7 Graphics
This chapter shows how to use the Axiom graphics facilities graphics under the X Window System. Axiom has two-dimensional and three-dimensional drawing and rendering packages that allow the drawing, coloring, transforming, mapping, clipping, and combining of graphic output from Axiom 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 viewport control-panel that uses interactive mouse commands. PostScript and other output forms are available so that Axiom PostScript images can be printed or used by other programs.
7.1 Two-Dimensional Graphics
The Axiom two-dimensional graphics package provides the ability to graphics:two-dimensional display
- curves defined by functions of a single real variable
- curves defined by parametric equations
- implicit non-singular curves defined by polynomial equations
- planar graphs generated from lists of point components.
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.
7.1.1 Plotting Two-Dimensional Functions of One Variable
curve:one variable function The first kind of two-dimensional graph is that of a curve defined by a function over a finite interval of the axis.
The general format for drawing a function defined by a formula is:
draw(f(x), x = a..b, options)
where defines the range of , and where options
prescribes zero or more options as described in
ugGraphTwoDOptions . An
example of an option is An alternative
format involving functions and is also available.
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, ), followed by an ``='', and the range of values.
Display this formula over the range . Axiom converts your formula to a compiled function so that the results can be computed quickly and efficiently.
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.
This time we first define the function.
To draw the function, the first argument is its name and the second is just the range with no independent variable.
7.1.2 Plotting Two-Dimensional Parametric Plane Curves
The second kind of two-dimensional graph is that of parametric plane curve curves produced by parametric equations. curve:parametric plane Let and be formulas or two functions and as the parameter ranges over an interval . The function curve takes the two functions and as its parameters.
The general format for drawing a two-dimensional plane curve defined by parametric formulas and is:
draw(curve(f(t), g(t)), t = a..b, options)
where defines the range of the independent variable , and where options prescribes zero or more options as described in ugGraphThreeDOptions . An example of an option is
Here's an example:
Define a parametric curve using a range involving , Axiom's way of saying . For parametric curves, Axiom compiles two functions, one for each of the functions and .
The title may be an arbitrary string and is an optional argument to the draw command.
If you plan on plotting , as ranges over several intervals, you may want to define functions and first, so that they need not be recompiled every time you create a new graph. Here's an example:
As before, you can first define the functions you wish to draw.
Function declaration f : DoubleFloat -> DoubleFloat has been
added to workspace.
Axiom compiles them to map DoubleFloat values to DoubleFloat values.
Function declaration f : DoubleFloat -> DoubleFloat has been added
to workspace.
Give to curve the names of the functions, then write the range without the name of the independent variable.
Here is another look at the same curve but over a different range. Notice that and are not recompiled. Also note that Axiom provides a default title based on the first function specified in curve.
7.1.3 Plotting Plane Algebraic Curves
A third kind of two-dimensional graph is a non-singular ``solution curve'' curve:plane algebraic in a rectangular region of the plane. A solution curve is a curve defined by a polynomial equation . plane algebraic curve 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 on the curve, that is, a point such that , the partial derivatives and are not both zero. curve:smooth curve:non-singular smooth curve non-singular curve
The general format for drawing a non-singular solution curve given by a polynomial of the form is:
draw(p(x,y) = 0, x, y, range == [a..b, c..d], options)
where the second and third arguments name the first and second
independent variables of . A range option is always given to
designate a bounding rectangular region of the plane
.
Zero or more additional options as described in
ugGraphTwoDOptions may be given.
We require that the polynomial has rational or integral coefficients. Here is an algebraic curve example (``Cartesian ovals''): Cartesian:ovals
The first argument is always expressed as an equation of the form where is a polynomial.
7.1.4 Two-Dimensional Options
The draw commands take an optional list of options, such as title shown above. Each option is given by the syntax: name == value. Here is a list of the available options in the order that they are described below.
| adaptive | clip | unit |
| clip | curveColor | range |
| toScale | pointColor | coordinates |
The option turns adaptive plotting on or off. adaptive plotting 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. graphics:2D options:adaptive
The adaptive option is normally on. Here we turn it off.
The clip option turns clipping on or off. graphics:2D options:clipping If on, large values are cut off according to clipPointsDefaultclipPointsDefaultGraphicsDefaults.
Option toScale does plotting to scale if true or uses the entire viewport if false. The default can be determined using drawToScaledrawToScaleGraphicsDefaults. graphics:2D options:to scale
Option clip with a range sets point clipping of a graph within the graphics:2D options:clip in a range ranges specified in the list . clipping If only one range is specified, clipping applies to the y-axis.
Option curveColor sets the color of the graph curves or lines to be the graphics:2D options:curve color indicated palette color curve:color (see ugGraphColor and ugGraphColorPalette ). color:curve
Option pointColor sets the color of the graph points to the indicated graphics:2D options:point color palette color (see ugGraphColor and ugGraphColorPalette ). color:point
Option unit sets the intervals at which the axis units are plotted graphics:2D options:set units according to the indicated steps [ interval, interval].
Option range sets the range of variables in a graph to be within the ranges graphics:2D options:range for solving plane algebraic curve plots.
A second example of a solution plot.
Option indicates the coordinate system in which the graph graphics:2D options:coordinates is plotted. The default is to use the Cartesian coordinate system. Cartesian:coordinate system For more details, see ugGraphCoord or CoordinateSystems. coordinate system:Cartesian
7.1.5 Color
The domain Color Color provides operations for manipulating graphics:color colors in two-dimensional graphs. color Colors are objects of Color. Each color has a hue and a weight. hue Hues are represented by integers that range from to the numberOfHues()numberOfHues()Color, normally graphics:color:number of hues . weight Weights are floats and have the value by default.
- color (integer)
- creates a color of hue integer and weight .
- hue (color)
- returns the hue of color as an integer. graphics:color:hue function
- red ()
- blue(), green(), and yellow() graphics:color:primary color functions create colors of that hue with weight .
- +
- returns the color that results from additively combining the indicated and . Color addition is not commutative: changing the order of the arguments produces different results.
- integer * color
- changes the weight of color by integer without affecting its hue. graphics:color:multiply function For example, produces a color closer to yellow than to red. Color multiplication is not associative: changing the order of grouping color:multiplication produces different results.
These functions can be used to change the point and curve colors for two- and three-dimensional graphs. Use the pointColor option for points.
Use the curveColor option for curves.
7.1.6 Palette
Domain Palette is the domain of shades of colors: dark, dim, bright, pastel, and light, designated by the integers through , respectively. Palette
Colors are normally ``bright.''
To change the shade of a color, apply the name of a shade to it. color:shade shade
The expression returns the value of a shade of .
The expression returns its hue.
Palettes can be used in specifying colors in two-dimensional graphs.
7.1.7 Two-Dimensional Control-Panel
graphics:2D 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.
7.1.7.1 Transformations
graphics:2D control-panel:transformations
Object transformations are executed from the control-panel by mouse-activated potentiometer windows.
- Scale:
- To scale a graph, click on a mouse button graphics:2D control-panel:scale within the 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 X On and Y On appearing, both axes are selected and scaling is uniform. If either is not selected, for example, if X Off appears, scaling is non-uniform.
- Translate:
- To translate a graph, click the mouse in the graphics:2D control-panel:translate 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 Translate window are two buttons for selecting the direction of translation. Translation along both coordinate axes results when X On and Y On appear or along one axis when one is on, for example, X On and Y Off appear.
7.1.7.2 Messages
graphics:2D control-panel:messages
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:
[scaleX, scaleY] graph [translateX, translateY]
The two values to the left show the scale factor along the X and Y coordinate axes. The two values to the right show the distance of translation from the center in the X and 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.
7.1.7.3 Multiple Graphs
graphics:2D control-panel:multiple graphs The Graphs window contains buttons that allow the placement of two-dimensional graphs into one of nine available slots in any other two-dimensional 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.
- Clear:
- The Clear button deselects every viewport graph slot. graphics:2D control-panel:clear A graph slot is reselected by selecting the button below its number.
- Query:
- The Query button is used to display the scale and graphics:2D control-panel:query 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 Graphs window. The scaling factor and translation offset of the graph are then displayed in the message window.
- Pick:
- The Pick button is used to select a graph graphics:2D control-panel:pick 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 Drop in some other graph.
- Drop:
- Once a graph has been picked up using the Pick button, graphics:2D control-panel:drop the Drop button places it into a new viewport slot. The message ``Click on the graph to drop'' appears in the message window when the Drop button is selected. By selecting one of the slot number buttons in the Graphs window, the graph currently being held is dropped into this slot and displayed.
7.1.7.4 Buttons
graphics:2D control-panel:buttons
- Axes
- turns the coordinate axes on or off. graphics:2D control-panel:axes
- Units
- turns the units along the x and y axis on or off. graphics:2D control-panel:units
- Box
- encloses the area of the viewport graph in a bounding box, or removes the box if already enclosed. graphics:2D control-panel:box
- Pts
- turns on or off the display of points. graphics:2D control-panel:points
- Lines
- turns on or off the display of lines connecting points. graphics:2D control-panel:lines
- PS
- writes the current viewport contents to graphics:2D control-panel:ps a file axiom2D.ps or to a name specified in the user's graphics:.Xdefaults:PostScript file name .Xdefaults file. file:.Xdefaults @ .Xdefaults The file is placed in the directory from which Axiom or the viewAlone program was invoked. PostScript
- Reset
- resets the object transformation characteristics and attributes back to their initial states. graphics:2D control-panel:reset
- Hide
- makes the control-panel disappear. graphics:2D control-panel:hide
- Quit
- queries whether the current viewport graphics:2D control-panel:quit session should be terminated.
7.1.8 Operations for Two-Dimensional Graphics
Here is a summary of useful Axiom operations for two-dimensional 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, integer). If appropriate, a default value for an argument is given in parentheses immediately following the name.
- adaptive ([boolean(true)])
- adaptive plotting sets or indicates whether graphs are plotted graphics:set 2D defaults:adaptive according to the adaptive refinement algorithm.
- axesColorDefault ([color(dark blue())])
- sets or indicates the default color of the graphics:set 2D defaults:axes color axes in a two-dimensional graph viewport.
- clipPointsDefault ([boolean(false)])
- sets or indicates whether point clipping is graphics:set 2D defaults:clip points to be applied as the default for graph plots.
- drawToScale ([boolean(false)])
- sets or indicates whether the plot of a graph graphics:set 2D defaults:to scale is ``to scale'' or uses the entire viewport space as the default.
- lineColorDefault ([color(pastel yellow())])
- sets or indicates the default color of the graphics:set 2D defaults:line color lines or curves in a two-dimensional graph viewport.
- maxPoints ([integer(500)])
- sets or indicates the default maximum number of graphics:set 2D defaults:max points possible points to be used when constructing a two-dimensional graph.
- minPoints ([integer(21)])
- sets or indicates the default minimum number of graphics:set 2D defaults:min points possible points to be used when constructing a two-dimensional graph.
- pointColorDefault ([color(bright red())])
- sets or indicates the default color of the graphics:set 2D defaults:point color points in a two-dimensional graph viewport.
- pointSizeDefault ([integer(5)])
- sets or indicates the default size of the graphics:set 2D defaults:point size dot used to plot points in a two-dimensional graph.
- screenResolution ([integer(600)])
- sets or indicates the default screen graphics:set 2D defaults:screen resolution resolution constant used in setting the computation limit of adaptively adaptive plotting generated curve plots.
- unitsColorDefault ([color(dim green())])
- sets or indicates the default color of the graphics:set 2D defaults:units color unit labels in a two-dimensional graph viewport.
- viewDefaults ()
- resets the default settings for the following graphics:set 2D defaults:reset viewport attributes: point color, line color, axes color, units color, point size, viewport upper left-hand corner position, and the viewport size.
- viewPosDefault ([list([100,100])])
- sets or indicates the default position of the graphics:set 2D defaults:viewport position upper left-hand corner of a two-dimensional viewport, relative to the display root window. The upper left-hand corner of the display is considered to be at the (0, 0) position.
- viewSizeDefault ([list([200,200])])
- sets or indicates the default size in which two graphics:set 2D defaults:viewport size dimensional viewport windows are shown. It is defined by a width and then a height.
- viewWriteAvailable ([list(["pixmap","bitmap", "postscript", "image"])])
- indicates the possible file types graphics:2D defaults:available viewport writes that can be created with the writewriteTwoDimensionalViewport function.
- viewWriteDefault ([list([])])
- sets or indicates the default types of files, in graphics:set 2D defaults:write viewport addition to the data file, that are created when a write function is executed on a viewport.
- units (viewport, integer(1), string("off"))
- turns the units on or off for the graph with index integer.
- axes (viewport, integer(1), string("on"))
- turns the axes on graphics:2D commands:axes or off for the graph with index integer.
- close (viewport)
- closes viewport. graphics:2D commands:close
- connect (viewport, integer(1), string("on"))
- declares whether lines graphics:2D commands:connect connecting the points are displayed or not.
- controlPanel (viewport, string("off"))
- declares whether the two-dimensional control-panel is automatically displayed or not.
- graphs (viewport)
- returns a list graphics:2D commands:graphs describing the state of each graph. If the graph state is not being used this is shown by "undefined", otherwise a description of the graph's contents is shown.
- graphStates (viewport)
- displays graphics:2D commands:state of graphs a list of all the graph states available for viewport, giving the values for every property.
- key (viewport)
- returns the process graphics:2D commands:key ID number for viewport.
- move (viewport, (viewPosDefault), (viewPosDefault))
- moves viewport on the screen so that the graphics:2D commands:move upper left-hand corner of viewport is at the position (x,y).
- options (viewport)
- returns a list graphics:2D commands:options of all the DrawOptions used by viewport.
- points (viewport, integer(1), string("on"))
- specifies whether the graph points for graph integer are graphics:2D commands:points to be displayed or not.
- region (viewport, integer(1), string("off"))
- declares whether graph integer is or is not to be displayed with a bounding rectangle.
- reset (viewport)
- resets all the properties of viewport.
- resize (viewport, , )
- graphics:2D commands:resize resizes viewport with a new width and height.
- scale (viewport, (1), (0.9), (0.9))
- scales values for the graphics:2D commands:scale x and y coordinates of graph n.
- show (viewport, (1), string("on"))
- indicates if graph n is shown or not.
- title (viewport, string("Axiom 2D"))
- designates the title for viewport.
- translate (viewport, (1), (0.0), (0.0))
- graphics:2D commands:translate causes graph n to be moved x and y units in the respective directions.
- write (viewport, , [strings])
- if no third argument is given, writes the data file onto the directory with extension data. The third argument can be a single string or a list of strings with some or all the entries "pixmap", "bitmap", "postscript", and "image".
7.1.9 Addendum: Building Two-Dimensional Graphs
In this section we demonstrate how to create two-dimensional graphs from lists of points and give an example showing how to read the lists of points from a file.
7.1.9.1 Creating a Two-Dimensional Viewport from a List of Points
Axiom creates lists of points in a two-dimensional viewport by utilizing the GraphImage and TwoDimensionalViewport domains. In this example, the makeGraphImagemakeGraphImageGraphImage 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.
The following expressions create a list of lists of points which will be read by Axiom and made into a two-dimensional viewport.
Finally, here is the list.
Now we set the point sizes for all components of the graph.
Here are the colors for the points.
Here are the colors for the lines.
Now the GraphImage is created according to the component specifications indicated above.
The makeViewport2DmakeViewport2DTwoDimensionalViewport function now creates a TwoDimensionalViewport for this graph according to the list of options specified within the brackets.
This example demonstrates the use of the GraphImage functions componentcomponentGraphImage and appendPointappendPointGraphImage in adding points to an empty GraphImage.
Here is the graph.
A list of points can also be made into a GraphImage by using the operation coercecoerceGraphImage. It is equivalent to adding each point to using componentcomponentGraphImage.
Now, create an empty TwoDimensionalViewport.
Place the graph into the viewport.
Take a look.
7.1.9.2 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, DoubleFloat values) as an alternating stream of - and -values. For example,
0.0 0.0 1.0 1.0 2.0 4.0
3.0 9.0 4.0 16.0 5.0 25.0
drawPoints(lp:List Point DoubleFloat):VIEW2D ==
g := graphImage()$GRIMAGE
for p in lp repeat
component(g,p,pointColorDefault(),lineColorDefault(),
pointSizeDefault())
gi := makeGraphImage(g)$GRIMAGE
makeViewport2D(gi,[title("Points")])$VIEW2D
drawLines(lp:List Point DoubleFloat):VIEW2D ==
g := graphImage()$GRIMAGE
component(g, lp, pointColorDefault(), lineColorDefault(),
pointSizeDefault())$GRIMAGE
gi := makeGraphImage(g)$GRIMAGE
makeViewport2D(gi,[title("Points")])$VIEW2D
plotData2D(name, title) ==
f:File(DFLOAT) := open(name,"input")
lp:LIST(Point DFLOAT) := empty()
while ((x := readIfCan!(f)) case DFLOAT) repeat
y : DFLOAT := read!(f)
lp := cons(point [x,y]$(Point DFLOAT), lp)
lp
close!(f)
drawPoints(lp)
drawLines(lp)
This command will actually create the viewport and the graph if the point data is in the file .
plotData2D("file.data", "2D Data Plot")
7.1.10 Addendum: Appending a Graph to a Viewport Window Containing a Graph
This section demonstrates how to append a two-dimensional graph to a viewport already containing other graphs. The default draw command places a graph into the first GraphImage slot position of the TwoDimensionalViewport.
This graph is in the first slot in its viewport.
So is this graph.
The operation getGraphgetGraphTwoDimensionalViewport retrieves the GraphImage from the first slot position in the viewport .
Now putGraphputGraphTwoDimensionalViewport places into the the second slot position of .
Display the new TwoDimensionalViewport containing both graphs.
7.2 Three-Dimensional Graphics
The Axiom three-dimensional graphics package provides the ability to graphics:three-dimensional
- generate surfaces defined by a function of two real variables
- generate space curves and tubes defined by parametric equations
- generate surfaces defined by parametric equations
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.
7.2.1 Plotting Three-Dimensional Functions of Two Variables
surface:two variable function The simplest three-dimensional graph is that of a surface defined by a function of two variables, .
The general format for drawing a surface defined by a formula of two variables and is:
draw(f(x,y), x = a..b, y = c..d, options)
where and define the range of
and , and where options prescribes zero or more
options as described in ugGraphThreeDOptions
.
An example of an option is
An alternative format involving a function is also
available.
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 = sign.
If you intend to use a function more than once, or it is long and complex, then first give its definition to Axiom.
To draw the function, just give its name and drop the variables from the range specifications. Axiom compiles your function for efficient computation of data for the graph. Notice that Axiom uses the text of your function as a default title.
7.2.2 Plotting Three-Dimensional Parametric Space Curves
A second kind of three-dimensional graph is a three-dimensional space curve curve:parametric space defined by the parametric equations for , , parametric space curve and as a function of an independent variable .
The general format for drawing a three-dimensional space curve defined by parametric formulas , , and is:
draw(curve(f(t),g(t),h(t)), t = a..b, options)
where defines the range of the independent variable
, and where options prescribes zero or more options
as described in ugGraphThreeDOptions
.
An example of an option is
An alternative format involving functions , and
is also available.
If you use explicit formulas to draw a space curve, always precede the range specification with the variable name and an = sign.
Alternatively, you can draw space curves by referring to functions.
Function declaration i1 : DoubleFloat -> DoubleFloat has been added
to workspace.
This is useful if the functions are to be used more than once ...
Function declaration i2 : DoubleFloat -> DoubleFloat has been added
to workspace.
or if the functions are long and complex.
Function declaration i3 : DoubleFloat -> DoubleFloat has been added
to workspace.
Give the names of the functions and drop the variable name specification in the second argument. Again, Axiom supplies a default title.
7.2.3 Plotting Three-Dimensional Parametric Surfaces
surface:parametric A third kind of three-dimensional graph is a surface defined by parametric surface parametric equations for , , and of two independent variables and .
The general format for drawing a three-dimensional graph defined by parametric formulas , , and is:
draw(surface(f(u,v),g(u,v),h(u,v)), u = a..b, v = c..d, options)
where and define the range of the
independent variables and , and where
options prescribes zero or more options as described in
ugGraphThreeDOptions .
An example of an option is
An alternative format involving functions , and
is also available.
This example draws a graph of a surface plotted using the parabolic cylindrical coordinate system option. coordinate system:parabolic cylindrical The values of the functions supplied to surface are parabolic cylindrical coordinate system interpreted in coordinates as given by a coordinates option, here as parabolic cylindrical coordinates (see ugGraphCoord ).
Again, you can graph these parametric surfaces using functions, if the functions are long and complex.
Here we declare the types of arguments and values to be of type DoubleFloat.
Function declaration n1 : DoubleFloat -> DoubleFloat has been added
to workspace.
As shown by previous examples, these declarations are necessary.
Function declaration n2 : DoubleFloat -> DoubleFloat has been added
to workspace.
In either case, Axiom compiles the functions when needed to graph a result.
Function declaration n3 : DoubleFloat -> DoubleFloat has been added
to workspace.
Without these declarations, you have to suffix floats with to get a DoubleFloat result. However, a call here with an unadorned float produces a DoubleFloat.
Compiling function n3 with type (DoubleFloat,DoubleFloat) ->
DoubleFloat
Draw the surface by referencing the function names, this time choosing the toroidal coordinate system. coordinate system:toroidal toroidal coordinate system
7.2.4 Three-Dimensional Options
graphics:3D options The draw commands optionally take an optional list of options such as coordinates as shown in the last example. Each option is given by the syntax: == . Here is a list of the available options in the order that they are described below:
| title | coordinates | var1Steps |
| style | tubeRadius | var2Steps |
| colorFunction | tubePoints | space |
The option gives your graph a title. graphics:3D options:title
The determines which of four rendering algorithms is used for rendering the graph. The choices are "wireMesh", "solid", "shade", and "smooth".
In all but the wire-mesh style, polygons in a surface or tube plot are normally colored in a graph according to their -coordinate value. Space curves are colored according to their parametric variable value. graphics:3D options:color function To change this, you can give a coloring function. function:coloring The coloring function is sampled across the range of its arguments, then normalized onto the standard Axiom colormap.
A function of one variable makes the color depend on the value of the parametric variable specified for a tube plot.
A function of two variables makes the color depend on the values of the independent variables.
Use the option colorFunction for special coloring.
With a three variable function, the color also depends on the value of the function.
Normally the Cartesian coordinate system is used. Cartesian:coordinate system To change this, use the coordinates option. coordinate system:Cartesian For details, see ugGraphCoord .
Function declaration m : (DoubleFloat,DoubleFloat) -> DoubleFloat
has been added to workspace.
Use the spherical spherical coordinate system coordinate system. coordinate system:spherical
Space curves may be displayed as tubes with polygonal cross sections. tube Two options, tubeRadius and tubePoints, control the size and shape of this cross section.
The tubeRadius option specifies the radius of the tube that tube:radius encircles the specified space curve.
The tubePoints option specifies the number of vertices tube:points in polygon 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.
graphics:3D options:variable steps
Options var1Stepsvar1StepsDrawOption and var2Stepsvar2StepsDrawOption 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).
The space option of a draw command lets you build multiple graphs in three space. To use this option, first create an empty three-space object, then use the space option thereafter. There is no restriction as to the number or kinds of graphs that can be combined this way.
Create an empty three-space object.
Function declaration m : (DoubleFloat,DoubleFloat) -> DoubleFloat
has been added to workspace.
Add a graph to this three-space object. The new graph destructively inserts the graph into .
Add a second graph to .
A three-space object can also be obtained from an existing three-dimensional viewport using the subspacesubspaceThreeSpace command. You can then use makeViewport3D to create a viewport window.
Assign to the three-space object in viewport .
Reset the space component of to the value of .
Create a viewport window from a three-space object.
7.2.5 The makeObject Command
An alternate way to create multiple graphs is to use makeObject. The makeObject command is similar to the draw command, except that it returns a three-space object rather than a ThreeDimensionalViewport. In fact, makeObject is called by the draw command to create the ThreeSpace then makeViewport3DmakeViewport3DThreeDimensionalViewport to create a viewport window.
Function declaration m : (DoubleFloat,DoubleFloat) -> DoubleFloat
has been added to workspace.
Do the last example a new way. First use makeObject to create a three-space object .
Compiling function m with type (DoubleFloat,DoubleFloat) ->
DoubleFloat
Add a second object to .
Compiling function %D with type DoubleFloat -> DoubleFloat
Compiling function %F with type DoubleFloat -> DoubleFloat
Compiling function %H with type DoubleFloat -> DoubleFloat
Create and display a viewport containing .
Note that an undefined ThreeSpace parameter declared in a makeObject or draw command results in an error. Use the create3Spacecreate3SpaceThreeSpace function to define a ThreeSpace, or obtain a ThreeSpace that has been previously generated before including it in a command line.
7.2.6 Building Three-Dimensional Objects From Primitives
Rather than using the draw and makeObject commands, graphics:advanced:build 3D objects you can create three-dimensional graphs from primitives. Operation create3Spacecreate3SpaceThreeSpace creates a three-space object to which points, curves and polygons can be added using the operations from the ThreeSpace domain. The resulting object can then be displayed in a viewport using makeViewport3DmakeViewport3DThreeDimensionalViewport.
Create the empty three-space object .
Objects can be sent to this using the operations exported by the ThreeSpace domain. ThreeSpace The following examples place curves into .
Add these eight curves to the space.
Create and display the viewport using makeViewport3D. Options may also be given but here are displayed as a list with values enclosed in parentheses.
7.2.6.1 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 three-dimensional objects.
Again start with an empty three-space object.
For convenience, give DoubleFloat values and names.
Define the vertices of the cube.
Add the faces of the cube as polygons to the space using a consistent orientation.
Create and display the viewport.
7.2.7 Coordinate System Transformations
graphics:advanced:coordinate systems
The CoordinateSystems package provides coordinate transformation functions that map a given data point from the coordinate system specified into the Cartesian coordinate system. CoordinateSystems The default coordinate system, given a triplet , assumes that , and , that is, reads the coordinates in order.
Function declaration m : (DoubleFloat,DoubleFloat) -> DoubleFloat
has been added to workspace.
Graph plotted in default coordinate system.
The coordinate comes first since the first argument of the draw command gives its values. In general, the coordinate systems Axiom provides, or any that you make up, must provide a map to an triplet in order to be compatible with the coordinatescoordinatesDrawOption DrawOption. DrawOption Here is an example.
Define the identity function.
Function declaration cartesian : Point DoubleFloat -> Point
DoubleFloat has been added to workspace.
Pass as the coordinatescoordinatesDrawOption parameter to the draw command.
What happened? The option coordinates == cartesian directs Axiom to treat the dependent variable defined by as the coordinate. Thus the triplet of values is transformed to coordinates and so we get the graph of .
Here is another example. The cylindricalcylindricalCoordinateSystems transform takes coordinate system:cylindrical input of the form , interprets it in the order cylindrical coordinate system ( , , ) and maps it to the Cartesian coordinates , , in which is the radius, is the angle and is the z-coordinate.
An example using the cylindricalcylindricalCoordinateSystems coordinates for the constant .
Function declaration f : (DoubleFloat,DoubleFloat) -> DoubleFloat
has been added to workspace.
Graph plotted in cylindrical coordinates.
Suppose you would like to specify as a function of and instead of just ? Well, you still can use the cylindrical Axiom transformation but we have to reorder the triplet before passing it to the transformation.
First, let's create a point to work with and call it with some color .
The reordering you want is to 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.
Define a function reorder to reorder the point elements.
Function declaration reorder : Point DoubleFloat -> Point
DoubleFloat has been added to workspace.
The function moves the second and third elements forward but the color does not change.
The function newmap converts our reordered version of the cylindrical coordinate system to the standard Cartesian system.
Function declaration newmap : Point DoubleFloat -> Point DoubleFloat
has been added to workspace.
Graph the same function using the coordinate mapping of the function , so it is now interpreted as :
The CoordinateSystems package exports the following coordinate system operations: bipolar, bipolarCylindrical, cartesian, conical, cylindrical, elliptic, ellipticCylindrical, oblateSpheroidal, parabolic, parabolicCylindrical, paraboloidal, polar, prolateSpheroidal, spherical, and toroidal. Use Browse or the )show system command show to get more information.
7.2.8 Three-Dimensional Clipping
A three-dimensional graph can be explicitly clipped within the draw graphics:advanced:clip command by indicating a minimum and maximum threshold for the clipping given function definition. These thresholds can be defined using the Axiom min and max functions.
gamma(x,y) ==
g := Gamma complex(x,y)
point [x, y, max( min(real g, 4), -4), argument g]
Here is an example that clips the gamma function in order to eliminate the extreme divergence it creates.
7.2.9 Three-Dimensional Control-Panel
graphics:3D 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.
7.2.9.1 Transformations
We recommend you first select the Bounds button while graphics:3D control-panel:transformations executing transformations since the bounding box displayed indicates the object's position as it changes.
- Rotate:
- A rotation transformation occurs by clicking the mouse
graphics:3D control-panel:rotate
within the 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 within the
range of 0 to 2 and the vertical mouse position
to increment or decrement the value of the latitudinal angle
within the range of -
to .
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.
- origin:
- The origin button indicates that the rotation is to occur with respect to the origin of the viewing space, that is indicated by the axes.
- object:
- The 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.
- Scale:
- A scaling transformation occurs by clicking the mouse
graphics:3D control-panel:scale
within the 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.
- uniform:
- Uniform scaling along the x, y and z axes occurs when all the axes buttons are selected.
- 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.
- Translate:
- Translation occurs by indicating with the mouse in the graphics:3D control-panel:translate 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 Translate window are three buttons ( XY, XZ, and 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.
7.2.9.2 Messages
graphics:3D control-panel:messages
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.
7.2.9.3 Colormap
graphics:3D control-panel:color map
Directly below the message window is the colormap range indicator window. colormap The Axiom 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 Smooth mode is selected. At each end of the Colormap are + and - buttons. When clicked on, these increment or decrement the top or bottom marker.
7.2.9.4 Buttons
graphics:3D control-panel:buttons
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.
- Wire
- displays surface and tube plots as a graphics:3D control-panel:wire 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.
- Solid
- displays the graph with hidden graphics:3D control-panel:solid 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.
- Shade
- displays the graph with hidden graphics:3D control-panel:shade 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. Phong:illumination model
- Smooth
- displays the graph using a graphics:3D control-panel:smooth 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 Phong:illumination model 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 dithering 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. Phong:smooth shading model 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.
- Bounds
- encloses the entire volume of the viewgraph within a bounding box, or removes the box if previously selected. graphics:3D control-panel:bounds The region that encloses the entire volume of the viewport graph is displayed.
- Axes
- displays Cartesian graphics:3D control-panel:axes coordinate axes of the space, or turns them off if previously selected.
- Outline
- causes graphics:3D control-panel:outline quadrilateral polygons forming the graph surface to be outlined in black when the graph is displayed in Shade mode.
- BW
- converts a color viewport to black and white, or vice-versa. graphics:3D control-panel:bw 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.
- Light
- takes you to a control-panel described below.
- ViewVolume
- takes you to another control-panel as described below. graphics:3D control-panel:save
- Save
- creates a menu of the possible file types that can be written using the control-panel. The Exit button leaves the save menu. The Pixmap button writes an Axiom pixmap of graphics:3D control-panel:pixmap the current viewport contents. The file is called axiom3D.pixmap and is located in the directory from which Axiom or viewAlone was started. The PS button writes the current viewport contents to graphics:3D control-panel:ps PostScript output rather than to the viewport window. By default the file is called axiom3D.ps; however, if a file file:.Xdefaults @ .Xdefaults name is specified in the user's .Xdefaults file it is graphics:.Xdefaults:PostScript file name used. The file is placed in the directory from which the Axiom or viewAlone session was begun. See also the writewriteThreeDimensionalViewport function. PostScript
- Reset
- returns the object transformation graphics:3D control-panel:reset characteristics back to their initial states.
- Hide
- causes the control-panel for the graphics:3D control-panel:hide corresponding viewport to disappear from the screen.
- Quit
- queries whether the current viewport graphics:3D control-panel:quit session should be terminated.
7.2.9.5 Light
graphics:3D control-panel:light
The Light button changes the control-panel into the 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 Abort button that cancels any changes to the lighting that were made, and a Return button that carries out the current set of lighting changes on the graph.
- XY:
- The XY lighting axes window is below the graphics:3D control-panel:move xy Lighting Control-Panel title and to the left. This changes the light vector within the XY view plane.
- Z:
- The Z lighting axis window is below the graphics:3D control-panel:move z Lighting Control-Panel title and in the center. This changes the Z location of the light vector.
- Intensity:
- Below the Lighting Control-Panel title graphics:3D control-panel:intensity 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.
7.2.9.6 View Volume
graphics:3D control-panel:view volume
The View Volume button changes the control-panel into the Viewing Volume Panel. At the bottom of the viewing panel is an Abort button that cancels any changes to the viewing volume that were made and a Return button that carries out the current set of viewing changes to the graph.
- Eye Reference:
- At the top of this panel is the graphics:3D control-panel:eye reference 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 Hither window. By moving the slider in this window the hither clipping plane sets hither clipping plane 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 Eye Distance slider to the right of the Hither slider is used to change the degree of perspective in the image.
- Clip Volume:
- The Clip Volume window is at the graphics:3D control-panel:clip volume bottom of the Viewing Volume Panel. On the right is a Settings menu. In this menu are buttons to select viewing attributes. Selecting the Perspective button computes the image using perspective projection. graphics:3D control-panel:perspective The Show Region button indicates whether the clipping region of the graphics:3D control-panel:show clip region volume is to be drawn in the viewport and the Clipping On button shows whether the view volume clipping is to be in effect when the image graphics:3D control-panel:clipping on is drawn. The left side of the Clip Volume window shows the clipping graphics:3D control-panel:clip volume boundary of the graph. Moving the knobs along the X, Y, and Z sliders adjusts the volume of the clipping region accordingly.
7.2.10 Operations for Three-Dimensional Graphics
Here is a summary of useful Axiom operations for three-dimensional 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, integer). If appropriate, a default value for an argument is given in parentheses immediately following the name.
- adaptive3D? ()
- tests whether space curves are to be plotted graphics:plot3d defaults:adaptive according to the adaptive plotting adaptive refinement algorithm.
- axes (viewport, string("on"))
- turns the axes on and off. graphics:3D commands:axes
- close (viewport)
- closes the viewport. graphics:3D commands:close
- colorDef (viewport, (1), (27))
- sets the colormap graphics:3D commands:define color range to be from to .
- controlPanel (viewport, string("off"))
- declares whether the graphics:3D commands:control-panel control-panel for the viewport is to be displayed or not.
- diagonals (viewport, string("off"))
- declares whether the graphics:3D commands:diagonals polygon outline includes the diagonals or not.
- drawStyle (viewport, style)
- selects which of four drawing styles graphics:3D commands:drawing style are used: "wireMesh", "solid", "shade", or "smooth".
- eyeDistance (viewport,float(500))
- sets the distance of the eye from the origin of the object graphics:3D commands:eye distance for use in the perspectiveperspectiveThreeDimensionalViewport.
- key (viewport)
- returns the operating graphics:3D commands:key system process ID number for the viewport.
- lighting (viewport, (-0.5), (0.5), (0.5))
- sets the Cartesian graphics:3D commands:lighting coordinates of the light source.
- modifyPointData (viewport,integer,point)
- replaces the coordinates of the point with graphics:3D commands:modify point data the index integer with point.
- move (viewport, (viewPosDefault), (viewPosDefault))
- moves the upper graphics:3D commands:move left-hand corner of the viewport to screen position ({ , }).
- options (viewport)
- returns a list of all current draw options.
- outlineRender (viewport, string("off"))
- turns polygon outlining graphics:3D commands:outline off or on when drawing in "shade" mode.
- perspective (viewport, string("on"))
- turns perspective graphics:3D commands:perspective viewing on and off.
- reset (viewport)
- resets the attributes of a viewport to their graphics:3D commands:reset initial settings.
- resize (viewport, (viewSizeDefault), (viewSizeDefault))
- resets the width and height graphics:3D commands:resize values for a viewport.
- rotate (viewport, (viewThetaDefapult), (viewPhiDefault))
- rotates the viewport by rotation angles for longitude ( ) and latitude ( ). Angles designate radians if given as floats, or degrees if given graphics:3D commands:rotate as integers.
- setAdaptive3D (boolean(true))
- sets whether space curves are to be plotted graphics:plot3d defaults:set adaptive according to the adaptive adaptive plotting refinement algorithm.
- setMaxPoints3D (integer(1000))
- sets the default maximum number of possible graphics:plot3d defaults:set max points points to be used when constructing a three-dimensional space curve.
- setMinPoints3D (integer(49))
- sets the default minimum number of possible graphics:plot3d defaults:set min points points to be used when constructing a three-dimensional space curve.
- setScreenResolution3D (integer(49))
- sets the default screen resolution constant graphics:plot3d defaults:set screen resolution used in setting the computation limit of adaptively adaptive plotting generated three-dimensional space curve plots.
- showRegion (viewport, string("off"))
- declares whether the bounding graphics:3D commands:showRegion box of a graph is shown or not.
- subspace (viewport)
- returns the space component.
- subspace (viewport, subspace)
- resets the space component graphics:3D commands:subspace to subspace.
- title (viewport, string)
- gives the viewport the graphics:3D commands:title title string.
- translate (viewport, (viewDeltaXDefault), (viewDeltaYDefault))
- translates graphics:3D commands:translate the object horizontally and vertically relative to the center of the viewport.
- intensity (viewport,float(1.0))
- resets the intensity I of the light source, graphics:3D commands:intensity
- tubePointsDefault ([integer(6)])
- sets or indicates the default number of graphics:3D defaults:tube points vertices defining the polygon that is used to create a tube around a space curve.
- tubeRadiusDefault ([float(0.5)])
- sets or indicates the default radius of graphics:3D defaults:tube radius the tube that encircles a space curve.
- var1StepsDefault ([integer(27)])
- sets or indicates the default number of graphics:3D defaults:var1 steps increments into which the grid defining a surface plot is subdivided with respect to the first parameter declared in the surface function.
- var2StepsDefault ([integer(27)])
- sets or indicates the default number of graphics:3D defaults:var2 steps increments into which the grid defining a surface plot is subdivided with respect to the second parameter declared in the surface function.
- viewDefaults ([ , , , , , , ])
- resets the default settings for the graphics:3D defaults:reset viewport defaults point color, line color, axes color, units color, point size, viewport upper left-hand corner position, and the viewport size.
- viewDeltaXDefault ([float(0)])
- resets the default horizontal offset graphics:3D commands:deltaX default from the center of the viewport, or returns the current default offset if no argument is given.
- viewDeltaYDefault ([float(0)])
- resets the default vertical offset graphics:3D commands:deltaY default from the center of the viewport, or returns the current default offset if no argument is given.
- viewPhiDefault ([float(- /4)])
- resets the default latitudinal view angle, or returns the current default angle if no argument is given. graphics:3D commands:phi default is set to this value.
- viewpoint (viewport, , , )
- sets the viewing position in Cartesian coordinates.
- viewpoint (viewport, , )
- sets the viewing position in spherical coordinates.
- viewpoint (viewport, , , , , )
- sets the viewing position in spherical coordinates, the scale factor, and offsets. graphics:3D commands:viewpoint (longitude) and (latitude) are in radians.
- viewPosDefault ([list([0,0])])
- sets or indicates the position of the upper graphics:3D defaults:viewport position left-hand corner of a two-dimensional viewport, relative to the display root window (the upper left-hand corner of the display is ).
- viewSizeDefault ([list([400,400])])
- sets or indicates the width and height dimensions graphics:3D defaults:viewport size of a viewport.
- viewThetaDefault ([float( /4)])
- resets the default longitudinal view angle, or returns the current default angle if no argument is given. graphics:3D commands:theta default When a parameter is specified, the default longitudinal view angle is set to this value.
- viewWriteAvailable ([list(["pixmap", "bitmap", "postscript", "image"])])
- indicates the possible file types graphics:3D defaults:available viewport writes that can be created with the writewriteThreeDimensionalViewport function.
- viewWriteDefault ([list([])])
- sets or indicates the default types of files that are created in addition to the data file when a writewriteThreeDimensionalViewport command graphics:3D defaults:viewport writes is executed on a viewport.
- viewScaleDefault ([float])
- sets the default scaling factor, or returns graphics:3D commands:scale default the current factor if no argument is given.
- write (viewport, directory, [option])
- writes the file data for viewport in the directory directory. An optional third argument specifies a file type (one of pixmap, bitmap, postscript, or image), or a list of file types. An additional file is written for each file type listed.
- scale (viewport, float(2.5))
- specifies the scaling factor. graphics:3D commands:scale scaling graphs
7.2.11 Customization using .Xdefaults
Both the two-dimensional and three-dimensional drawing facilities consult the .Xdefaults file for various defaults. file:.Xdefaults @ .Xdefaults The list of defaults that are recognized by the graphing routines is discussed in this section. These defaults are preceded by Axiom.3D. for three-dimensional viewport defaults, Axiom.2D. for two-dimensional viewport defaults, or Axiom* (no dot) for those defaults that are acceptable to either viewport type.
- Axiom*buttonFont: font
-
This indicates which graphics:.Xdefaults:button font font type is used for the button text on the control-panel. Rom11 - Axiom.2D.graphFont: font
- (2D only)
This indicates graphics:.Xdefaults:graph number font which font type is used for displaying the graph numbers and slots in the Graphs section of the two-dimensional control-panel. Rom22 - Axiom.3D.headerFont: font
-
This indicates which graphics:.Xdefaults:graph label font font type is used for the axes labels and potentiometer header names on three-dimensional viewport windows. This is also used for two-dimensional control-panels for indicating which font type is used for potentionmeter header names and multiple graph title headers. Itl14 - Axiom*inverse: switch
-
This indicates whether the graphics:.Xdefaults:inverting background background color is to be inverted from white to black. If on, the graph viewports use black as the background color. If off or no declaration is made, the graph viewports use a white background. off - Axiom.3D.lightingFont: font
- (3D only)
This indicates which font type is used for the x, graphics:.Xdefaults:lighting font y, and z labels of the two lighting axes potentiometers, and for the Intensity title on the lighting control-panel. Rom10 - Axiom.2D.messageFont, Axiom.3D.messageFont: font
-
These indicate the font type graphics:.Xdefaults:message font to be used for the text in the control-panel message window. Rom14 - Axiom*monochrome: switch
-
This indicates whether the graphics:.Xdefaults:monochrome graph viewports are to be displayed as if the monitor is black and white, that is, a 1 bit plane. If on is specified, the viewport display is black and white. If off is specified, or no declaration for this default is given, the viewports are displayed in the normal fashion for the monitor in use. off - Axiom.2D.postScript: filename
-
This specifies graphics:.Xdefaults:PostScript file name the name of the file that is generated when a 2D PostScript graph PostScript is saved. axiom2D.ps - Axiom.3D.postScript: filename
-
This specifies graphics:.Xdefaults:PostScript file name the name of the file that is generated when a 3D PostScript graph PostScript is saved. axiom3D.ps - Axiom*titleFont font
-
This graphics:.Xdefaults:title font indicates which font type is used for the title text and, for three-dimensional graphs, in the lighting and viewing-volume control-panel windows. graphics:Xdefaults:2d Rom14 - Axiom.2D.unitFont: font
- (2D only)
This indicates graphics:.Xdefaults:unit label font which font type is used for displaying the unit labels on two-dimensional viewport graphs. 6x10 - Axiom.3D.volumeFont: font
- (3D only)
This indicates which font type is used for the x, graphics:.Xdefaults:volume label font y, and z labels of the clipping region sliders; for the Perspective, Show Region, and Clipping On buttons under Settings, and above the windows for the Hither and Eye Distance sliders in the Viewing Volume Panel of the three-dimensional control-panel. Rom8