGraphColorPalette}).
+%-% \HDindex{color!point}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+}{
+\graphpaste{draw(sin(x),x=-\%pi..\%pi, pointColor == pastel yellow())}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptPtC.ps}
+}
+%
+\psXtc{
+Option {\tt unit} sets the intervals at which the axis units are plotted
+%-% \HDindex{graphics!2D options!set units}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+according to the indicated steps [\axiom{x} interval, \axiom{y} interval].
+}{
+\graphpaste{draw(curve(9*sin(3*t/4),8*sin(t)), t = -4*\%pi..4*\%pi, unit == [2.0,1.0])}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptUt.ps}
+}
+%
+%
+\psXtc{
+Option {\tt range} sets the range of variables in a graph to be
+within the ranges
+%-% \HDindex{graphics!2D options!range}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+for solving plane algebraic curve plots.
+}{
+\graphpaste{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1], unit==[1.0,1.0])}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptRgA.ps}
+}
+%
+%
+\psXtc{
+A second example of a solution plot.
+}{
+\graphpaste{draw(x**2 + y**2 = 1, x, y, range == [-3/2..3/2,-3/2..3/2], unit==[0.5,0.5])}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptRgB.ps}
+}
+%
+%
+\psXtc{
+Option \axiom{coordinates} indicates the coordinate system
+in which the graph
+%-% \HDindex{graphics!2D options!coordinates}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+is plotted.
+The default is to use the Cartesian coordinate system.
+%-% \HDindex{Cartesian!coordinate system}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+For more details, see \downlink{``\ugGraphCoordTitle''}{ugGraphCoordPage} in Section \ugGraphCoordNumber\ignore{ugGraphCoord} \texht{.}{or
+\axiomType{CoordinateSystems}.}
+%-% \HDindex{coordinate system!Cartesian}{ugGraphTwoDOptionsPage}{7.1.4.}{Two-Dimensional Options}
+}{
+\graphpaste{draw(curve(sin(5*t),t),t=0..2*\%pi, coordinates == polar)}
+}{
+\epsffile[0 0 295 295]{../ps/2DOptPlr.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphColorTitle}{Color}
+\newcommand{\ugGraphColorNumber}{7.1.5.}
+%
+% =====================================================================
+\begin{page}{ugGraphColorPage}{7.1.5. Color}
+% =====================================================================
+\beginscroll
+
+The domain \axiomType{Color}
+%-% \HDexptypeindex{Color}{ugGraphColorPage}{7.1.5.}{Color}
+provides operations for manipulating
+%-% \HDindex{graphics!color}{ugGraphColorPage}{7.1.5.}{Color}
+colors in \twodim{} graphs.
+%-% \HDindex{color}{ugGraphColorPage}{7.1.5.}{Color}
+Colors are objects of \axiomType{Color}.
+Each color has a {\it hue} and a {\it weight}.
+%-% \HDindex{hue}{ugGraphColorPage}{7.1.5.}{Color}
+Hues are represented by integers that range from \axiom{1} to the
+\axiomFunFrom{numberOfHues()}{Color}, normally
+%-% \HDindex{graphics!color!number of hues}{ugGraphColorPage}{7.1.5.}{Color}
+\axiom{27}.
+%\footnote{Use \axiomFun{colorDef} to
+%change these values to any range you want for a given \threedim{} viewport}
+%-% \HDindex{weight}{ugGraphColorPage}{7.1.5.}{Color}
+Weights are floats and  have the value \axiom{1.0} by default.
+%
+\indent{0}
+\beginitems
+%
+\item[\axiomFun{color}]\funArgs{integer}
+creates a color of hue {\it integer} and weight \axiom{1.0}.
+%
+\item[\axiomFun{hue}]\funArgs{color}
+returns the hue of {\it color} as an integer.
+%-% \HDindex{graphics!color!hue function}{ugGraphColorPage}{7.1.5.}{Color}
+%
+\item[\axiomFun{red}]\funArgs{},
+\funSyntax{blue}{},
+\funSyntax{green}{}, and \funSyntax{yellow}{}
+%-% \HDindex{graphics!color!primary color functions}{ugGraphColorPage}{7.1.5.}{Color}
+create colors of that hue with weight \axiom{1.0}.
+%
+\item[\subscriptIt{color}{1} {\tt +} \subscriptIt{color}{2}] returns the
+color that results from additively combining the indicated
+\subscriptIt{color}{1} and \subscriptIt{color}{2}.
+Color addition is not commutative: changing the order of the arguments
+produces different results.
+%
+\item[{\it integer} {\tt *} {\it color}]
+changes the weight of {\it color} by {\it integer}
+without affecting its hue.
+%-% \HDindex{graphics!color!multiply function}{ugGraphColorPage}{7.1.5.}{Color}
+For example,
+\axiom{red() + 3*yellow()} produces a color closer to yellow than to red.
+Color multiplication is not associative: changing the order of grouping
+%-% \HDindex{color!multiplication}{ugGraphColorPage}{7.1.5.}{Color}
+produces different results.
+\enditems
+\indent{0}
+%
+\psXtc{
+These functions can be used to change the point and curve colors
+for two- and \threedim{} graphs.
+Use the {\tt pointColor} option for points.
+}{
+\graphpaste{draw(x**2,x=-1..1,pointColor == green())}
+}{
+\epsffile[0 0 295 295]{../ps/23DColA.ps}
+}
+%
+\psXtc{
+Use the {\tt curveColor} option for curves.
+}{
+\graphpaste{draw(x**2,x=-1..1,curveColor == color(13) + 2*blue())}
+}{
+\epsffile[0 0 295 295]{../ps/23DColB.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphColorPaletteTitle}{Palette}
+\newcommand{\ugGraphColorPaletteNumber}{7.1.6.}
+%
+% =====================================================================
+\begin{page}{ugGraphColorPalettePage}{7.1.6. Palette}
+% =====================================================================
+\beginscroll
+%-% \HDindex{graphics!palette}{ugGraphColorPalettePage}{7.1.6.}{Palette}
+
+Domain \axiomType{Palette} is the domain of shades of colors:
+\axiomFun{dark}, \axiomFun{dim}, \axiomFun{bright}, \axiomFun{pastel}, and \axiomFun{light},
+designated by the integers \axiom{1} through \axiom{5}, respectively.
+%-% \HDexptypeindex{Palette}{ugGraphColorPalettePage}{7.1.6.}{Palette}
+\xtc{
+Colors are normally ``bright.''
+}{
+\spadpaste{shade red()}
+}
+\xtc{
+To change the shade of a color, apply the name of a shade to it.
+%-% \HDindex{color!shade}{ugGraphColorPalettePage}{7.1.6.}{Palette}
+%-% \HDindex{shade}{ugGraphColorPalettePage}{7.1.6.}{Palette}
+}{
+\spadpaste{myFavoriteColor := dark blue() \bound{mfc}}
+}
+\xtc{
+The expression \axiom{shade(color)}
+returns the value of a shade of \axiom{color}.
+}{
+\spadpaste{shade myFavoriteColor \free{mfc}}
+}
+\xtc{
+The expression \axiom{hue(color)} returns its hue.
+}{
+\spadpaste{hue myFavoriteColor \free{mfc}}
+}
+\psXtc{
+Palettes can be used in specifying colors in \twodim{} graphs.
+}{
+\graphpaste{draw(x**2,x=-1..1,curveColor == dark blue())}
+}{
+\epsffile[0 0 295 295]{../ps/23DPal.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphTwoDControlTitle}{Two-Dimensional Control-Panel}
+\newcommand{\ugGraphTwoDControlNumber}{7.1.7.}
+%
+% =====================================================================
+\begin{page}{ugGraphTwoDControlPage}{7.1.7. Two-Dimensional Control-Panel}
+% =====================================================================
+\beginscroll
+%-% \HDindex{graphics!2D control-panel}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+Once you have created a viewport, move your mouse to the viewport and click
+with your left mouse button to display a control-panel.
+The panel is displayed on the side of the viewport closest to
+where you clicked.  Each of the buttons which toggle on and off show the
+current state of the graph.
+
+
+\subsubsection{Transformations}
+%-% \HDindex{graphics!2D control-panel!transformations}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+
+Object transformations are executed from the control-panel by mouse-activated
+potentiometer windows.
+%
+\indent{0}
+\beginitems
+%
+\item[Scale:] To scale a graph, click on a mouse button
+%-% \HDindex{graphics!2D control-panel!scale}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+within the {\bf Scale} window in the upper left corner of the control-panel.
+The axes along which the scaling is to occur are indicated by setting the
+toggles above the arrow.
+With {\tt X On} and {\tt Y On} appearing, both axes are selected and scaling
+is uniform.
+If either is not selected, for example, if {\tt X Off} appears, scaling is
+non-uniform.
+%
+\item[Translate:] To translate a graph, click the mouse in the
+%-% \HDindex{graphics!2D control-panel!translate}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+{\bf Translate} window in the direction you wish the graph to move.
+This window is located in the upper right corner of the control-panel.
+Along the top of the {\bf Translate} window are two buttons for selecting
+the direction of translation.
+Translation along both coordinate axes results when {\tt X On} and {\tt Y
+On} appear or along one axis when one is on, for example, {\tt X On} and
+{\tt Y Off} appear.
+\enditems
+\indent{0}
+
+\subsubsection{Messages}
+%-% \HDindex{graphics!2D control-panel!messages}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+
+The window directly below the transformation potentiometer windows is
+used to display system messages relating to the viewport and the control-panel.
+The following format is displayed: \newline
+%
+\centerline{{[scaleX, scaleY] \axiom{>}graph\axiom{<} [translateX, translateY] \newline}}
+The two values to the left show the scale factor along the {\tt X} and
+{\tt Y} coordinate axes.  The two values to the right show the distance of
+translation from the center in the {\tt X} and {\tt Y} directions.  The number
+in the center shows which graph in the viewport this data pertains to.
+When multiple graphs exist in the same viewport,
+the graph must be selected (see ``Multiple Graphs,'' below) in
+order for its transformation data to be shown, otherwise the number
+is 1.
+
+\subsubsection{Multiple Graphs}
+
+%-% \HDindex{graphics!2D control-panel!multiple graphs}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+The {\bf Graphs} window contains buttons that allow the placement
+of \twodim{} graphs into one of nine available slots in any other
+\twodim{} viewport.
+In the center of the window are numeral buttons from one to nine
+that show whether a graph is displayed in the viewport.
+Below each number button is a button showing whether a graph
+that is present is selected for application of some
+transformation.
+When the caret symbol is displayed, then the graph in that slot
+will be manipulated.
+Initially, the graph for which the viewport is created occupies
+the first slot, is displayed, and is selected.
+%
+%
+\indent{0}
+\beginitems
+%
+\item[Clear:]  The {\bf Clear} button deselects every viewport graph slot.
+%-% \HDindex{graphics!2D control-panel!clear}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+A graph slot is reselected by selecting the button below its number.
+%
+\item[Query:]  The {\bf Query} button is used to display the scale and
+%-% \HDindex{graphics!2D control-panel!query}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+translate data for the indicated graph.  When this button is selected the
+message ``Click on the graph to query'' appears.  Select a slot
+number button from the {\bf Graphs} window. The scaling factor and translation
+offset of the graph are then displayed in the message window.
+%
+\item[Pick:]  The {\bf Pick} button is used to select a graph
+%-% \HDindex{graphics!2D control-panel!pick}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+to be placed or dropped into the indicated viewport.  When this button is
+selected, the message ``Click on the graph to pick'' appears.
+Click on the slot with the graph number of the desired
+graph.  The graph information is held waiting for
+you to execute a {\bf Drop} in some other graph.
+%
+\item[Drop:]  Once a graph has been picked up using the {\bf Pick} button,
+%-% \HDindex{graphics!2D control-panel!drop}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+the {\bf Drop} button places it into a new viewport slot.
+The message ``Click on the graph to drop'' appears in the message
+window when the {\bf Drop} button is selected.
+By selecting one of the slot number buttons in the {\bf Graphs}
+window, the graph currently being held is dropped into this slot
+and displayed.
+\enditems
+\indent{0}
+
+\subsubsection{Buttons}
+%-% \HDindex{graphics!2D control-panel!buttons}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+
+%
+\indent{0}
+\beginitems
+%
+\item[Axes] turns the coordinate axes on or off.
+%-% \HDindex{graphics!2D control-panel!axes}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+%
+\item[Units] turns the units along the {\tt x}
+and {\tt y} axis on or off.
+%-% \HDindex{graphics!2D control-panel!units}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+%
+\item[Box] encloses the area of the viewport graph
+in a bounding box, or removes the box if already enclosed.
+%-% \HDindex{graphics!2D control-panel!box}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+%
+\item[Pts] turns on or off the display of points.
+%-% \HDindex{graphics!2D control-panel!points}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+%
+\item[Lines] turns on or off the display
+of lines connecting points.
+%-% \HDindex{graphics!2D control-panel!lines}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+%
+\item[PS] writes the current viewport contents to
+%-% \HDindex{graphics!2D control-panel!ps}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+a file {\bf axiom2D.ps} or to a name specified in the user's {\bf
+%-% \HDindex{graphics!.Xdefaults!PostScript file name}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+.Xdefaults} file.
+%-% \HDindex{file!.Xdefaults @{\bf .Xdefaults}}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+The file is placed in the directory from which \Language{} or the {\bf
+viewAlone} program was invoked.
+%-% \HDindex{PostScript}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+%
+\item[Reset] resets the object transformation
+characteristics and attributes back to their initial states.
+%-% \HDindex{graphics!2D control-panel!reset}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+%
+\item[Hide] makes the control-panel disappear.
+%-% \HDindex{graphics!2D control-panel!hide}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+%
+\item[Quit] queries whether the current viewport
+%-% \HDindex{graphics!2D control-panel!quit}{ugGraphTwoDControlPage}{7.1.7.}{Two-Dimensional Control-Panel}
+session should be terminated.
+\enditems
+\indent{0}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphTwoDopsTitle}{Operations for Two-Dimensional Graphics}
+\newcommand{\ugGraphTwoDopsNumber}{7.1.8.}
+%
+% =====================================================================
+\begin{page}{ugGraphTwoDopsPage}{7.1.8. Operations for Two-Dimensional Graphics}
+% =====================================================================
+\beginscroll
+
+Here is a summary of useful \Language{} operations for \twodim{}
+graphics.
+Each operation name is followed by a list of arguments.
+Each argument is written as a variable informally named according
+to the type of the argument (for example, {\it integer}).
+If appropriate, a default value for an argument is given in
+parentheses immediately following the name.
+
+%
+\texht{\bgroup\hbadness = 10001\sloppy}{}
+\indent{0}
+\beginitems
+%
+\item[\axiomFun{adaptive}]\funArgs{\optArg{boolean\argDef{true}}}
+%-% \HDindex{adaptive plotting}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+sets or indicates whether graphs are plotted
+%-% \HDindex{graphics!set 2D defaults!adaptive}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+according to the adaptive refinement algorithm.
+%
+\item[\axiomFun{axesColorDefault}]\funArgs{\optArg{color\argDef{dark blue()}}}
+sets or indicates the default color of the
+%-% \HDindex{graphics!set 2D defaults!axes color}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+axes in a \twodim{} graph viewport.
+%
+\item[\axiomFun{clipPointsDefault}]\funArgs{\optArg{boolean\argDef{false}}}
+sets or
+indicates whether point clipping is
+%-% \HDindex{graphics!set 2D defaults!clip points}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+to be applied as the default for graph plots.
+%
+\item[\axiomFun{drawToScale}]\funArgs{\optArg{boolean\argDef{false}}}
+sets or
+indicates whether the plot of a graph
+%-% \HDindex{graphics!set 2D defaults!to scale}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+is ``to scale'' or uses the entire viewport space as the default.
+%
+\item[\axiomFun{lineColorDefault}]\funArgs{\optArg{color\argDef{pastel yellow()}}}
+sets or indicates the default color of the
+%-% \HDindex{graphics!set 2D defaults!line color}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+lines or curves in a \twodim{} graph viewport.
+%
+\item[\axiomFun{maxPoints}]\funArgs{\optArg{integer\argDef{500}}}
+sets or indicates
+the default maximum number of
+%-% \HDindex{graphics!set 2D defaults!max points}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+possible points to be used when constructing a \twodim{} graph.
+%
+\item[\axiomFun{minPoints}]\funArgs{\optArg{integer\argDef{21}}}
+sets or indicates the default minimum number of
+%-% \HDindex{graphics!set 2D defaults!min points}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+possible points to be used when constructing a \twodim{} graph.
+%
+\item[\axiomFun{pointColorDefault}]\funArgs{\optArg{color\argDef{bright red()}}}
+sets or indicates the default color of the
+%-% \HDindex{graphics!set 2D defaults!point color}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+points in a \twodim{} graph viewport.
+%
+\item[\axiomFun{pointSizeDefault}]\funArgs{\optArg{integer\argDef{5}}}
+sets or indicates the default size of the
+%-% \HDindex{graphics!set 2D defaults!point size}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+dot used to plot points in a \twodim{} graph.
+%
+\item[\axiomFun{screenResolution}]\funArgs{\optArg{integer\argDef{600}}}
+sets or indicates the default screen
+%-% \HDindex{graphics!set 2D defaults!screen resolution}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+resolution constant used in setting the computation limit of adaptively
+%-% \HDindex{adaptive plotting}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+generated curve plots.
+%
+\item[\axiomFun{unitsColorDefault}]\funArgs{\optArg{color\argDef{dim green()}}}
+sets or indicates the default color of the
+%-% \HDindex{graphics!set 2D defaults!units color}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+unit labels in a \twodim{} graph viewport.
+%
+\item[\axiomFun{viewDefaults}]\funArgs{}
+resets the default settings for the following
+%-% \HDindex{graphics!set 2D defaults!reset viewport}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+attributes:  point color, line color, axes color, units color, point size,
+viewport upper left-hand corner position, and the viewport size.
+%
+\item[\axiomFun{viewPosDefault}]\funArgs{\optArg{list\argDef{[100,100]}}}
+sets or indicates the default position of the
+%-% \HDindex{graphics!set 2D defaults!viewport position}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+upper left-hand corner of a \twodim{} viewport, relative to the
+display root window.
+The upper left-hand corner of the display is considered to be at the
+(0, 0) position.
+%
+\item[\axiomFun{viewSizeDefault}]\funArgs{\optArg{list\argDef{[200,200]}}}
+sets or
+indicates the default size in which two
+%-% \HDindex{graphics!set 2D defaults!viewport size}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+dimensional viewport windows are shown.
+It is defined by a width and then a height.
+%
+\item[\axiomFun{viewWriteAvailable}]\funArgs{\optArg{list\argDef{["pixmap",
+"bitmap", "postscript", \"image"}}}
+indicates the possible file types
+%-% \HDindex{graphics!2D defaults!available viewport writes}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+that can be created with the \axiomFunFrom{write}{TwoDimensionalViewport} function.
+%
+\item[\axiomFun{viewWriteDefault}]
+\funArgs{\optArg{list\argDef{[]}}}
+sets or indicates the default types of files, in
+%-% \HDindex{graphics!set 2D defaults!write viewport}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+addition to the {\bf data} file, that are created when a
+\axiomFun{write} function is executed on a viewport.
+%
+\item[\axiomFun{units}]\funArgs{viewport, integer\argDef{1}, string\argDef{"off"}}
+turns the units on or off for the graph with index {\it integer}.
+%
+\item[\axiomFun{axes}]\funArgs{viewport, integer\argDef{1}, string\argDef{"on"}}
+turns the axes on
+%-% \HDindex{graphics!2D commands!axes}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+or off for the graph with index {\it integer}.
+%
+\item[\axiomFun{close}]\funArgs{viewport}
+closes {\it viewport}.
+%-% \HDindex{graphics!2D commands!close}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+%
+\item[\axiomFun{connect}]\funArgs{viewport, integer\argDef{1}, string\argDef{"on"}}
+declares whether lines
+%-% \HDindex{graphics!2D commands!connect}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+connecting the points are displayed or not.
+%
+\item[\axiomFun{controlPanel}]\funArgs{viewport, string\argDef{"off"}}
+declares
+whether the \twodim{} control-panel is automatically displayed
+or not.
+%
+\item[\axiomFun{graphs}]\funArgs{viewport}
+returns a list
+%-% \HDindex{graphics!2D commands!graphs}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+describing the state of each graph.
+If the graph state is not being used this is shown by {\tt "undefined"},
+otherwise a description of the graph's contents is shown.
+%
+\item[\axiomFun{graphStates}]\funArgs{viewport}
+displays
+%-% \HDindex{graphics!2D commands!state of graphs}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+a list of all the graph states available for {\it viewport}, giving the
+values for every property.
+%
+\item[\axiomFun{key}]\funArgs{viewport}
+returns the process
+%-% \HDindex{graphics!2D commands!key}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+ID number for {\it viewport}.
+%
+\item[\axiomFun{move}]\funArgs{viewport,
+\subscriptText{integer}{x}(viewPosDefault),
+\subscriptText{integer}{y}(viewPosDefault)}
+moves {\it viewport} on the screen so that the
+%-% \HDindex{graphics!2D commands!move}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+upper left-hand corner of {\it viewport} is at the position {\it (x,y)}.
+%
+\item[\axiomFun{options}]\funArgs{\it viewport}
+returns a list
+%-% \HDindex{graphics!2D commands!options}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+of all the \axiomType{DrawOption}s used by {\it viewport}.
+%
+\item[\axiomFun{points}]\funArgs{viewport, integer\argDef{1}, string\argDef{"on"}}
+specifies whether the graph points for graph {\it integer} are
+%-% \HDindex{graphics!2D commands!points}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+to be displayed or not.
+%
+\item[\axiomFun{region}]\funArgs{viewport, integer\argDef{1}, string\argDef{"off"}}
+declares whether graph {\it integer} is or is not to be displayed
+with a bounding rectangle.
+%
+\item[\axiomFun{reset}]\funArgs{viewport}
+resets all the properties of {\it viewport}.
+%
+\item[\axiomFun{resize}]\funArgs{viewport,
+\subscriptText{integer}{width}, \subscriptText{integer}{height}}
+%-% \HDindex{graphics!2D commands!resize}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+resizes {\it viewport} with a new {\it width} and {\it height}.
+%
+\item[\axiomFun{scale}]\funArgs{viewport, \subscriptText{integer}{n}\argDef{1},
+\subscriptText{integer}{x}\argDef{0.9}, \subscriptText{integer}{y}\argDef{0.9}}
+scales values for the
+%-% \HDindex{graphics!2D commands!scale}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+{\it x} and {\it y} coordinates of graph {\it n}.
+%
+\item[\axiomFun{show}]\funArgs{viewport, \subscriptText{integer}{n}\argDef{1},
+string\argDef{"on"}}
+indicates if graph {\it n} is shown or not.
+%
+\item[\axiomFun{title}]\funArgs{viewport, string\argDef{"Axiom 2D"}}
+designates the title for {\it viewport}.
+%
+\item[\axiomFun{translate}]\funArgs{viewport,
+\subscriptText{integer}{n}\argDef{1},
+\subscriptText{float}{x}\argDef{0.0}, \subscriptText{float}{y}\argDef{0.0}}
+%-% \HDindex{graphics!2D commands!translate}{ugGraphTwoDopsPage}{7.1.8.}{Operations for Two-Dimensional Graphics}
+causes graph {\it n} to be moved {\it x} and {\it y} units in the respective directions.
+%
+\item[\axiomFun{write}]\funArgs{viewport, \subscriptText{string}{directory},
+\optArg{strings}}
+if no third argument is given, writes the {\bf data} file onto the directory
+with extension {\bf data}.
+The third argument can be a single string or a list of strings with some or
+all the entries {\tt "pixmap"}, {\tt "bitmap"}, {\tt "postscript"}, and
+{\tt "image"}.
+\enditems
+\indent{0}
+\texht{\egroup}{}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphTwoDbuildTitle}{Addendum: Building Two-Dimensional Graphs}
+\newcommand{\ugGraphTwoDbuildNumber}{7.1.9.}
+%
+% =====================================================================
+\begin{page}{ugGraphTwoDbuildPage}{7.1.9. Addendum: Building Two-Dimensional Graphs}
+% =====================================================================
+\beginscroll
+
+In this section we demonstrate how to create \twodim{} graphs from
+lists of points and give an example showing how to read the lists
+of points from a file.
+
+\subsubsection{Creating a Two-Dimensional Viewport from a List of Points}
+
+\Language{} creates lists of points in a \twodim{} viewport by utilizing
+the \axiomType{GraphImage} and \axiomType{TwoDimensionalViewport} domains.
+In this example, the \axiomFunFrom{makeGraphImage}{GraphImage}
+function takes a list of lists of points parameter, a list of colors for
+each point in the graph, a list of colors for each line in the graph, and
+a list of sizes for each point in the graph.
+%
+\xtc{
+The following expressions create a list of lists of points which will be read
+by \Language{} and made into a \twodim{} viewport.
+}{
+\spadpaste{p1 := point [1,1]\$(Point DFLOAT) \bound{p1}}
+}
+\xtc{
+}{
+\spadpaste{p2 := point [0,1]\$(Point DFLOAT) \bound{p2}}
+}
+\xtc{
+}{
+\spadpaste{p3 := point [0,0]\$(Point DFLOAT) \bound{p3}}
+}
+\xtc{
+}{
+\spadpaste{p4 := point [1,0]\$(Point DFLOAT) \bound{p4}}
+}
+\xtc{
+}{
+\spadpaste{p5 := point [1,.5]\$(Point DFLOAT) \bound{p5}}
+}
+\xtc{
+}{
+\spadpaste{p6 := point [.5,0]\$(Point DFLOAT) \bound{p6}}
+}
+\xtc{
+}{
+\spadpaste{p7 := point [0,0.5]\$(Point DFLOAT) \bound{p7}}
+}
+\xtc{
+}{
+\spadpaste{p8 := point [.5,1]\$(Point DFLOAT) \bound{p8}}
+}
+\xtc{
+}{
+\spadpaste{p9 := point [.25,.25]\$(Point DFLOAT) \bound{p9}}
+}
+\xtc{
+}{
+\spadpaste{p10 := point [.25,.75]\$(Point DFLOAT) \bound{p10}}
+}
+\xtc{
+}{
+\spadpaste{p11 := point [.75,.75]\$(Point DFLOAT) \bound{p11}}
+}
+\xtc{
+}{
+\spadpaste{p12 := point [.75,.25]\$(Point DFLOAT) \bound{p12}}
+}
+\xtc{
+Finally, here is the list.
+}{
+\spadpaste{llp := [[p1,p2], [p2,p3], [p3,p4], [p4,p1], [p5,p6], [p6,p7], [p7,p8], [p8,p5], [p9,p10], [p10,p11], [p11,p12], [p12,p9]] \free{p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12} \bound{llp}}
+}
+\xtc{
+Now we set the point sizes for all components of the graph.
+}{
+\spadpaste{size1 := 6::PositiveInteger \bound{size1}}
+}
+\xtc{
+}{
+}
+\xtc{
+}{
+\spadpaste{size2 := 8::PositiveInteger \bound{size2}}
+}
+\xtc{
+}{
+\spadpaste{size3 := 10::PositiveInteger \bound{size3}}
+}
+\xtc{
+}{
+\spadpaste{lsize := [size1, size1, size1, size1, size2, size2, size2, size2, size3, size3, size3, size3] \bound{lsize} \free{size1 size2 size3}}
+}
+\xtc{
+Here are the colors for the points.
+}{
+\spadpaste{pc1 := pastel red() \bound{pc1}}
+}
+\xtc{
+}{
+\spadpaste{pc2 := dim green() \bound{pc2}}
+}
+\xtc{
+}{
+\spadpaste{pc3 := pastel yellow() \bound{pc3}}
+}
+\xtc{
+}{
+\spadpaste{lpc := [pc1, pc1, pc1, pc1, pc2, pc2, pc2, pc2, pc3, pc3, pc3, pc3] \free{pc1 pc2 pc3} \bound{lpc}}
+}
+\xtc{
+Here are the colors for the lines.
+}{
+\spadpaste{lc := [pastel blue(), light yellow(), dim green(), bright red(), light green(), dim yellow(), bright blue(), dark red(), pastel red(), light blue(), dim green(), light yellow()] \bound{lc}}
+}
+\xtc{
+Now the \axiomType{GraphImage} is created according to the component
+specifications indicated above.
+}{
+\spadpaste{g := makeGraphImage(llp,lpc,lc,lsize)\$GRIMAGE \bound{g} \free{llp lpc lc lsize}}
+}
+\psXtc{
+The \axiomFunFrom{makeViewport2D}{TwoDimensionalViewport} function now
+creates a \axiomType{TwoDimensionalViewport} for this graph according to the
+list of options specified within the brackets.
+}{
+\graphpaste{makeViewport2D(g,[title("Lines")])\$VIEW2D \free{g}}
+}{
+%
+}
+%See Figure #.#.
+\xtc{
+This example demonstrates the use of the \axiomType{GraphImage} functions
+\axiomFunFrom{component}{GraphImage} and \axiomFunFrom{appendPoint}{GraphImage}
+in adding points to an empty \axiomType{GraphImage}.
+}{
+\spadpaste{)clear all \bound{clearAll}}
+}
+\xtc{
+}{
+\spadpaste{g := graphImage()\$GRIMAGE \bound{Sg}\free{clearAll}}
+}
+\xtc{
+}{
+\spadpaste{p1 := point [0,0]\$(Point DFLOAT) \bound{Sp1}}
+}
+\xtc{
+}{
+\spadpaste{p2 := point [.25,.25]\$(Point DFLOAT) \bound{Sp2}}
+}
+\xtc{
+}{
+\spadpaste{p3 := point [.5,.5]\$(Point DFLOAT) \bound{Sp3}}
+}
+\xtc{
+}{
+\spadpaste{p4 := point [.75,.75]\$(Point DFLOAT) \bound{Sp4}}
+}
+\xtc{
+}{
+\spadpaste{p5 := point [1,1]\$(Point DFLOAT) \bound{Sp5}}
+}
+\xtc{
+}{
+\spadpaste{component(g,p1)\$GRIMAGE\free{Sg Sp1}\bound{gp1}}
+}
+\xtc{
+}{
+\spadpaste{component(g,p2)\$GRIMAGE\free{Sg Sp2}\bound{gp2}}
+}
+\xtc{
+}{
+\spadpaste{appendPoint(g,p3)\$GRIMAGE\free{gp1 gp2 Sp3}\bound{gp3}}
+}
+\xtc{
+}{
+\spadpaste{appendPoint(g,p4)\$GRIMAGE\free{gp3 Sp4}\bound{gp4}}
+}
+\xtc{
+}{
+\spadpaste{appendPoint(g,p5)\$GRIMAGE\free{gp4 Sp5}\bound{gp5}}
+}
+\xtc{
+}{
+\spadpaste{g1 := makeGraphImage(g)\$GRIMAGE \bound{Sg1} \free{gp5}}
+}
+\psXtc{
+Here is the graph.
+}{
+\graphpaste{makeViewport2D(g1,[title("Graph Points")])\$VIEW2D \free{Sg1}}
+}{
+%
+}
+%
+%See Figure #.#.
+%
+\xtc{
+A list of points can also be made into a \axiomType{GraphImage} by using
+the operation \axiomFunFrom{coerce}{GraphImage}.  It is equivalent to adding
+each point to \axiom{g2} using \axiomFunFrom{component}{GraphImage}.
+}{
+\spadpaste{g2 := coerce([[p1],[p2],[p3],[p4],[p5]])\$GRIMAGE  \free{Sp1 Sp2 Sp3 Sp4 Sp5} \bound{Sg2}}
+}
+\xtc{
+Now, create an empty \axiomType{TwoDimensionalViewport}.
+}{
+\spadpaste{v := viewport2D()\$VIEW2D \bound{Sv}}
+}
+\xtc{
+}{
+\spadpaste{options(v,[title("Just Points")])\$VIEW2D \free{Sv}\bound{Svo}}
+}
+\xtc{
+Place the graph into the viewport.
+}{
+\spadpaste{putGraph(v,g2,1)\$VIEW2D \free{Sg2 Svo}\bound{Svog2}}
+}
+\psXtc{
+Take a look.
+}{
+\graphpaste{makeViewport2D(v)\$VIEW2D \free{Svog2}}
+}{
+%
+}
+
+%See Figure #.#.
+
+\subsubsection{Creating a Two-Dimensional Viewport of a List of Points from a File}
+
+The following three functions read a list of points from a
+file and then draw the points and the connecting lines. The
+points are stored in the file in readable form as floating point numbers
+(specifically, \axiomType{DoubleFloat} values) as an alternating
+stream of \axiom{x}- and \axiom{y}-values. For example,
+\begin{verbatim}
+0.0 0.0     1.0 1.0     2.0 4.0
+3.0 9.0     4.0 16.0    5.0 25.0
+\end{verbatim}
+
+\beginImportant
+  
+\noindent
+{\tt 1.\ \ \ drawPoints(lp:List\ Point\ DoubleFloat):VIEW2D\ ==}\newline
+{\tt 2.\ \ \ \ \ g\ :=\ graphImage()\$GRIMAGE}\newline
+{\tt 3.\ \ \ \ \ for\ p\ in\ lp\ repeat}\newline
+{\tt 4.\ \ \ \ \ \ \ component(g,p,pointColorDefault(),lineColorDefault(),}\newline
+{\tt 5.\ \ \ \ \ \ \ \ \ pointSizeDefault())}\newline
+{\tt 6.\ \ \ \ \ gi\ :=\ makeGraphImage(g)\$GRIMAGE}\newline
+{\tt 7.\ \ \ \ \ makeViewport2D(gi,[title("Points")])\$VIEW2D}\newline
+{\tt 8.\ \ \ }\newline
+{\tt 9.\ \ \ drawLines(lp:List\ Point\ DoubleFloat):VIEW2D\ ==}\newline
+{\tt 10.\ \ \ \ g\ :=\ graphImage()\$GRIMAGE}\newline
+{\tt 11.\ \ \ \ component(g,\ lp,\ pointColorDefault(),\ lineColorDefault(),}\newline
+{\tt 12.\ \ \ \ \ \ pointSizeDefault())\$GRIMAGE}\newline
+{\tt 13.\ \ \ \ gi\ :=\ makeGraphImage(g)\$GRIMAGE}\newline
+{\tt 14.\ \ \ \ makeViewport2D(gi,[title("Points")])\$VIEW2D}\newline
+{\tt 15.\ \ }\newline
+{\tt 16.\ \ plotData2D(name,\ title)\ ==}\newline
+{\tt 17.\ \ \ \ f:File(DFLOAT)\ :=\ open(name,"input")}\newline
+{\tt 18.\ \ \ \ lp:LIST(Point\ DFLOAT)\ :=\ empty()}\newline
+{\tt 19.\ \ \ \ while\ ((x\ :=\ readIfCan!(f))\ case\ DFLOAT)\ repeat}\newline
+{\tt 20.\ \ \ \ \ \ y\ :\ DFLOAT\ :=\ read!(f)}\newline
+{\tt 21.\ \ \ \ \ \ lp\ :=\ cons(point\ [x,y]\$(Point\ DFLOAT),\ lp)}\newline
+{\tt 22.\ \ \ \ \ \ lp}\newline
+{\tt 23.\ \ \ \ close!(f)}\newline
+{\tt 24.\ \ \ \ drawPoints(lp)}\newline
+{\tt 25.\ \ \ \ drawLines(lp)}\newline
+\endImportant
+%
+This command will actually create the viewport and the graph if
+the point data is in the file \axiom{"file.data"}.
+\beginImportant
+  
+\noindent
+{\tt 1.\ \ \ plotData2D("file.data",\ "2D\ Data\ Plot")}\newline
+\endImportant
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphTwoDappendTitle}{Addendum: Appending a Graph to a Viewport Window Containing a Graph}
+\newcommand{\ugGraphTwoDappendNumber}{7.1.10.}
+%
+% =====================================================================
+\begin{page}{ugGraphTwoDappendPage}{7.1.10. Addendum: Appending a Graph to a Viewport Window Containing a Graph}
+% =====================================================================
+\beginscroll
+
+This section demonstrates how to append a \twodim{} graph to a viewport
+already containing other graphs.
+The default \axiomFun{draw} command places a graph into the first
+\axiomType{GraphImage} slot position of the \axiomType{TwoDimensionalViewport}.
+
+\xtc{
+This graph is in the first slot in its viewport.
+}{
+\spadpaste{v1 := draw(sin(x),x=0..2*\%pi) \bound{v1}}
+}
+\xtc{
+So is this graph.
+}{
+\spadpaste{v2 := draw(cos(x),x=0..2*\%pi, curveColor==light red()) \bound{v2}}
+}
+\xtc{
+The operation \axiomFunFrom{getGraph}{TwoDimensionalViewport}
+retrieves the \axiomType{GraphImage} \axiom{g1} from the first slot position
+in the viewport \axiom{v1}.
+}{
+\spadpaste{g1 := getGraph(v1,1) \bound{g1}\free{v1}}
+}
+\xtc{
+Now \axiomFunFrom{putGraph}{TwoDimensionalViewport}
+places \axiom{g1} into the the second slot position of \axiom{v2}.
+}{
+\spadpaste{putGraph(v2,g1,2) \bound{v22}\free{g1 v2}}
+}
+\psXtc{
+Display the new \axiomType{TwoDimensionalViewport} containing both graphs.
+}{
+\graphpaste{makeViewport2D(v2) \free{v22}}
+}{
+%
+}
+%
+%See Figure #.#.
+%
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphThreeDTitle}{Three-Dimensional Graphics}
+\newcommand{\ugGraphThreeDNumber}{7.2.}
+%
+% =====================================================================
+\begin{page}{ugGraphThreeDPage}{7.2. Three-Dimensional Graphics}
+% =====================================================================
+\beginscroll
+%
+The \Language{} \threedim{} graphics package provides the ability to
+%-% \HDindex{graphics!three-dimensional}{ugGraphThreeDPage}{7.2.}{Three-Dimensional Graphics}
+%
+\indent{4}
+\beginitems
+%
+\item[-] generate surfaces defined by a function of two real variables
+%
+\item[-] generate space curves and tubes defined by parametric equations
+%
+\item[-] generate surfaces defined by parametric equations
+\enditems
+\indent{0}
+These graphs can be modified by using various options, such as calculating
+points in the spherical coordinate system or changing the polygon grid size
+of a surface.
+
+\beginmenu
+    \menudownlink{{7.2.1. Plotting Three-Dimensional Functions of Two Variables}}{ugGraphThreeDPlotPage}
+    \menudownlink{{7.2.2. Plotting Three-Dimensional Parametric Space Curves}}{ugGraphThreeDParmPage}
+    \menudownlink{{7.2.3. Plotting Three-Dimensional Parametric Surfaces}}{ugGraphThreeDParPage}
+    \menudownlink{{7.2.4. Three-Dimensional Options}}{ugGraphThreeDOptionsPage}
+    \menudownlink{{7.2.5. The makeObject Command}}{ugGraphMakeObjectPage}
+    \menudownlink{{7.2.6. Building Three-Dimensional Objects From Primitives}}{ugGraphThreeDBuildPage}
+    \menudownlink{{7.2.7. Coordinate System Transformations}}{ugGraphCoordPage}
+    \menudownlink{{7.2.8. Three-Dimensional Clipping}}{ugGraphClipPage}
+    \menudownlink{{7.2.9. Three-Dimensional Control-Panel}}{ugGraphThreeDControlPage}
+    \menudownlink{{7.2.10. Operations for Three-Dimensional Graphics}}{ugGraphThreeDopsPage}
+    \menudownlink{{7.2.11. Customization using .Xdefaults}}{ugXdefaultsPage}
+\endmenu
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphThreeDPlotTitle}{Plotting Three-Dimensional Functions of Two Variables}
+\newcommand{\ugGraphThreeDPlotNumber}{7.2.1.}
+%
+% =====================================================================
+\begin{page}{ugGraphThreeDPlotPage}{7.2.1. Plotting Three-Dimensional Functions of Two Variables}
+% =====================================================================
+\beginscroll
+
+%-% \HDindex{surface!two variable function}{ugGraphThreeDPlotPage}{7.2.1.}{Plotting Three-Dimensional Functions of Two Variables}
+The simplest \threedim{} graph is that of a surface defined by a function
+of two variables, \axiom{z = f(x,y)}.
+
+%
+\beginImportant
+The general format for drawing a surface defined by a formula \axiom{f(x,y)}
+of two variables \axiom{x} and \axiom{y} is:
+%
+\centerline{{{\tt draw(f(x,y), x = a..b, y = c..d, {\it options})}}}
+where \axiom{a..b} and \axiom{c..d} define the range of \axiom{x}
+and \axiom{y}, and where {\it options} prescribes zero or more
+options as described in \downlink{``\ugGraphThreeDOptionsTitle''}{ugGraphThreeDOptionsPage} in Section \ugGraphThreeDOptionsNumber\ignore{ugGraphThreeDOptions}.
+An example of an option is \axiom{title == "Title of Graph".}
+An alternative format involving a function \axiom{f} is also
+available.
+\endImportant
+
+%
+\psXtc{
+The simplest way to plot a function of two variables is to use a formula.
+With formulas you always precede the range specifications with
+the variable name and an \spadSyntax{=} sign.
+}{
+\graphpaste{draw(cos(x*y),x=-3..3,y=-3..3)}
+}{
+\epsffile[0 0 295 295]{../ps/3D2VarA.ps}
+}
+%
+\xtc{
+If you intend to use a function more than once,
+or it is long and complex, then first
+give its definition to \Language{}.
+}{
+\spadpaste{f(x,y) == sin(x)*cos(y) \bound{f}}
+}
+%
+%
+\psXtc{
+To draw the function, just give its name and drop the variables
+from the range specifications.
+\Language{} compiles your function for efficient computation
+of data for the graph.
+Notice that \Language{} uses the text of your function as a
+default title.
+}{
+\graphpaste{draw(f,-\%pi..\%pi,-\%pi..\%pi) \free{f}}
+}{
+\epsffile[0 0 295 295]{../ps/3D2VarB.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphThreeDParmTitle}{Plotting Three-Dimensional Parametric Space Curves}
+\newcommand{\ugGraphThreeDParmNumber}{7.2.2.}
+%
+% =====================================================================
+\begin{page}{ugGraphThreeDParmPage}{7.2.2. Plotting Three-Dimensional Parametric Space Curves}
+% =====================================================================
+\beginscroll
+
+A second kind of \threedim{} graph is a \threedim{} space curve
+%-% \HDindex{curve!parametric space}{ugGraphThreeDParmPage}{7.2.2.}{Plotting Three-Dimensional Parametric Space Curves}
+defined by the parametric equations for \axiom{x(t)}, \axiom{y(t)},
+%-% \HDindex{parametric space curve}{ugGraphThreeDParmPage}{7.2.2.}{Plotting Three-Dimensional Parametric Space Curves}
+and \axiom{z(t)} as a function of an independent variable \axiom{t}.
+
+%
+\beginImportant
+The general format for drawing a \threedim{} space curve defined by
+parametric formulas \axiom{x = f(t)}, \axiom{y = g(t)}, and
+\axiom{z = h(t)} is:
+%
+\centerline{{{\tt draw(curve(f(t),g(t),h(t)), t = a..b, {\it options})}}}
+where \axiom{a..b} defines the range of the independent variable
+\axiom{t}, and where {\it options} prescribes zero or more options
+as described in \downlink{``\ugGraphThreeDOptionsTitle''}{ugGraphThreeDOptionsPage} in Section \ugGraphThreeDOptionsNumber\ignore{ugGraphThreeDOptions}.
+An example of an option is \axiom{title == "Title of Graph".}
+An alternative format involving functions \axiom{f}, \axiom{g} and
+\axiom{h} is also available.
+\endImportant
+
+%
+\psXtc{
+If you use explicit formulas to draw a space curve, always precede
+the range specification with the variable name and an
+\spadSyntax{=} sign.
+}{
+\graphpaste{draw(curve(5*cos(t), 5*sin(t),t), t=-12..12)}
+}{
+\epsffile[0 0 295 295]{../ps/3DpscA.ps}
+}
+%
+\xtc{
+Alternatively, you can draw space curves by referring to functions.
+}{
+\spadpaste{i1(t:DFLOAT):DFLOAT == sin(t)*cos(3*t/5) \bound{i1}}
+}
+\xtc{
+This is useful if the functions are to be used more than once \ldots
+}{
+\spadpaste{i2(t:DFLOAT):DFLOAT == cos(t)*cos(3*t/5) \bound{i2}}
+}
+\xtc{
+or if the functions are long and complex.
+}{
+\spadpaste{i3(t:DFLOAT):DFLOAT == cos(t)*sin(3*t/5) \bound{i3}}
+}
+%
+%
+\psXtc{
+Give the names of the functions and
+drop the variable name specification in the second argument.
+Again, \Language{} supplies a default title.
+}{
+\graphpaste{draw(curve(i1,i2,i3),0..15*\%pi) \free{i1 i2 i3}}
+}{
+\epsffile[0 0 295 295]{../ps/3DpscB.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphThreeDParTitle}{Plotting Three-Dimensional Parametric Surfaces}
+\newcommand{\ugGraphThreeDParNumber}{7.2.3.}
+%
+% =====================================================================
+\begin{page}{ugGraphThreeDParPage}{7.2.3. Plotting Three-Dimensional Parametric Surfaces}
+% =====================================================================
+\beginscroll
+
+%-% \HDindex{surface!parametric}{ugGraphThreeDParPage}{7.2.3.}{Plotting Three-Dimensional Parametric Surfaces}
+A third kind of \threedim{} graph is a surface defined by
+%-% \HDindex{parametric surface}{ugGraphThreeDParPage}{7.2.3.}{Plotting Three-Dimensional Parametric Surfaces}
+parametric equations for \axiom{x(u,v)}, \axiom{y(u,v)}, and
+\axiom{z(u,v)} of two independent variables \axiom{u} and \axiom{v}.
+
+%
+\beginImportant
+The general format for drawing a \threedim{} graph defined by
+parametric formulas \axiom{x = f(u,v)}, \axiom{y = g(u,v)},
+and \axiom{z = h(u,v)} is:
+%
+\centerline{{{\tt draw(surface(f(u,v),g(u,v),h(u,v)), u = a..b, v = c..d, {\it options})}}}
+where \axiom{a..b} and \axiom{c..d} define the range of the
+independent variables \axiom{u} and \axiom{v}, and where
+{\it options} prescribes zero or more options as described in
+\downlink{``\ugGraphThreeDOptionsTitle''}{ugGraphThreeDOptionsPage} in Section \ugGraphThreeDOptionsNumber\ignore{ugGraphThreeDOptions}.
+An example of an option is \axiom{title == "Title of Graph".}
+An alternative format involving functions \axiom{f}, \axiom{g} and
+\axiom{h} is also available.
+\endImportant
+
+%
+\psXtc{
+This example draws a graph of a surface plotted using the
+parabolic cylindrical coordinate system option.
+%-% \HDindex{coordinate system!parabolic cylindrical}{ugGraphThreeDParPage}{7.2.3.}{Plotting Three-Dimensional Parametric Surfaces}
+The values of the functions supplied to \axiomFun{surface} are
+%-% \HDindex{parabolic cylindrical coordinate system}{ugGraphThreeDParPage}{7.2.3.}{Plotting Three-Dimensional Parametric Surfaces}
+interpreted in coordinates as given by a {\tt coordinates} option,
+here as parabolic cylindrical coordinates (see
+\downlink{``\ugGraphCoordTitle''}{ugGraphCoordPage} in Section \ugGraphCoordNumber\ignore{ugGraphCoord}).
+}{
+\graphpaste{draw(surface(u*cos(v), u*sin(v), v*cos(u)), u=-4..4, v=0..\%pi, coordinates== parabolicCylindrical)}
+}{
+\epsffile[0 0 295 295]{../ps/3DpsA.ps}
+}
+%
+Again, you can graph these parametric surfaces using functions,
+if the functions are long and complex.
+\xtc{
+Here we declare the types of arguments and values to be of type
+\axiomType{DoubleFloat}.
+}{
+\spadpaste{n1(u:DFLOAT,v:DFLOAT):DFLOAT == u*cos(v) \bound{n1}}
+}
+\xtc{
+As shown by previous examples, these declarations are necessary.
+}{
+\spadpaste{n2(u:DFLOAT,v:DFLOAT):DFLOAT == u*sin(v) \bound{n2}}
+}
+\xtc{
+In either case, \Language{} compiles the functions
+when needed to graph a result.
+}{
+\spadpaste{n3(u:DFLOAT,v:DFLOAT):DFLOAT == u \bound{n3}}
+}
+\xtc{
+Without these declarations, you have to suffix floats
+with \axiom{@DFLOAT} to get a \axiomType{DoubleFloat} result.
+However, a call here with an unadorned float produces a \axiomType{DoubleFloat}.
+}{
+\spadpaste{n3(0.5,1.0)\free{n3}}
+}
+%
+%
+\psXtc{
+Draw the surface by referencing the function names, this time
+choosing the toroidal coordinate system.
+%-% \HDindex{coordinate system!toroidal}{ugGraphThreeDParPage}{7.2.3.}{Plotting Three-Dimensional Parametric Surfaces}
+%-% \HDindex{toroidal coordinate system}{ugGraphThreeDParPage}{7.2.3.}{Plotting Three-Dimensional Parametric Surfaces}
+}{
+\graphpaste{draw(surface(n1,n2,n3), 1..4, 1..2*\%pi, coordinates == toroidal(1\$DFLOAT)) \free{n1 n2 n3}}
+}{
+\epsffile[0 0 295 295]{../ps/3DpsB.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphThreeDOptionsTitle}{Three-Dimensional Options}
+\newcommand{\ugGraphThreeDOptionsNumber}{7.2.4.}
+%
+% =====================================================================
+\begin{page}{ugGraphThreeDOptionsPage}{7.2.4. Three-Dimensional Options}
+% =====================================================================
+\beginscroll
+
+%-% \HDindex{graphics!3D options}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+The \axiomFun{draw} commands optionally take an optional list of options such
+as {\tt coordinates} as shown in the last example.
+Each option is given by the syntax: \axiom{name} {\tt ==} \axiom{value}.
+Here is a list of the available options in the order that they are
+described below:
+
+\table{ {title} {coordinates} {var1Steps} {style} {tubeRadius} {var2Steps}
+{colorFunction} {tubePoints} {space}}
+
+\psXtc{
+The option \axiom{title} gives your graph a title.
+%-% \HDindex{graphics!3D options!title}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+}{
+\graphpaste{draw(cos(x*y),x=0..2*\%pi,y=0..\%pi,title == "Title of Graph") }
+}{
+\epsffile[0 0 295 295]{../ps/3DOptTtl.ps}
+}
+%
+\psXtc{
+The \axiom{style} determines which of four rendering algorithms is used for
+%-% \HDindex{rendering}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+the graph.
+The choices are
+{\tt "wireMesh"}, {\tt "solid"}, {\tt "shade"}, and {\tt "smooth"}.
+}{
+\graphpaste{draw(cos(x*y),x=-3..3,y=-3..3, style=="smooth", title=="Smooth Option")}
+}{
+\epsffile[0 0 295 295]{../ps/3DOptSty.ps}
+}
+%
+
+In all but the wire-mesh style, polygons in a surface or tube plot
+are normally colored in a graph according to their
+\axiom{z}-coordinate value.  Space curves are colored according to their
+parametric variable value.
+%-% \HDindex{graphics!3D options!color function}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+To change this, you can give a coloring function.
+%-% \HDindex{function!coloring}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+The coloring function is sampled across the range of its arguments, then
+normalized onto the standard \Language{} colormap.
+
+\xtc{
+A function of one variable  makes the color depend on the
+value of the parametric variable specified for a tube plot.
+}{
+\spadpaste{color1(t) == t \bound{colorFxn1}}
+}
+\psXtc{
+}{
+\graphpaste{draw(curve(sin(t), cos(t),0), t=0..2*\%pi, tubeRadius == .3, colorFunction == color1) \free{colorFxn1}}
+}{
+\epsffile[0 0 295 295]{../ps/3DOptCf1.ps}
+}
+%
+\xtc{
+A function of two variables makes the color depend on the
+values of the independent variables.
+}{
+\spadpaste{color2(u,v) == u**2 - v**2 \bound{colorFxn2}}
+}
+\psXtc{
+Use the option {\tt colorFunction} for special coloring.
+}{
+\graphpaste{draw(cos(u*v), u=-3..3, v=-3..3, colorFunction == color2) \free{colorFxn2}}
+}{
+\epsffile[0 0 295 295]{../ps/3DOptCf2.ps}
+}
+%
+\xtc{
+With a three variable function, the
+color also depends on the value of the function.
+}{
+\spadpaste{color3(x,y,fxy) == sin(x*fxy) + cos(y*fxy) \bound{colorFxn3}}
+}
+\psXtc{
+}{
+\graphpaste{draw(cos(x*y), x=-3..3, y=-3..3, colorFunction == color3) \free{colorFxn3}}
+}{
+\epsffile[0 0 295 295]{../ps/3DOptCf3.ps}
+}
+%
+Normally the Cartesian coordinate system is used.
+%-% \HDindex{Cartesian!coordinate system}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+To change this, use the {\tt coordinates} option.
+%-% \HDindex{coordinate system!Cartesian}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+For details, see \downlink{``\ugGraphCoordTitle''}{ugGraphCoordPage} in Section \ugGraphCoordNumber\ignore{ugGraphCoord}.
+%
+%
+\xtc{
+}{
+\spadpaste{m(u:DFLOAT,v:DFLOAT):DFLOAT == 1 \bound{m}}
+}
+\psXtc{
+Use the spherical
+%-% \HDindex{spherical coordinate system}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+coordinate system.
+%-% \HDindex{coordinate system!spherical}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+}{
+\graphpaste{draw(m, 0..2*\%pi,0..\%pi, coordinates == spherical, style=="shade") \free{m}}
+}{
+\epsffile[0 0 295 295]{../ps/3DOptCrd.ps}
+}
+%
+Space curves may be displayed as tubes with polygonal cross sections.
+%-% \HDindex{tube}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+Two options, {\tt tubeRadius} and {\tt tubePoints},  control the size and
+shape of this cross section.
+%
+\psXtc{
+The {\tt tubeRadius} option specifies the radius of the tube that
+%-% \HDindex{tube!radius}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+encircles the specified space curve.
+}{
+\graphpaste{draw(curve(sin(t),cos(t),0),t=0..2*\%pi, style=="shade", tubeRadius == .3)}
+}{
+\epsffile[0 0 295 295]{../ps/3DOptRad.ps}
+}
+%
+%
+\psXtc{
+The {\tt tubePoints} option specifies the number of vertices
+%-% \HDindex{tube!points in polygon}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+defining the polygon that is used to create a tube around the
+specified space curve.
+The larger this number is, the more cylindrical the tube becomes.
+}{
+\graphpaste{draw(curve(sin(t), cos(t), 0), t=0..2*\%pi, style=="shade", tubeRadius == .25, tubePoints == 3)}
+}{
+\epsffile[0 0 295 295]{../ps/3DOptPts.ps}
+}
+%
+%-% \HDindex{graphics!3D options!variable steps}{ugGraphThreeDOptionsPage}{7.2.4.}{Three-Dimensional Options}
+%
+%
+\psXtc{
+Options \axiomFunFrom{var1Steps}{DrawOption} and
+\axiomFunFrom{var2Steps}{DrawOption} specify the number of intervals into
+which the grid defining a surface plot is subdivided with respect to the
+first and second parameters of the surface function(s).
+}{
+\graphpaste{draw(cos(x*y),x=-3..3,y=-3..3, style=="shade", var1Steps == 30, var2Steps == 30)}
+}{
+\epsffile[0 0 295 295]{../ps/3DOptvB.ps}
+}
+%
+The {\tt space} option
+of a \axiomFun{draw} command lets you build multiple graphs in three space.
+To use this option, first create an empty three-space object,
+then use the {\tt space} option thereafter.
+There is no restriction as to the number or kinds
+of graphs that can be combined this way.
+\xtc{
+Create an empty three-space object.
+}{
+\spadpaste{s := create3Space()\$(ThreeSpace DFLOAT) \bound{s}}
+}
+%
+%
+\xtc{
+}{
+\spadpaste{m(u:DFLOAT,v:DFLOAT):DFLOAT == 1 \bound{m}}
+}
+\psXtc{
+Add a graph to this three-space object.
+The new graph destructively inserts the graph
+into \axiom{s}.
+}{
+\graphpaste{draw(m,0..\%pi,0..2*\%pi, coordinates == spherical, space == s) \free{s m}}
+}{
+\epsffile[0 0 295 295]{../ps/3Dmult1A.ps}
+}
+%
+%
+\psXtc{
+Add a second graph to \axiom{s}.
+}{
+\graphpaste{v := draw(curve(1.5*sin(t), 1.5*cos(t),0), t=0..2*\%pi, tubeRadius == .25, space == s) \free{s} \bound{v}}
+}{
+\epsffile[0 0 295 295]{../ps/3Dmult1B.ps}
+}
+%
+A three-space object can also be obtained from an existing \threedim{} viewport
+using the \axiomFunFrom{subspace}{ThreeSpace} command.
+You can then use \axiomFun{makeViewport3D} to create a viewport window.
+\xtc{
+Assign to \axiom{subsp} the three-space object in viewport \axiom{v}.
+}{
+\spadpaste{subsp := subspace v \free{v} \bound{su}}
+}
+\xtc{
+Reset the space component of \axiom{v} to the value of \axiom{subsp}.
+}{
+\spadpaste{subspace(v, subsp) \bound{sp} \free{su}}
+}
+\noOutputXtc{
+Create a viewport window from a three-space object.
+}{
+\graphpaste{makeViewport3D(subsp,"Graphs") \free{sp}}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphMakeObjectTitle}{The makeObject Command}
+\newcommand{\ugGraphMakeObjectNumber}{7.2.5.}
+%
+% =====================================================================
+\begin{page}{ugGraphMakeObjectPage}{7.2.5. The makeObject Command}
+% =====================================================================
+\beginscroll
+
+An alternate way to create multiple graphs is to use
+\axiomFun{makeObject}.
+The \axiomFun{makeObject} command is similar to the \axiomFun{draw}
+command, except that it returns a three-space object rather than a
+\axiomType{ThreeDimensionalViewport}.
+In fact, \axiomFun{makeObject} is called by the \axiomFun{draw}
+command to create the \axiomType{ThreeSpace} then
+\axiomFunFrom{makeViewport3D}{ThreeDimensionalViewport} to create a
+viewport window.
+
+\xtc{
+}{
+\spadpaste{m(u:DFLOAT,v:DFLOAT):DFLOAT == 1 \bound{m}}
+}
+\noOutputXtc{
+Do the last example a new way.
+First use \axiomFun{makeObject} to
+create a three-space object \axiom{sph}.
+}{
+\spadpaste{sph := makeObject(m, 0..\%pi, 0..2*\%pi, coordinates==spherical)\bound{sph}\free{m}}
+}
+\noOutputXtc{
+Add a second object to \axiom{sph}.
+}{
+\spadpaste{makeObject(curve(1.5*sin(t), 1.5*cos(t), 0), t=0..2*\%pi, space == sph, tubeRadius == .25) \free{sph}\bound{v1}}
+}
+\noOutputXtc{
+Create and display a viewport
+containing \axiom{sph}.
+}{
+\graphpaste{makeViewport3D(sph,"Multiple Objects") \free{v1}}
+}
+
+Note that an undefined \axiomType{ThreeSpace} parameter declared in a
+\axiomFun{makeObject} or \axiomFun{draw} command results in an error.
+Use the \axiomFunFrom{create3Space}{ThreeSpace} function to define a
+\axiomType{ThreeSpace}, or obtain a \axiomType{ThreeSpace} that has been
+previously generated before including it in a command line.
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphThreeDBuildTitle}{Building Three-Dimensional Objects From Primitives}
+\newcommand{\ugGraphThreeDBuildNumber}{7.2.6.}
+%
+% =====================================================================
+\begin{page}{ugGraphThreeDBuildPage}{7.2.6. Building Three-Dimensional Objects From Primitives}
+% =====================================================================
+\beginscroll
+
+Rather than using the \axiomFun{draw} and \axiomFun{makeObject} commands,
+%-% \HDindex{graphics!advanced!build 3D objects}{ugGraphThreeDBuildPage}{7.2.6.}{Building Three-Dimensional Objects From Primitives}
+you can create \threedim{} graphs from primitives.
+Operation \axiomFunFrom{create3Space}{ThreeSpace} creates a
+three-space object to which points, curves and polygons
+can be added using the operations from the \axiomType{ThreeSpace}
+domain.
+The resulting object can then be displayed in a viewport using
+\axiomFunFrom{makeViewport3D}{ThreeDimensionalViewport}.
+
+\xtc{
+Create the empty three-space object \axiom{space}.
+}{
+\spadpaste{space := create3Space()\$(ThreeSpace DFLOAT) \bound{space}}
+}
+
+Objects can be sent to this \axiom{space} using the operations
+exported by the \axiomType{ThreeSpace} domain.
+%-% \HDexptypeindex{ThreeSpace}{ugGraphThreeDBuildPage}{7.2.6.}{Building Three-Dimensional Objects From Primitives}
+The following examples place curves into \axiom{space}.
+
+\xtc{
+Add these eight curves to the space.
+}{
+\spadpaste{closedCurve(space,[[0,30,20], [0,30,30], [0,40,30], [0,40,100], [0,30,100],[0,30,110], [0,60,110], [0,60,100], [0,50,100], [0,50,30], [0,60,30], [0,60,20]]) \bound{curve1} \free{space}}
+}
+\xtc{
+}{
+\spadpaste{closedCurve(space,[[80,0,30], [80,0,100], [70,0,110], [40,0,110], [30,0,100], [30,0,90], [40,0,90], [40,0,95], [45,0,100], [65,0,100], [70,0,95], [70,0,35]]) \bound{curve2} \free{space}}
+}
+\xtc{
+}{
+\spadpaste{closedCurve(space,[[70,0,35], [65,0,30], [45,0,30], [40,0,35], [40,0,60], [50,0,60], [50,0,70], [30,0,70], [30,0,30], [40,0,20], [70,0,20], [80,0,30]]) \bound{curve3} \free{space}}
+}
+\xtc{
+}{
+\spadpaste{closedCurve(space,[[0,70,20], [0,70,110], [0,110,110], [0,120,100], [0,120,70], [0,115,65], [0,120,60], [0,120,30], [0,110,20], [0,80,20], [0,80,30], [0,80,20]]) \bound{curve4} \free{space}}
+}
+\xtc{
+}{
+\spadpaste{closedCurve(space,[[0,105,30], [0,110,35], [0,110,55], [0,105,60], [0,80,60], [0,80,70], [0,105,70], [0,110,75], [0,110,95], [0,105,100], [0,80,100], [0,80,20], [0,80,30]]) \bound{curve5} \free{space}}
+}
+\xtc{
+}{
+\spadpaste{closedCurve(space,[[140,0,20], [140,0,110], [130,0,110], [90,0,20], [101,0,20],[114,0,50], [130,0,50], [130,0,60], [119,0,60], [130,0,85], [130,0,20]]) \bound{curve6} \free{space}}
+}
+\xtc{
+}{
+\spadpaste{closedCurve(space,[[0,140,20], [0,140,110], [0,150,110], [0,170,50], [0,190,110], [0,200,110], [0,200,20], [0,190,20], [0,190,75], [0,175,35], [0,165,35],[0,150,75], [0,150,20]]) \bound{curve7} \free{space}}
+}
+\xtc{
+}{
+\spadpaste{closedCurve(space,[[200,0,20], [200,0,110], [189,0,110], [160,0,45], [160,0,110], [150,0,110], [150,0,20], [161,0,20], [190,0,85], [190,0,20]]) \bound{curve8} \free{space}}
+}
+\psXtc{
+Create and display the viewport using \axiomFun{makeViewport3D}.
+Options may also be given but here are displayed as a list with values
+enclosed in parentheses.
+}{
+\graphpaste{makeViewport3D(space, title == "Letters") \free{space curve1 curve2 curve3 curve4 curve5 curve6 curve7 curve8}}
+}{
+\epsffile[0 0 295 295]{../ps/3DBuildA.ps}
+}
+
+\subsubsection{Cube Example}
+
+As a second example of the use of primitives, we generate a cube using a
+polygon mesh.
+It is important to use a consistent orientation of the polygons for
+correct generation of \threedim{} objects.
+
+\xtc{
+Again start with an empty three-space object.
+}{
+\spadpaste{spaceC := create3Space()\$(ThreeSpace DFLOAT) \bound{spaceC}}
+}
+\xtc{
+For convenience,
+give \axiomType{DoubleFloat} values \axiom{+1} and \axiom{-1} names.
+}{
+\spadpaste{x: DFLOAT := 1 \bound{x}}
+}
+\xtc{
+}{
+\spadpaste{y: DFLOAT := -1 \bound{y}}
+}
+\xtc{
+Define the vertices of the cube.
+}{
+\spadpaste{a := point [x,x,y,1::DFLOAT]\$(Point DFLOAT) \bound{a} \free{x y}}
+}
+\xtc{
+}{
+\spadpaste{b := point [y,x,y,4::DFLOAT]\$(Point DFLOAT) \bound{b} \free{x y}}
+}
+\xtc{
+}{
+\spadpaste{c := point [y,x,x,8::DFLOAT]\$(Point DFLOAT) \bound{c} \free{x y}}
+}
+\xtc{
+}{
+\spadpaste{d := point [x,x,x,12::DFLOAT]\$(Point DFLOAT) \bound{d} \free{x y}}
+}
+\xtc{
+}{
+\spadpaste{e := point [x,y,y,16::DFLOAT]\$(Point DFLOAT) \bound{e} \free{x y}}
+}
+\xtc{
+}{
+\spadpaste{f := point [y,y,y,20::DFLOAT]\$(Point DFLOAT) \bound{f} \free{x y}}
+}
+\xtc{
+}{
+\spadpaste{g := point [y,y,x,24::DFLOAT]\$(Point DFLOAT) \bound{g} \free{x y}}
+}
+\xtc{
+}{
+\spadpaste{h := point [x,y,x,27::DFLOAT]\$(Point DFLOAT) \bound{h} \free{x y}}
+}
+\xtc{
+Add the faces of the cube as polygons to the space using a
+consistent orientation.
+}{
+\spadpaste{polygon(spaceC,[d,c,g,h]) \free{d c g h spaceC} \bound{pol1}}
+}
+\xtc{
+}{
+\spadpaste{polygon(spaceC,[d,h,e,a]) \free{d h e a spaceC} \bound{pol2}}
+}
+\xtc{
+}{
+\spadpaste{polygon(spaceC,[c,d,a,b]) \free{c d a b spaceC} \bound{pol3}}
+}
+\xtc{
+}{
+\spadpaste{polygon(spaceC,[g,c,b,f]) \free{g c b f spaceC} \bound{pol4}}
+}
+\xtc{
+}{
+\spadpaste{polygon(spaceC,[h,g,f,e]) \free{h g f e spaceC} \bound{pol5}}
+}
+\xtc{
+}{
+\spadpaste{polygon(spaceC,[e,f,b,a]) \free{e f b a spaceC} \bound{pol6}}
+}
+\psXtc{
+Create and display the viewport.
+}{
+\graphpaste{makeViewport3D(spaceC, title == "Cube") \free{pol1 pol2 pol3 pol4 pol5 pol6}}
+}{
+\epsffile[0 0 295 295]{../ps/3DBuildB.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphCoordTitle}{Coordinate System Transformations}
+\newcommand{\ugGraphCoordNumber}{7.2.7.}
+%
+% =====================================================================
+\begin{page}{ugGraphCoordPage}{7.2.7. Coordinate System Transformations}
+% =====================================================================
+\beginscroll
+%-% \HDindex{graphics!advanced!coordinate systems}{ugGraphCoordPage}{7.2.7.}{Coordinate System Transformations}
+
+The \axiomType{CoordinateSystems} package provides coordinate transformation
+functions that map a given data point from the coordinate system specified
+into the Cartesian coordinate system.
+%-% \HDexptypeindex{CoordinateSystems}{ugGraphCoordPage}{7.2.7.}{Coordinate System Transformations}
+The default coordinate system, given a triplet \axiom{(f(u,v), u, v)}, assumes
+that \axiom{z = f(u, v)}, \axiom{x = u} and \axiom{y = v},
+that is, reads the coordinates in \axiom{(z, x, y)} order.
+
+\xtc{
+}{
+\spadpaste{m(u:DFLOAT,v:DFLOAT):DFLOAT == u**2 \bound{m}}
+}
+%
+\psXtc{
+Graph plotted in default coordinate system.
+}{
+\graphpaste{draw(m,0..3,0..5) \free{m}}
+}{
+\epsffile[0 0 295 295]{../ps/defcoord.ps}
+}
+
+The \axiom{z} coordinate comes first since the first argument of
+the \axiomFun{draw} command gives its values.
+In general, the coordinate systems \Language{} provides, or any
+that you make up, must provide a map to an \axiom{(x, y, z)} triplet in
+order to be compatible with the
+\axiomFunFrom{coordinates}{DrawOption} \axiomType{DrawOption}.
+%-% \HDexptypeindex{DrawOption}{ugGraphCoordPage}{7.2.7.}{Coordinate System Transformations}
+Here is an example.
+
+\xtc{
+Define the identity function.
+}{
+\spadpaste{cartesian(point:Point DFLOAT):Point DFLOAT == point \bound{cart}}
+}
+\psXtc{
+Pass \axiom{cartesian} as the \axiomFunFrom{coordinates}{DrawOption}
+parameter to the \axiomFun{draw} command.
+}{
+\graphpaste{draw(m,0..3,0..5,coordinates==cartesian) \free{m cart}}
+}{
+\epsffile[0 0 295 295]{../ps/cartcoord.ps}
+}
+%
+
+What happened?
+The option {\tt coordinates == cartesian} directs \Language{} to
+treat the dependent variable \axiom{m} defined by
+\texht{$m=u^2$}{m=u**2} as the \axiom{x} coordinate.
+Thus the triplet of values \axiom{(m, u, v)} is transformed to
+coordinates \axiom{(x, y, z)} and so we get the graph of
+\texht{$x=y^2$}{x=y**2}.
+
+Here is another example.
+The \axiomFunFrom{cylindrical}{CoordinateSystems} transform takes
+%-% \HDindex{coordinate system!cylindrical}{ugGraphCoordPage}{7.2.7.}{Coordinate System Transformations}
+input of the form \axiom{(w,u,v)}, interprets it in the order
+%-% \HDindex{cylindrical coordinate system}{ugGraphCoordPage}{7.2.7.}{Coordinate System Transformations}
+\texht{($r$,$\theta$,$z$)}{(\axiom{r}, \axiom{theta}, \axiom{z})}
+and maps it to the Cartesian coordinates
+\texht{$x=r\cos(\theta)$, $y=r\sin(\theta)$, $z=z$}
+{\axiom{x = r * cos(theta)}, \axiom{y = r * sin(theta)}, \axiom{z = z}}
+in which
+\texht{$r$}{\axiom{r}} is the radius,
+\texht{$\theta$}{\axiom{theta}} is the angle and
+\texht{$z$}{\axiom{z}} is the z-coordinate.
+\xtc{
+An example using the \axiomFunFrom{cylindrical}{CoordinateSystems}
+coordinates for the constant \axiom{r = 3}.
+}{
+\spadpaste{f(u:DFLOAT,v:DFLOAT):DFLOAT == 3 \bound{f}}
+}
+\psXtc{
+Graph plotted in cylindrical coordinates.
+}{
+\graphpaste{draw(f,0..\%pi,0..6,coordinates==cylindrical) \free{f}}
+}{
+\epsffile[0 0 295 295]{../ps/cylCoord.ps}
+}
+
+Suppose you would like to specify \smath{z} as a function of
+\smath{r} and \texht{$\theta$}{\axiom{theta}} instead of just
+\smath{r}?
+Well, you still can use the \axiomFun{cylindrical} \Language{}
+transformation but we have to reorder the triplet before
+passing it to the transformation.
+
+\xtc{
+First, let's create a point to
+work with and call it \axiom{pt} with some color \axiom{col}.
+}{
+\spadpaste{col := 5 \bound{c}}
+}
+\xtc{
+}{
+\spadpaste{pt := point[1,2,3,col]\$(Point DFLOAT) \free{c} \bound{pt}}
+}
+The reordering you want is
+\texht{$(z,r, \theta)$}{\axiom{(z,r,theta)}} to
+\texht{$(r, \theta,z)$}{\axiom{(r,theta,z)}}
+so that the first element is moved to the third element, while the second
+and third elements move forward and the color element does not change.
+\xtc{
+Define a function \userfun{reorder} to reorder the point elements.
+}{
+\spadpaste{reorder(p:Point DFLOAT):Point DFLOAT == point[p.2, p.3, p.1, p.4] \bound{freo}}
+}
+\xtc{
+The function moves the second and third elements
+forward but the color does not change.
+}{
+\spadpaste{reorder pt \free{pt freo}}
+}
+\xtc{
+The function \userfun{newmap} converts our reordered version of
+the cylindrical coordinate system to the standard
+\texht{$(x,y,z)$}{\axiom{(x,y,z)}} Cartesian system.
+}{
+\spadpaste{newmap(pt:Point DFLOAT):Point DFLOAT == cylindrical(reorder pt) \free{freo} \bound{fnewmap}}
+}
+\xtc{
+}{
+\spadpaste{newmap pt \free{fnewmap pt} \bound{new}}
+}
+%
+\psXtc{
+Graph the same function \axiom{f} using the coordinate mapping of the function
+\axiom{newmap}, so it is now interpreted as
+\texht{$z=3$}{\axiom{z = 3}}:
+}{
+\graphpaste{draw(f,0..3,0..2*\%pi,coordinates==newmap) \free{f new}}
+}{
+\epsffile[0 0 295 295]{../ps/newmap.ps}
+}
+
+{\texht{\sloppy}{}
+The \axiomType{CoordinateSystems} package exports the following
+%-% \HDindex{coordinate system}{ugGraphCoordPage}{7.2.7.}{Coordinate System Transformations}
+operations:
+\axiomFun{bipolar},
+\axiomFun{bipolarCylindrical},
+\axiomFun{cartesian},
+\axiomFun{conical},
+\axiomFun{cylindrical},
+\axiomFun{elliptic},
+\axiomFun{ellipticCylindrical},
+\axiomFun{oblateSpheroidal},
+\axiomFun{parabolic},
+\axiomFun{parabolicCylindrical},
+\axiomFun{paraboloidal},
+\axiomFun{polar},
+\axiomFun{prolateSpheroidal},
+\axiomFun{spherical}, and
+\axiomFun{toroidal}.
+Use \Browse{} or the \spadcmd{)show} system command
+%-% \HDsyscmdindex{show}{ugGraphCoordPage}{7.2.7.}{Coordinate System Transformations}
+to get more information.
+
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphClipTitle}{Three-Dimensional Clipping}
+\newcommand{\ugGraphClipNumber}{7.2.8.}
+%
+% =====================================================================
+\begin{page}{ugGraphClipPage}{7.2.8. Three-Dimensional Clipping}
+% =====================================================================
+\beginscroll
+
+A \threedim{} graph can be explicitly clipped within the \axiomFun{draw}
+%-% \HDindex{graphics!advanced!clip}{ugGraphClipPage}{7.2.8.}{Three-Dimensional Clipping}
+command by indicating a minimum and maximum threshold for the
+%-% \HDindex{clipping}{ugGraphClipPage}{7.2.8.}{Three-Dimensional Clipping}
+given function definition.
+These thresholds can be defined using the \Language{} \axiomFun{min}
+and \axiomFun{max} functions.
+\xtc{
+}{
+\begin{spadsrc}[\bound{g}]
+gamma(x,y) ==
+  g := Gamma complex(x,y)
+  point [x, y, max( min(real g, 4), -4), argument g]
+\end{spadsrc}
+}
+\psXtc{
+Here is an example that clips
+the gamma function in order to eliminate the extreme divergence it creates.
+}{
+\graphpaste{draw(gamma,-\%pi..\%pi,-\%pi..\%pi,var1Steps==50,var2Steps==50) \free{g}}
+}{
+\epsffile[0 0 295 295]{../ps/clipGamma.ps}
+}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphThreeDControlTitle}{Three-Dimensional Control-Panel}
+\newcommand{\ugGraphThreeDControlNumber}{7.2.9.}
+%
+% =====================================================================
+\begin{page}{ugGraphThreeDControlPage}{7.2.9. Three-Dimensional Control-Panel}
+% =====================================================================
+\beginscroll
+%-% \HDindex{graphics!3D control-panel}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+Once you have created a viewport, move your mouse to the viewport
+and click with your left mouse button.
+This displays a control-panel on the side of the viewport
+that is closest to where you clicked.
+
+
+\subsubsection{Transformations}
+
+We recommend you first select the {\bf Bounds} button while
+%-% \HDindex{graphics!3D control-panel!transformations}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+executing transformations since the bounding box displayed
+indicates the object's position as it changes.
+%
+\indent{0}
+\beginitems
+%
+\item[Rotate:]  A rotation transformation occurs by clicking the mouse
+%-% \HDindex{graphics!3D control-panel!rotate}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+within the {\bf Rotate} window in the upper left corner of the
+control-panel.
+The rotation is computed in spherical coordinates, using the
+horizontal mouse position to increment or decrement the value of
+the longitudinal angle \texht{$\theta$}{\axiom{theta}} within the
+range of 0 to \texht{2$\pi$}{2*pi} and the vertical mouse position
+to increment or decrement the value of the latitudinal angle
+\texht{$\phi$}{\axiom{phi}} within the range of \texht{-$\pi$}{pi}
+to \texht{$\pi$}{pi}.
+The active mode of rotation is displayed in green on a color
+monitor or in clear text on a black and white monitor, while the
+inactive mode is displayed in red for color display or a mottled
+pattern for black and white.
+%
+\indent{0}
+\beginitems
+%
+\item[origin:]  The {\bf origin} button indicates that the
+rotation is to occur with respect to the origin of the viewing space, that is
+indicated by the axes.
+%
+\item[object:]  The {\bf object} button indicates that the
+rotation is to occur with respect to the center of volume of the object,
+independent of the axes' origin position.
+\enditems
+\indent{0}
+%
+\item[Scale:]  A scaling transformation occurs by clicking the mouse
+%-% \HDindex{graphics!3D control-panel!scale}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+within the {\bf Scale} window in the upper center of the
+control-panel, containing a zoom arrow.
+The axes along which the scaling is to occur are indicated by
+selecting the appropriate button above the zoom arrow window.
+The selected axes are displayed in green on a color monitor or in
+clear text on a black and white monitor, while the unselected axes
+are displayed in red for a color display or a mottled pattern for
+black and white.
+%
+\indent{0}
+\beginitems
+%
+\item[uniform:]  Uniform scaling along the {\tt x}, {\tt y}
+and {\tt z} axes occurs when all the axes buttons are selected.
+%
+\item[non-uniform:]  If any of the axes buttons are
+not selected, non-uniform scaling occurs, that is, scaling occurs only in the
+direction of the axes that are selected.
+\enditems
+\indent{0}
+%
+\item[Translate:]  Translation occurs by indicating with the mouse in the
+%-% \HDindex{graphics!3D control-panel!translate}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+{\bf Translate} window the direction you want the graph to move.
+This window is located in the upper right corner of the
+control-panel and contains a potentiometer with crossed arrows
+pointing up, down, left and right.
+Along the top of the {\bf Translate} window are three buttons
+({\bf XY},
+{\bf XZ}, and {\bf YZ}) indicating the three orthographic projection planes.
+Each orientates the group as a view into that plane.
+Any translation of the graph occurs only along this plane.
+\enditems
+\indent{0}
+
+\subsubsection{Messages}
+%-% \HDindex{graphics!3D control-panel!messages}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+
+The window directly below the potentiometer windows for transformations is
+used to display system messages relating to the viewport, the control-panel
+and the current graph displaying status.
+
+\subsubsection{Colormap}
+%-% \HDindex{graphics!3D control-panel!color map}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+
+Directly below the message window is the colormap range indicator
+window.
+%-% \HDindex{colormap}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+The \Language{} Colormap shows a sampling of the spectrum from
+which hues can be drawn to represent the colors of a surface.
+The Colormap is composed of five shades for each of the hues along
+this spectrum.
+By moving the markers above and below the Colormap, the range of
+hues that are used to color the existing surface are set.
+The bottom marker shows the hue for the low end of the color range
+and the top marker shows the hue for the upper end of the range.
+Setting the bottom and top markers at the same hue results in
+monochromatic smooth shading of the graph when {\bf Smooth} mode is selected.
+At each end of the Colormap are {\bf +} and {\bf -} buttons.
+When clicked on, these increment or decrement the top or bottom
+marker.
+
+\subsubsection{Buttons}
+%-% \HDindex{graphics!3D control-panel!buttons}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+
+Below the Colormap window and to the left are located various
+buttons that determine the characteristics of a graph.
+The buttons along the bottom and right hand side all have special
+meanings; the remaining buttons in the first row indicate the mode
+or style used to display the graph.
+The second row are toggles that turn on or off a property of the
+graph.
+On a color monitor, the property is on if green (clear text, on a
+monochrome monitor) and off if red (mottled pattern, on a
+monochrome monitor).
+Here is a list of their functions.
+%
+\indent{0}
+\beginitems
+%
+\item[Wire] displays surface and tube plots as a
+%-% \HDindex{graphics!3D control-panel!wire}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+wireframe image in a single color (blue) with no hidden surfaces removed,
+or displays space curve plots in colors based upon their parametric variables.
+This is the fastest mode for displaying a graph.
+This is very useful when you
+want to find a good orientation of your graph.
+%
+\item[Solid] displays the graph with hidden
+%-% \HDindex{graphics!3D control-panel!solid}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+surfaces removed, drawing each polygon beginning with the furthest
+from the viewer.
+The edges of the polygons are displayed in the hues specified by
+the range in the Colormap window.
+%
+\item[Shade] displays the graph with hidden
+%-% \HDindex{graphics!3D control-panel!shade}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+surfaces removed and with the polygons shaded, drawing each
+polygon beginning with the furthest from the viewer.
+Polygons are shaded in the hues specified by the range in the
+Colormap window using the Phong illumination model.
+%-% \HDindex{Phong!illumination model}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+%
+\item[Smooth] displays the graph using a
+%-% \HDindex{graphics!3D control-panel!smooth}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+renderer that computes the graph one line at a time.
+The location and color of the graph at each visible point on the
+screen are determined and displayed using the Phong illumination
+%-% \HDindex{Phong!illumination model}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+model.
+Smooth shading is done in one of two ways, depending on the range
+selected in the colormap window and the number of colors available
+from the hardware and/or window manager.
+When the top and bottom markers of the colormap range are set to
+different hues, the graph is rendered by dithering between the
+%-% \HDindex{dithering}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+transitions in color hue.
+When the top and bottom markers of the colormap range are set to
+the same hue, the graph is rendered using the Phong smooth shading
+model.
+%-% \HDindex{Phong!smooth shading model}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+However, if enough colors cannot be allocated for this purpose,
+the renderer reverts to the color dithering method until a
+sufficient color supply is available.
+For this reason, it may not be possible to render multiple Phong
+smooth shaded graphs at the same time on some systems.
+%
+\item[Bounds] encloses the entire volume of the
+viewgraph within a bounding box, or removes the box if previously selected.
+%-% \HDindex{graphics!3D control-panel!bounds}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+The region that encloses the entire volume of the viewport graph is displayed.
+%
+\item[Axes] displays Cartesian
+%-% \HDindex{graphics!3D control-panel!axes}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+coordinate axes of the space, or turns them off if previously selected.
+%
+\item[Outline] causes
+%-% \HDindex{graphics!3D control-panel!outline}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+quadrilateral polygons forming the graph surface to be outlined in black when
+the graph is displayed in {\bf Shade} mode.
+%
+\item[BW] converts a color viewport to black and white, or vice-versa.
+%-% \HDindex{graphics!3D control-panel!bw}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+When this button is selected the
+control-panel and viewport switch to an immutable colormap composed of a range
+of grey scale patterns or tiles that are used wherever shading is necessary.
+%
+\item[Light] takes you to a control-panel described below.
+%
+\item[ViewVolume] takes you to another control-panel as described below.
+%-% \HDindex{graphics!3D control-panel!save}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+%
+\item[Save] creates a menu of the possible file types that can
+be written using the control-panel.
+The {\bf Exit} button leaves the save menu.
+The {\bf Pixmap} button writes an \Language{} pixmap of
+%-% \HDindex{graphics!3D control-panel!pixmap}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+the current viewport contents.  The file is called {\bf axiom3D.pixmap} and is
+located in the directory from which \Language{} or {\bf viewAlone} was
+started.
+The {\bf PS} button writes the current viewport contents to
+%-% \HDindex{graphics!3D control-panel!ps}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+PostScript output rather than to the viewport window.
+By default the file is called {\bf axiom3D.ps}; however, if a file
+%-% \HDindex{file!.Xdefaults @{\bf .Xdefaults}}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+name is specified in the user's {\bf .Xdefaults} file it is
+%-% \HDindex{graphics!.Xdefaults!PostScript file name}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+used.
+The file is placed in the directory from which the \Language{} or
+{\bf viewAlone} session was begun.
+See also the \axiomFunFrom{write}{ThreeDimensionalViewport}
+function.
+%-% \HDindex{PostScript}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+%
+\item[Reset] returns the object transformation
+%-% \HDindex{graphics!3D control-panel!reset}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+characteristics back to their initial states.
+%
+\item[Hide] causes the control-panel for the
+%-% \HDindex{graphics!3D control-panel!hide}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+corresponding viewport to disappear from the screen.
+%
+\item[Quit]  queries whether the current viewport
+%-% \HDindex{graphics!3D control-panel!quit}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+session should be terminated.
+\enditems
+\indent{0}
+
+\subsubsection{Light}
+%-% \HDindex{graphics!3D control-panel!light}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+
+%
+%>>>\begin{texonly}
+%
+%>>>\begin{figure}[htbp]
+%>>>\begin{picture}(183,252)(-125,0)
+%>>>\special{psfile=../ps/3Dlight.ps}
+%>>>\end{picture}
+%>>>\caption{Three-Dimensional Lighting Panel.}
+%>>>\end{figure}
+%>>>\end{texonly}
+%
+
+The {\bf Light} button changes the control-panel into the
+{\bf Lighting Control-Panel}.  At the top of this panel, the three axes
+are shown with the same orientation as the object.  A light vector from
+the origin of the axes shows the current position of the light source
+relative to the object.  At the bottom of the panel is an {\bf Abort}
+button that cancels any changes to the lighting that were made, and a
+{\bf Return} button that carries out the current set of lighting changes
+on the graph.
+%
+\indent{0}
+\beginitems
+%
+\item[XY:]  The {\bf XY} lighting axes window is below the
+%-% \HDindex{graphics!3D control-panel!move xy}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+{\bf Lighting Control-Panel} title and to the left.
+This changes the light vector within the {\bf XY} view plane.
+%
+\item[Z:]  The {\bf Z} lighting axis window is below the
+%-% \HDindex{graphics!3D control-panel!move z}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+{\bf Lighting Control-Panel} title and in the center.  This
+changes the {\bf Z}
+location of the light vector.
+%
+\item[Intensity:]
+Below the {\bf Lighting Control-Panel} title
+%-% \HDindex{graphics!3D control-panel!intensity}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+and to the right is the light intensity meter.
+Moving the intensity indicator down decreases the amount of
+light emitted from the light source.
+When the indicator is at the top of the meter the light source is
+emitting at 100\% intensity.
+At the bottom of the meter the light source is emitting at a level
+slightly above ambient lighting.
+\enditems
+\indent{0}
+
+\subsubsection{View Volume}
+%-% \HDindex{graphics!3D control-panel!view volume}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+
+The {\bf View Volume} button changes the control-panel into
+the {\bf Viewing Volume Panel}.
+At the bottom of the viewing panel is an {\bf Abort} button that
+cancels any changes to the viewing volume that were made and a
+{\it Return} button that carries out the current set of
+viewing changes to the graph.
+%
+%>>>\begin{texonly}
+%
+%>>>\begin{figure}[htbp]
+%>>>\begin{picture}(183,252)(-125,0)
+%>>>\special{psfile=../ps/3Dvolume.ps}
+%>>>\end{picture}
+%>>>\caption{Three-Dimensional Volume Panel.}
+%>>>\end{figure}
+%>>>\end{texonly}
+%
+\indent{0}
+\beginitems
+%
+\item[Eye Reference:]  At the top of this panel is the
+%-% \HDindex{graphics!3D control-panel!eye reference}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+{\bf Eye Reference} window.
+It shows a planar projection of the viewing pyramid from the eye
+of the viewer relative to the location of the object.
+This has a bounding region represented by the rectangle on the
+left.
+Below the object rectangle is the {\bf Hither} window.
+By moving the slider in this window the hither clipping plane sets
+%-% \HDindex{hither clipping plane}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+the front of the view volume.
+As a result of this depth clipping all points of the object closer
+to the eye than this hither plane are not shown.
+The {\bf Eye Distance} slider to the right of the {\bf Hither}
+slider is used to change the degree of perspective in the image.
+%
+\item[Clip Volume:]  The {\bf Clip Volume} window is at the
+%-% \HDindex{graphics!3D control-panel!clip volume}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+bottom of the {\bf Viewing Volume Panel}.
+On the right is a {\bf Settings} menu.
+In this menu are buttons to select viewing attributes.
+Selecting the {\bf Perspective} button computes the image using
+perspective projection.
+%-% \HDindex{graphics!3D control-panel!perspective}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+The {\bf Show Region} button indicates whether the clipping region
+of the
+%-% \HDindex{graphics!3D control-panel!show clip region}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+volume is to be drawn in the viewport and the {\bf Clipping On}
+button shows whether the view volume clipping is to be in effect
+when the image
+%-% \HDindex{graphics!3D control-panel!clipping on}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+is drawn.
+The left side of the {\bf Clip Volume} window shows the clipping
+%-% \HDindex{graphics!3D control-panel!clip volume}{ugGraphThreeDControlPage}{7.2.9.}{Three-Dimensional Control-Panel}
+boundary of the graph.
+Moving the knobs along the {\bf X}, {\bf Y}, and {\bf Z} sliders
+adjusts the volume of the clipping region accordingly.
+\enditems
+\indent{0}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugGraphThreeDopsTitle}{Operations for Three-Dimensional Graphics}
+\newcommand{\ugGraphThreeDopsNumber}{7.2.10.}
+%
+% =====================================================================
+\begin{page}{ugGraphThreeDopsPage}{7.2.10. Operations for Three-Dimensional Graphics}
+% =====================================================================
+\beginscroll
+
+Here is a summary of useful \Language{} operations for \threedim{}
+graphics.
+Each operation name is followed by a list of arguments.
+Each argument is written as a variable informally named according
+to the type of the argument (for example, {\it integer}).
+If appropriate, a default value for an argument is given in
+parentheses immediately following the name.
+
+%
+\texht{\bgroup\hbadness = 10001\sloppy}{}
+\indent{0}
+\beginitems
+%
+\item[\axiomFun{adaptive3D?}]\funArgs{}
+tests whether space curves are to be plotted
+%-% \HDindex{graphics!plot3d defaults!adaptive}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+according to the
+%-% \HDindex{adaptive plotting}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+adaptive refinement algorithm.
+
+%
+\item[\axiomFun{axes}]\funArgs{viewport, string\argDef{"on"}}
+turns the axes on and off.
+%-% \HDindex{graphics!3D commands!axes}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+
+%
+\item[\axiomFun{close}]\funArgs{viewport}
+closes the viewport.
+%-% \HDindex{graphics!3D commands!close}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+
+%
+\item[\axiomFun{colorDef}]\funArgs{viewport,
+\subscriptIt{color}{1}\argDef{1}, \subscriptIt{color}{2}\argDef{27}}
+sets the colormap
+%-% \HDindex{graphics!3D commands!define color}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+range to be from
+\subscriptIt{color}{1} to \subscriptIt{color}{2}.
+
+%
+\item[\axiomFun{controlPanel}]\funArgs{viewport, string\argDef{"off"}}
+declares whether the
+%-% \HDindex{graphics!3D commands!control-panel}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+control-panel for the viewport is to be displayed or not.
+
+%
+\item[\axiomFun{diagonals}]\funArgs{viewport, string\argDef{"off"}}
+declares whether the
+%-% \HDindex{graphics!3D commands!diagonals}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+polygon outline includes the diagonals or not.
+
+%
+\item[\axiomFun{drawStyle}]\funArgs{viewport, style}
+selects which of four drawing styles
+%-% \HDindex{graphics!3D commands!drawing style}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+are used: {\tt "wireMesh", "solid", "shade",} or {\tt "smooth".}
+
+%
+\item[\axiomFun{eyeDistance}]\funArgs{viewport,float\argDef{500}}
+sets the distance of the eye from the origin of the object
+%-% \HDindex{graphics!3D commands!eye distance}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+for use in the \axiomFunFrom{perspective}{ThreeDimensionalViewport}.
+
+%
+\item[\axiomFun{key}]\funArgs{viewport}
+returns the operating
+%-% \HDindex{graphics!3D commands!key}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+system process ID number for the viewport.
+
+%
+\item[\axiomFun{lighting}]\funArgs{viewport,
+\subscriptText{float}{x}\argDef{-0.5},
+\subscriptText{float}{y}\argDef{0.5}, \subscriptText{float}{z}\argDef{0.5}}
+sets the Cartesian
+%-% \HDindex{graphics!3D commands!lighting}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+coordinates of the light source.
+
+%
+\item[\axiomFun{modifyPointData}]\funArgs{viewport,integer,point}
+replaces the coordinates of the point with
+%-% \HDindex{graphics!3D commands!modify point data}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+the index {\it integer} with {\it point}.
+
+%
+\item[\axiomFun{move}]\funArgs{viewport,
+\subscriptText{integer}{x}\argDef{viewPosDefault},
+\subscriptText{integer}{y}\argDef{viewPosDefault}}
+moves the upper
+%-% \HDindex{graphics!3D commands!move}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+left-hand corner of the viewport to screen position
+\allowbreak
+({\small \subscriptText{integer}{x}, \subscriptText{integer}{y}}).
+
+%
+\item[\axiomFun{options}]\funArgs{viewport}
+returns a list of all current draw options.
+
+%
+\item[\axiomFun{outlineRender}]\funArgs{viewport, string\argDef{"off"}}
+turns polygon outlining
+%-% \HDindex{graphics!3D commands!outline}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+off or on when drawing in {\tt "shade"} mode.
+
+%
+\item[\axiomFun{perspective}]\funArgs{viewport, string\argDef{"on"}}
+turns perspective
+%-% \HDindex{graphics!3D commands!perspective}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+viewing on and off.
+
+%
+\item[\axiomFun{reset}]\funArgs{viewport}
+resets the attributes of a viewport to their
+%-% \HDindex{graphics!3D commands!reset}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+initial settings.
+
+%
+\item[\axiomFun{resize}]\funArgs{viewport,
+\subscriptText{integer}{width} \argDef{viewSizeDefault},
+\subscriptText{integer}{height} \argDef{viewSizeDefault}}
+resets the width and height
+%-% \HDindex{graphics!3D commands!resize}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+values for a viewport.
+
+%
+\item[\axiomFun{rotate}]\funArgs{viewport,
+\subscriptText{number}{\texht{$\theta$}{\axiom{theta}}}\argDef{viewThetaDefault},
+\subscriptText{number}{\texht{$\phi$}{\axiom{phi}}}\argDef{viewPhiDefault}}
+rotates the viewport by rotation angles for longitude
+({\it \texht{$\theta$}{\axiom{theta}}}) and
+latitude ({\it \texht{$\phi$}{\axiom{phi}}}).
+Angles designate radians if given as floats, or degrees if given
+%-% \HDindex{graphics!3D commands!rotate}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+as integers.
+
+%
+\item[\axiomFun{setAdaptive3D}]\funArgs{boolean\argDef{true}}
+sets whether space curves are to be plotted
+%-% \HDindex{graphics!plot3d defaults!set adaptive}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+according to the adaptive
+%-% \HDindex{adaptive plotting}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+refinement algorithm.
+
+%
+\item[\axiomFun{setMaxPoints3D}]\funArgs{integer\argDef{1000}}
+ sets the default maximum number of possible
+%-% \HDindex{graphics!plot3d defaults!set max points}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+points to be used when constructing a \threedim{} space curve.
+
+%
+\item[\axiomFun{setMinPoints3D}]\funArgs{integer\argDef{49}}
+sets the default minimum number of possible
+%-% \HDindex{graphics!plot3d defaults!set min points}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+points to be used when constructing a \threedim{} space curve.
+
+%
+\item[\axiomFun{setScreenResolution3D}]\funArgs{integer\argDef{500}}
+sets the default screen resolution constant
+%-% \HDindex{graphics!plot3d defaults!set screen resolution}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+used in setting the computation limit of adaptively
+%-% \HDindex{adaptive plotting}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+generated \threedim{} space curve plots.
+
+%
+\item[\axiomFun{showRegion}]\funArgs{viewport, string\argDef{"off"}}
+declares whether the bounding
+%-% \HDindex{graphics!3D commands!showRegion}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+box of a graph is shown or not.
+%
+\item[\axiomFun{subspace}]\funArgs{viewport}
+returns the space component.
+%
+\item[\axiomFun{subspace}]\funArgs{viewport, subspace}
+resets the space component
+%-% \HDindex{graphics!3D commands!subspace}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+to {\it subspace}.
+
+%
+\item[\axiomFun{title}]\funArgs{viewport, string}
+gives the viewport the
+%-% \HDindex{graphics!3D commands!title}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+title {\it string}.
+
+%
+\item[\axiomFun{translate}]\funArgs{viewport,
+\subscriptText{float}{x}\argDef{viewDeltaXDefault},
+\subscriptText{float}{y}\argDef{viewDeltaYDefault}}
+translates
+%-% \HDindex{graphics!3D commands!translate}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+the object horizontally and vertically relative to the center of the viewport.
+
+%
+\item[\axiomFun{intensity}]\funArgs{viewport,float\argDef{1.0}}
+resets the intensity {\it I} of the light source,
+%-% \HDindex{graphics!3D commands!intensity}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+\texht{$0 \le I \le 1.$}{{\it 0 \le I \le 1}.}
+
+%
+\item[\axiomFun{tubePointsDefault}]\funArgs{\optArg{integer\argDef{6}}}
+sets or indicates the default number of
+%-% \HDindex{graphics!3D defaults!tube points}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+vertices defining the polygon that is used to create a tube around
+a space curve.
+
+%
+\item[\axiomFun{tubeRadiusDefault}]\funArgs{\optArg{float\argDef{0.5}}}
+sets or indicates the default radius of
+%-% \HDindex{graphics!3D defaults!tube radius}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+the tube that encircles a space curve.
+
+%
+\item[\axiomFun{var1StepsDefault}]\funArgs{\optArg{integer\argDef{27}}}
+sets or indicates the default number of
+%-% \HDindex{graphics!3D defaults!var1 steps}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+increments into which the grid defining a surface plot is subdivided with
+respect to the first parameter declared in the surface function.
+
+%
+\item[\axiomFun{var2StepsDefault}]\funArgs{\optArg{integer\argDef{27}}}
+sets or indicates the default number of
+%-% \HDindex{graphics!3D defaults!var2 steps}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+increments into which the grid defining a surface plot is subdivided with
+respect to the second parameter declared in the surface function.
+
+%
+\item[\axiomFun{viewDefaults}]\funArgs{{\tt [}\subscriptText{integer}{%
+point}, \subscriptText{integer}{line}, \subscriptText{integer}{axes},
+\subscriptText{integer}{units}, \subscriptText{float}{point},
+\allowbreak\subscriptText{list}{position},
+\subscriptText{list}{size}{\tt ]}}
+resets the default settings for the
+%-% \HDindex{graphics!3D defaults!reset viewport defaults}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+point color, line color, axes color, units color, point size,
+viewport upper left-hand corner position, and the viewport size.
+
+%
+\item[\axiomFun{viewDeltaXDefault}]\funArgs{\optArg{float\argDef{0}}}
+resets the default horizontal offset
+%-% \HDindex{graphics!3D commands!deltaX default}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+from the center of the viewport, or returns the current default offset if no argument is given.
+
+%
+\item[\axiomFun{viewDeltaYDefault}]\funArgs{\optArg{float\argDef{0}}}
+resets the default vertical offset
+%-% \HDindex{graphics!3D commands!deltaY default}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+from the center of the viewport, or returns the current default offset if no argument is given.
+
+%
+\item[\axiomFun{viewPhiDefault}]\funArgs{\optArg{float\argDef{-\texht{$\pi$}{{\it pi}}/4}}}
+resets the default latitudinal view angle,
+or returns the current default angle if no argument is given.
+%-% \HDindex{graphics!3D commands!phi default}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+\texht{$\phi$}{{\it phi}} is set to this value.
+
+%
+\item[\axiomFun{viewpoint}]\funArgs{viewport, \subscriptText{float}{x},
+\subscriptText{float}{y}, \subscriptText{float}{z}}
+sets the viewing position in Cartesian coordinates.
+
+%
+\item[\axiomFun{viewpoint}]\funArgs{viewport,
+\subscriptText{float}{\texht{$\theta$}{\axiom{theta}}},
+\subscriptText{Float}{\texht{$\phi$}{\axiom{phi}}}}
+sets the viewing position in spherical coordinates.
+
+%
+\item[\axiomFun{viewpoint}]\funArgs{viewport,
+\subscriptText{Float}{\texht{$\theta$}{\axiom{theta}}},
+\subscriptText{Float}{\texht{$\phi$}{\axiom{phi}}},
+\subscriptText{Float}{scaleFactor},
+\subscriptText{Float}{xOffset}, \subscriptText{Float}{yOffset}}
+sets the viewing position in spherical coordinates,
+the scale factor, and offsets.
+%-% \HDindex{graphics!3D commands!viewpoint}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+\texht{$\theta$}{{\it theta}} (longitude) and
+\texht{$\phi$}{{\it phi}} (latitude) are in radians.
+
+%
+\item[\axiomFun{viewPosDefault}]\funArgs{\optArg{list\argDef{[0,0]}}}
+sets or indicates the position of the upper
+%-% \HDindex{graphics!3D defaults!viewport position}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+left-hand corner of a \twodim{} viewport, relative to the display root
+window (the upper left-hand corner of the display is \axiom{[0, 0]}).
+
+%
+\item[\axiomFun{viewSizeDefault}]\funArgs{\optArg{list\argDef{[400,400]}}}
+sets or indicates the width and height dimensions
+%-% \HDindex{graphics!3D defaults!viewport size}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+of a viewport.
+
+%
+\item[\axiomFun{viewThetaDefault}]\funArgs{\optArg{float\argDef{\texht{$\pi$}{{\it pi}}/4}}}
+resets the default longitudinal view angle,
+or returns the current default angle if no argument is given.
+%-% \HDindex{graphics!3D commands!theta default}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+When a parameter is specified, the default longitudinal view angle
+\texht{$\theta$}{{\it theta}} is set to this value.
+
+%
+\item[\axiomFun{viewWriteAvailable}]\funArgs{\optArg{list\argDef{["pixmap",
+"bitmap", "postscript", "image"}}}
+indicates the possible file types
+%-% \HDindex{graphics!3D defaults!available viewport writes}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+that can be created with the \axiomFunFrom{write}{ThreeDimensionalViewport} function.
+
+%
+\item[\axiomFun{viewWriteDefault}]\funArgs{\optArg{list\argDef{[]}}}
+sets or indicates the default types of files
+that are created in addition to the {\bf data} file when a
+\axiomFunFrom{write}{ThreeDimensionalViewport} command
+%-% \HDindex{graphics!3D defaults!viewport writes}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+is executed on a viewport.
+
+%
+\item[\axiomFun{viewScaleDefault}]\funArgs{\optArg{float}}
+sets the default scaling factor, or returns
+%-% \HDindex{graphics!3D commands!scale default}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+the current factor if no argument is given.
+
+%
+\item[\axiomFun{write}]\funArgs{viewport, directory, \optArg{option}}
+writes the file {\bf data} for {\it viewport}
+in the directory {\it directory}.
+An optional third argument specifies a file type (one of {\tt
+pixmap}, {\tt bitmap}, {\tt postscript}, or {\tt image}), or a
+list of file types.
+An additional file is written for each file type listed.
+
+%
+\item[\axiomFun{scale}]\funArgs{viewport, float\argDef{2.5}}
+specifies the scaling factor.
+%-% \HDindex{graphics!3D commands!scale}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+%-% \HDindex{scaling graphs}{ugGraphThreeDopsPage}{7.2.10.}{Operations for Three-Dimensional Graphics}
+\enditems
+\indent{0}
+\texht{\egroup}{}
+
+\endscroll
+\autobuttons
+\end{page}
+%
+%
+\newcommand{\ugXdefaultsTitle}{Customization using .Xdefaults}
+\newcommand{\ugXdefaultsNumber}{7.2.11.}
+%
+% =====================================================================
+\begin{page}{ugXdefaultsPage}{7.2.11. Customization using .Xdefaults}
+% =====================================================================
+\beginscroll
+%-% \HDindex{graphics!.Xdefaults}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+
+Both the \twodim{} and \threedim{} drawing facilities consult
+the {\bf .Xdefaults} file for various defaults.
+%-% \HDindex{file!.Xdefaults @{\bf .Xdefaults}}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+The list of defaults that are recognized by the graphing routines
+is discussed in this section.
+These defaults are preceded by {\tt Axiom.3D.}
+for \threedim{} viewport defaults, {\tt Axiom.2D.}
+for \twodim{} viewport defaults, or {\tt Axiom*} (no dot) for
+those defaults that are acceptable to either viewport type.
+
+%
+\indent{0}
+\beginitems
+%
+\item[{\tt Axiom*buttonFont:\ \it font}] \ \newline
+This indicates which
+%-% \HDindex{graphics!.Xdefaults!button font}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+font type is used for the button text on the control-panel.
+\xdefault{Rom11}
+%
+\item[{\tt Axiom.2D.graphFont:\ \it font}] \quad (2D only) \newline
+This indicates
+%-% \HDindex{graphics!.Xdefaults!graph number font}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+which font type is used for displaying the graph numbers and
+slots in the {\bf Graphs} section of the \twodim{} control-panel.
+\xdefault{Rom22}
+%
+\item[{\tt Axiom.3D.headerFont:\ \it font}] \ \newline
+This indicates which
+%-% \HDindex{graphics!.Xdefaults!graph label font}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+font type is used for the axes labels and potentiometer
+header names on \threedim{} viewport windows.
+This is also used for \twodim{} control-panels for indicating
+which font type is used for potentionmeter header names and
+multiple graph title headers.
+%for example, {\tt Axiom.2D.headerFont: 8x13}.
+\xdefault{Itl14}
+%
+\item[{\tt Axiom*inverse:\ \it switch}] \ \newline
+This indicates whether the
+%-% \HDindex{graphics!.Xdefaults!inverting background}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+background color is to be inverted from white to black.
+If {\tt on}, the graph viewports use black as the background
+color.
+If {\tt off} or no declaration is made, the graph viewports use a
+white background.
+\xdefault{off}
+%
+\item[{\tt Axiom.3D.lightingFont:\ \it font}] \quad (3D only) \newline
+This indicates which font type is used for the {\bf x},
+%-% \HDindex{graphics!.Xdefaults!lighting font}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+{\bf y}, and {\bf z} labels of the two lighting axes potentiometers, and for
+the {\bf Intensity} title on the lighting control-panel.
+\xdefault{Rom10}
+%
+\item[{\tt Axiom.2D.messageFont, Axiom.3D.messageFont:\ \it font}] \ \newline
+These indicate the font type
+%-% \HDindex{graphics!.Xdefaults!message font}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+to be used for the text in the control-panel message window.
+\xdefault{Rom14}
+%
+\item[{\tt Axiom*monochrome:\ \it switch}] \ \newline
+This indicates whether the
+%-% \HDindex{graphics!.Xdefaults!monochrome}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+graph viewports are to be displayed as if the monitor is black and
+white, that is, a 1 bit plane.
+If {\tt on} is specified, the viewport display is black and white.
+If {\tt off} is specified, or no declaration for this default is
+given, the viewports are displayed in the normal fashion for the
+monitor in use.
+\xdefault{off}
+%
+\item[{\tt Axiom.2D.postScript:\ \it filename}] \ \newline
+This specifies
+%-% \HDindex{graphics!.Xdefaults!PostScript file name}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+the name of the file that is generated when a 2D PostScript graph
+%-% \HDindex{PostScript}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+is saved.
+\xdefault{axiom2D.ps}
+%
+\item[{\tt Axiom.3D.postScript:\ \it filename}] \ \newline
+This specifies
+%-% \HDindex{graphics!.Xdefaults!PostScript file name}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+the name of the file that is generated when a 3D PostScript graph
+%-% \HDindex{PostScript}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+is saved.
+\xdefault{axiom3D.ps}
+%
+\item[{\tt Axiom*titleFont \it font}] \ \newline
+This
+%-% \HDindex{graphics!.Xdefaults!title font}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+indicates which font type is used
+for the title text and, for \threedim{} graphs,
+in the lighting and viewing-volume control-panel windows.
+%-% \HDindex{graphics!Xdefaults!2d}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+\xdefault{Rom14}
+%
+\item[{\tt Axiom.2D.unitFont:\ \it font}] \quad (2D only) \newline
+This indicates
+%-% \HDindex{graphics!.Xdefaults!unit label font}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+which font type is used for displaying the unit labels on
+\twodim{} viewport graphs.
+\xdefault{6x10}
+%
+\item[{\tt Axiom.3D.volumeFont:\ \it font}] \quad (3D only) \newline
+This indicates which font type is used for the {\bf x},
+%-% \HDindex{graphics!.Xdefaults!volume label font}{ugXdefaultsPage}{7.2.11.}{Customization using .Xdefaults}
+{\bf y}, and {\bf z} labels of the clipping region sliders; for the
+{\bf Perspective}, {\bf Show Region}, and {\bf Clipping On} buttons under
+{\bf Settings}, and above the windows for the {\bf Hither} and
+{\bf Eye Distance} sliders in the {\bf Viewing Volume Panel} of the
+\threedim{} control-panel.
+\xdefault{Rom8}
+\enditems
+\indent{0}
+\endscroll
+\autobuttons
+\end{page}
+%