A plot in Maple is a 2-D or 3-D graphical representation of a mathematical object, such as a function or a set of statistical data. Most of this chapter will be assuming a Cartesian coordinate system for this purpose. In general, the horizontal and vertical axes in 2-D plots will be referred to as the $x$ and $y$ axes, respectively, while the axes in 3-D plots will be called the $x$, $y$, and $z$ axes.

The following command generates a 2-D plot of the function $x^3-x^2\+3$ over the range -2 to 2.

The plot command is commonly used to create 2-D plots and it is described in more detail in Generating 2-D and 3-D Plots. There is a corresponding plot3d command for creating 3-D plots. In the previous statement, the three arguments to the plot command are the Maple expression x^3-x^2+3 representing the function to be plotted, an equation specifying the plotting variable and range, and an option indicating that a title be added.

If you are using Standard Interface in Maple, executing the previous statement produces a plot in the current document. You can also create plotting output for other interfaces (for example, plots that open in a different window) and plots that are saved as a graphics file. For more information, see Interfaces and Devices.

The plot and plot3d commands are not the only ways to generate plots. Maple has an extensive library of commands for plotting and related tasks. These are described in The Plot Library. A plot that is generated with a library command is returned as a plot data structure. This is described in the section Data Structures.

Maple also provides interactive ways to create and modify plots, including:

More information about these topics can be found in the Maple User Manual. If you are interested in simply creating a plot to be displayed in a Maple worksheet, then these easy-to-use, interactive methods are recommended. However, if you want to write programs that build and manipulate plots, then it is necessary to be familiar with Maple's plotting library commands.

Plots can also be used as embedded components, which means they are created as graphical interface components that can be manipulated through various actions. For more information, see Programming Interactive Elements

This section describes how to use the plots:-display command to combine plots, or more specifically, plot data structures. Two or more plots can be merged into a single plot or they can be placed side-by-side in a tabular arrangement.

When a plot is generated using any library command, a plot data structure is created. This structure can be assigned to a variable to be reused or modified. A detailed explanation of how the structures are formed is available in Data Structures, but it is not necessary to understand the details in order to manipulate the structures as described here.

Merging Plots

To combine the elements of two or more plots into a single plot, use the plots:-display command, with the plots contained in a list as the first argument. >  sinecurve := plot(sin(x), x=-Pi..Pi): >  maxtext := textplot([Pi/2, 1, "maximum"], 'align'='above'): >  display([sinecurve, maxtext], 'caption'="This plot shows a local maximum of the sin function."); Any combination of plot structures created from arbitrary Maple plotting commands can be combined using the display command, with a some restrictions. Usually, different types of plots (2-D, 3-D, arrays of plots, and animations) cannot be mixed. When plots are merged, their options are also merged if possible. If there is a conflict, the display command will try to resolve it. For example, if two plots with different titles are merged, the display command will arbitrarily choose one for the merged plot. The display command allows additional options to be provided. In the case of global options (ones that apply to the entire plot such as caption), these additional options will override those given for the individual plots. However, local options specified within the plots are generally not overridden. The display command accepts the option insequence=true, which causes the plots to be displayed sequentially in an animation rather than merged. This use of the display command is discussed in Animations.

Generating an Array of Plots

The display command can be used to generate a tabular display of plots by providing a one-dimensional or two-dimensional Array of plot structures as the first argument. An animation plot structure can also be given, in which case the frames of the animation are displayed in tabular form. Unlike the situation where plots are merged, you can mix different types of plots in an array of plots. For example, you can create an array containing both 2-D and 3-D plots. A limited number of options can be passed to this command. Most global plot options are accepted and are applied to each plot in the Array individually. For more information about this feature, including the aligncolumns option that allows you to align the $x$-axes of plots within a column, refer to the plot/arrayplot help page.

In this section, a few commonly used commands for specialty plots are introduced. Refer to the Maple Plotting Guide for a complete list of commands available.

The plots:-implicitplot and plots:-implicitplot3d commands generate plots of implicitly defined curves and surfaces.

The plots:-contourplot command generates a contour plot for an expression in two variables. The plots:-contourplot3d command does the same but generates a 3-D display.

The plots:-polarplot command generates a plot in polar coordinates with polar axes. This command offers a number of options to control the look of the radial and angular axes.

To plot in other coordinate systems, you can use the coords option. However, unlike with the polarplot command, these plots are drawn with Cartesian axes. For a complete list of supported coordinate systems, refer to the coords help page,

The plots:-dualaxisplot command creates a plot with two $y$-axes located at the left and right sides of the plot. You can provide either two expressions or two plot data structures.

The plots:-densityplot command creates a plot of a function of two variables colored by the function value. You can create a grayscale or RGB-colored plot.

The plots:-fieldplot and plots:-fieldplot3d commands generate plots of 2-D or 3-D vector fields.

Many of the plotting commands introduced so far are part of the plots package. Several other packages in Maple also contain visualization commands.

The plottools package includes commands for generating and transforming graphical objects. This package is described in Creating Plot Structures.

The Student package consists of several subpackages designed to assist with the teaching and learning of mathematics. Each Student package has a collection of visualization commands. For example, for Calculus, refer to the Student/Calculus1/VisualizationOverview help page.

The Statistics package contains a large number of commands for visualizing univariate and multivariate data. These are listed in the Statistics/Visualization help page.

As mentioned in Polygons and Polyhedra, geometric objects can be created and displayed with the geometry and geom3d packages.

In the GraphTheory package, directed and undirected graphs can be drawn with the GraphTheory:-DrawGraph command. In addition, the package provides many predefined graphs as well as visualizations of some algorithms.

This first example shows how plotting commands can be combined to create a single plot.

You can make this code more general and reusable by defining a procedure to produce a similar plot given an expression as the first argument, and an equation involving the plotting variable and range as the second argument.

There are a few modifications that can be made to improve derivativeplot, such as error-checking and processing of additional plotting options.

In the derivativeplot procedure, the name=range type is specified for the r parameter, and the type-checking of this argument is done automatically by the built-in parameter processing facilities in Maple. However, it is useful to check for correctness of the first expression. Specifically, derivativeplot should check that the first argument is an expression in one variable and that variable matches the one given in the second argument. For example, the following incorrect call would produce an empty plot.

Many visualization commands in the Maple library that use the basic plotting procedures plot, plot3d, and plots:-display assume that additional arguments are global plot options to be passed along for processing by these commands. In the modified derivativeplot procedure below, the unprocessed arguments in _rest are passed to the display command. For more information on _rest, see Special Sequences for Referring to Parameters and Arguments.

Here is the new derivativeplot procedure.

Notice that the title option in the last derivativeplot call replaces the default title specified within the procedure. The convention followed by many Maple commands is that, when there are duplicate option names in the calling sequence, the last value given is the one that is applied. However, if you added the option color="Green", that would not change the default colors of the two curves. That is because the color="DarkRed" and color="Navy" options have been saved in the plot data structures p1 and p2 as local options, and they will not be overridden by plot options passed to the display command.

The next example defines a procedure that accepts a list of expressions in one variable and displays these as "ribbons" in a 3-D plot.

The following ribbonplot procedure accepts a list of expressions in one variable, an equation containing the variable name and range, and an optional keyword parameter, numberpoints. The numberpoints option specifies the number of points along the ribbon and is set to 25 by default. For brevity, this procedure does not include the error-checking of the list of expressions as for the derivativeplot example.

In the procedure ribbonplot, a Vector is used to store the n plot structures generated by the plot3d command. The grid option is passed to plot3d to specify the number of sample points in each plot direction. As with the previous example, additional global plot options are passed directly to the plots:-display command.

Call ribbonplot with four expressions as the input and using the default options. Then, call it again with more sample points and constrained scaling.

Now, change the ribbonplot procedure so that it accepts input in operator form instead of expression form. Following the convention of the plot and plot3d command, in the modified procedure, the second argument is the plotting range, with no plotting variable specified. In addition, this version of ribbonplot allows a ribboncolors option that lets the user specify the color of each ribbon. If no such option is provided, the ribbons are colored with the default surface shading for 3-D plots.

This procedure contains a check to ensure that the number of ribbon colors is the same as the number of procedures in the list f. Also, each procedure in f must be turned into a procedure with two input parameters before being passed to the plot3d command. In the call to plot3d, the color option is passed only if the ribboncolors option had originally been provided.

This section provides an overview of the major components in plot data structures. Full details are available in the plot/structure help page. Note that some data structure names, those introduced in Maple 10 or later versions, are prefixed with underscores.

Basic Structures

•  PLOT -- 2-D plot. Contains any of the object data structures listed below, except for MESH and ISOSURFACE, followed by any number of 2-D option structures. Can also contain an ANIMATE structure. •  PLOT3D -- 3-D plot. Contains any of the object data structures listed below, followed by any number of 3-D option structures. Can also contain an ANIMATE structure. •  _PLOTARRAY -- Array of plots. Contains a single Matrix, each element of which is a PLOT or PLOT3D structure. •  ANIMATE -- Animation. Contains a sequence of lists, each corresponding to a single frame in the animation and containing object and option structures.

Object Structures

In the following description, $d$ refers to the dimension (2 or 3) of the plot object. A collection of $n$ points in $d$ dimensions is specified as a list of $n$ $d$-element sublists or as an $n$ by $d$ Matrix. Each sublist or Matrix row holds the coordinates of a single point. •  CURVES -- 2-D or 3-D curve(s). Contains one or more collections of points in list or Matrix format as described above. Each collection of points defines a single curve. •  POLYGONS -- 2-D or 3-D polygon(s). Contains one or more collections of points in list or Matrix format, each defining the vertices of a single polygon. •  POINTS -- 2-D or 3-D points. Contains a collection of points in list or Matrix format. •  TEXT -- 2-D or 3-D text object. Contains a point in list format followed by the string or expression to be displayed. •  GRID -- 3-D surface over a regular grid. Contains ranges in the $x$ and $y$ directions, followed by a two-dimensional Array or list of lists containing the grid data. •  MESH -- 3-D surface over an arbitrary grid. Contains the $x$, $y$, and $z$ coordinates corresponding to points over an $m$ by $n$ grid. This data is contained in a three-dimensional Array or in nested lists. •  ISOSURFACE -- 3-D volume of data, which consists of function values over a regular grid. This results in a rendering of a 3-D surface approximating the zero surface of the function. Contains $x$, $y$, $z$, and $f\left(x\,y\,z\right)$ values over an $m$ by $n$ by $k$ grid. The data is contained in a four-dimensional Array or in nested lists. Each object structure may contain one or more local option structures following the required data. For example, the following structure produces two polygons, one blue and one purple. >  PLOT(POLYGONS([[0., 0.], [0., 1.], [1., 1.], [1., 0.]], COLOR(RGB, 0., 0., 1.)), POLYGONS([[1., 1.], [1., 2.], [2., 2.], [2., 1.]], COLOR(RGB, .5, 0., .5)));

Option Structures

There are a large number of option structures, some used for either 2-D plots or 3-D plots only, and some that apply to both. Most of the option structures have a direct correspondence to plot options described on the plot/options and plot3d/option help pages. (Note that the converse is not necessarily true. Several plot options do not have associated option structures.) Here are a few examples. •  The symbol=asterisk option is translated to SYMBOL(_ASTERISK) in the plot data structure. •  The color="Turquoise" option is translated to COLOUR(RGB, 0.25098039, 0.87843137, 0.81568627). •  The title="Another Plot" and titlefont=["Helvetica", 30] options together translate to TITLE("Another plot", FONT("Helvetica", 30)). In The Plot Library, the concept of global options (options that apply to the entire plot) and local options (ones that apply to a particular plot object) was introduced. This concept applies in a similar way to plot structures. Local option structures, such as STYLE or TRANSPARENCY can appear inside one or more plot object structures (CURVES, TEXT, etc.). Global option structures, such as TITLE, appear outside the plot object structures and usually there is only one instance of each kind of structure. Some options, such as COLOR, can appear as a global option as well as a local option. In this situation, the value of the local option is applied to the plot object with which it is associated, and it is not overridden by the global option. If a plot structure has duplicate options at the same level (all global, or all local within the same plot object structure), such as two CAPTION entries, then the last one appearing in the structure is the one that is applied when the plot is rendered. The plots:-display command can be used to merge plot data structures. Details on how option structures are combined are given in Merging Plots. The display command can also be used to add an option structure to an existing plot. In the following example, the display command accepts the thickness=3 plot option and adds THICKNESS(3) to the data structure. >  p := plot(x^2-2*x+1, x=-4..4, 'color'="Niagara DarkOrchid"): >  p; >  plots:-display(p, 'thickness'=3);

Complete plot structures are normally created with commands such as the ones in the plots package. If you want to generate data structures for individual plot objects, it is recommended that you use the commands in the plottools package rather than build them yourself.

The plottools commands do not produce complete plots, so the output will consist of the data structure in text form rather than a rendered image. To view the result of a plottools command, you must pass it to the plots:-display command.

As shown in this example, options may be passed to the plottools commands. These must be local options that are applicable to the type of structure that is produced. The color option applies to any plot object, while the transparency option is used only with plot objects that are rendered as surfaces. The scaling option is a global option that applies to an entire plot; thus, it is included in the call to display instead of the calls to torus and sphere.

In addition to the commands for building plot structures, the plottools package also contains commands for altering structures. These commands, which accept 2-D or 3-D plots as input, include ones for translation, scaling, and rotation of a plot.

You can apply an arbitrary transformation to a 2-D or 3-D plot using the plottools:-transform command. To do this, define a procedure f that represents a mapping $f$ from $R^m$ to $R^n$, where $m$ and $n$ can take values 2 or 3. The procedure must take as input $m$ arguments and return a list of $n$ components. If you pass f to the transform command, it returns a procedure that takes a 2-D or 3-D plot data structure as its argument and returns a transformed plot.

The commands for plotting curves and surfaces generate points by sampling the function to be plotted over the specified range or ranges. Several options are available to control how the sampling is done. All these options must be provided when the curve or surface is first created. They cannot be used with the plots:-display command or with the plottools commands that alter existing plot structures.

Number of Points

The numpoints option sets the minimum number of sampling points used by the plot and plot3d commands. Because the plot command uses an adaptive plotting scheme, it usually generates more points than this number. The plot3d command does not use an adaptive scheme and generates a number of points close to the specified numpoints value. The grid option is an alternative way of specifying the number of sample points in 3-D plots. This option takes a list of two positive integers that specify the dimensions of the rectangular grid over which the points are generated. >  p1 := plot3d(.5*sin(x+y), x = -Pi .. Pi, y = -Pi .. Pi, grid = [10, 10]): >  p2 := plot3d(.5*sin(x+y)+1, x = -Pi .. Pi, y = -Pi .. Pi): >  p3 := plot3d(.5*sin(x+y)+2, x = -Pi .. Pi, y = -Pi .. Pi, grid=[40, 40]): >  plots:-display([p1, p2, p3]);

Adaptive Plotting

In 2-D plotting, the numpoints value is used to set the initial sample points. When the adaptive option value is set to true (the default value), the intervals defined by the initial sample points are further subdivided in an attempt to get a better representation of the function. The attempts at subdivision are based on the current sample values, and intervals are subdivided a maximum of six times. The adaptive option can also take a positive integer value that controls the maximum times intervals are subdivided. If the adaptive option is set to false, the number of points generated is the same as the numpoints value (or the default value, if it is not provided). The sample option allows you to provide a set of points at which the function is to be sampled. If adaptive plotting is allowed, the final set of sample points includes those in the provided list but normally consists of many more. To use exactly the list of points given by the sample option, specify adaptive=false. >  plot(x^2, x=0..4, 'adaptive'='false', 'sample'=[seq(0.1*i, i=0..40)], style=point); The adaptive and sample options are not available for 3-D plotting.

Discontinuities

If a function with a discontinuity is being plotted, then evaluation at the point of discontinuity will lead to an undefined value, which results in a gap in the plotted curve or surface. It is more likely that the function is evaluated at points very close to the discontinuity, and this can lead to a distorted view of the plot when the values are extremely large or small and an inappropriate connecting of the points over the discontinuity. In the 2-D case, the discont option can be used with the plot command when you suspect a discontinuity. The plot command uses the discont and fdiscont commands to detect discontinuities and divides the plotting range into subranges over which the plot is continuous. In the following example, the plot on the left contains extraneous vertical lines. These are avoided in the right-hand-side plot generated with the discont option. >  plots:-display(Array([plot(ceil(sin(Pi*x)), x=-4..4), plot(ceil(sin(Pi*x)), x=-4..4, 'discont'=true)])); Usually, removable discontinuities are ignored. However, you can use the showremovable suboption to draw a circle on the plot to mark the point of discontinuity. Another suboption is usefdiscont, which controls how the fdiscont command is used to find discontinuities numerically. For more information about all the suboptions available for the discont option, refer to the plot/discont help page.

The color option is used to specify the color of plot objects in 2-D and 3-D plots, and its value can take several forms. A few of these are described in this section. For more details, refer to the plot/color help page. Default colors are chosen by Maple when none are specified.

Specifying a Single Color

The easiest way to apply a color to a plot object is to provide the name of a color known to the Maple plotting commands. The list of all such color names and their associated RGB values is available on the plot/colornames help page. These names correspond to commonly used HTML color names. >  plot3d(binomial, 0..5, 0..5, 'color'="Niagara GreenishBlue"); Alternatively, a plot color structure can be used as the value for the color option. This takes one of the following forms: COLOR(RGB, v1, v2, v3), COLOR(HSV, v1, v2, v3), or COLOR(HUE, v1). More information about the COLOR structure is available in the plot/structure help page.

Using Multiple Colors

The color option can be applied to individual objects that are then combined using the plots:-display command. Some commands, such as plot, allow you to provide a list of objects to be plotted as well as a list of colors to be applied in order. >  plot([seq(i+sin(x), i = 1 .. 4)], x = 0 .. 4*Pi, 'color'= ["Niagara Navy", "Niagara Burgundy", "Niagara Olive", "Niagara PaleRed"]); If no colors are provided, the plot command uses a default list of colors. To see the default list used by plot and several other 2-D plotting commands, use the plots:-setcolors command. >  plots:-setcolors(); $\left[''\#78000E''\,''\#000E78''\,''\#4A7800''\,''\#3E578A''\,''\#780072''\,''\#00786A''\,''\#604191''\,''\#004A78''\,''\#784C00''\,''\#91414A''\,''\#3E738A''\,''\#78003B''\,''\#00783F''\,''\#914186''\right]$ (2) >  plot([seq(i+sin(x), i = 1 .. 4)], x = 0 .. 4*Pi); The plots:-setcolors command also allows you to set new default colors. If there are fewer colors than curves, the colors are repeated in order. >  plots:-setcolors(["Indigo", "ForestGreen"]): >  plot([seq(i+sin(x), i = 1 .. 4)], x = 0 .. 4*Pi); The following command resets the colors to the original default colors. >  plots:-setcolors('default'):

	The ColorTools Package
	The ColorTools package contains commands for working with colors and color palettes, as well as converting between supported color formats. For a complete list of ColorTools commands and supported color formats, see the ColorTools help page.

Coloring Surfaces

When you plot a 3-D surface, the surface is shaded using a default shading scheme based on the coordinates of the points that define the surface. As with 2-D plots, a single color can be provided through the color option. Alternatively, a different shading may be specified with the shading option. >  plot3d(x^2*y, x=-1..1, y=-1..1, 'shading'='zgreyscale'); You can obtain a customized shading parametrized by the plot variables. To do this, provide an expression or a list of three expressions in terms of the plot variables. If a single expression is given, it is taken to be a hue value; if a list of three expressions is given, the triplet is taken to be RGB values. >  plot3d(x^2*y, x = -Pi/2 .. Pi/2, y = -1 .. 1, color = y^2*cos(x)); Similarly, if the input is given as procedures instead of expressions in two plotting variables, the color can be specified by a procedure or a list of three procedures that take two input parameters and return a single value. More details are provided in the plot3d/colorfunc help page. The colorscheme option is another way of coloring either a 3-D surface or a density plot generated by the plots:-densityplot command. This option allows you color a surface based on a function value $f\left(x\,y\right)$ or to supply your own procedure implementing a color scheme. More details are given in the plot/colorscheme help page. >  plots:-densityplot(x*cos(x)+y^2, x=-5..5, y=-5..5, colorscheme=["Green", "Violet", "NavyBlue"], style=surface);

Images and Backgrounds

Surfaces can be colored with an image using the image option, as described in the plot3d/options help page. >  imgfile := cat(kernelopts(mapledir), "/data/images/rollercoaster.jpg"): >  plot3d(sin(y)*cos(x), x=0..Pi, y=0..Pi, image=imgfile, lightmodel=none, orientation=[-80, 0, -10]); You can also use an image as a background for a 2-D plot by providing the background=t option where t is an image file or filename. The background option also allows you to use a solid color as the plot background. For more information, see the plot/options help page. >  plot(sin(x), color="Orange", background="DarkBlue", thickness=3, axis=[color="LightGrey"]);

The size option, for 2-D plots only, allows you to specify the size of the plot window. The size is usually specified in numbers of pixels but an aspect ratio or fraction of the worksheet width may be provided. In the following example, the width is specified as 300 pixels and the height as 1.5 times the width.

The view option determines the extent of the axes in the rendered plot. In the next example, the plot data structure produced by the plot command contains all the points generated from the given range, -2..4. However, the view is restricted to the portion of the plot in the box defined by $x$ values in the range -1..3 and $y$ values in the range -3..0.

In the next example, the specified $x$-axis view is much larger than the range.  Since the computed points are based on the range $x\=-2..4$, the displayed curve is only shown for this range. To generate the curve for the entire $x$ range from -5 to 7, you must re-execute the plot with x=-5..7 as the second argument.

In certain cases, the plotting command automatically sets the view option based on the provided ranges. Otherwise, the default view is determined by the minimum and maximum values of the data points generated.

	smartview option
	The plot command generates data based on the range provided by the user or on a default range, if the user does not provide range data. When the smartview=true option is provided, the view is restricted to the most important regions of the plot. To prevent such a restriction use the smartview=false option. For example: >  plot(1/(x-1)); >  plot(1/(x-1),smartview=false);

Typeset text and mathematics can appear anywhere in a 2-D or 3-D plot where text is allowed. This includes text provided by the plots:-textplot command and the following options: annotation, caption, labels, legend, tickmarks, and title.

You can provide arbitrary expressions to the textplot command or as values for the options to the command. These expressions are displayed on the plot as typeset output whenever possible. Strings are displayed as plain text without the quotation marks, but names such as x, y, and Pi are typeset. To concatenate several expressions, wrap them inside a typeset structure.

The plot/typesetting help page provides more details about using typeset mathematics in plots. It includes tips on using 2-D math input to generate typeset expressions that are not easily expressed in 1-D math input. These expressions can then be made into atomic variables through the context menu and then converted to 1-D math to be used programmatically. For more information about 1-D and 2-D math input modes, see 2-D Math.

Several options are available for customizing the look of axes and gridlines, including:

You can obtain greater control over the look of each axis by using the axis or axis[dir] option and providing a list of suboptions. To apply suboptions to one axis, use the indexed axis[dir] option, where the direction dir is 1, 2, or 3, with 3 applicable to 3-D plots only. To apply the suboptions to all axes, use the axis option without the index.

The suboptions include gridlines and tickmarks options, which are similar to the regular options of these names but offer more flexibility. Other suboptions are color (to change the color of an axis), location (to move an axis to the lowest or highest value of the view range or to the origin), and mode. This last suboption allows you to use logarithmic scaling for an axis. (Note that you can also create log plots with the plots:-logplot, plots:-semilogplot, and plots:-loglogplot commands.)

Plots are normally plotted in the Cartesian coordinate system, but you can use the coords option to plot in a different system. The 2-D and 3-D coordinate systems recognized by Maple and the transformations that they represent are listed in the coords help page.

The coords option must be used at the time the plot is generated. However, the plots:-changecoords command can be used to transform a plot structure that has already been created to one that uses a different coordinate system.

When working with alternate coordinate systems, two useful commands are plots:-coordplot and plots:-coordplot3d, which provide graphical representations of coordinate systems using lines or surfaces of constant value.

Because the polar coordinate system is commonly used, Maple has a plots:-polarplot command for plotting in this system. Polar axes are displayed by default, and special options are available for customizing the look of these axes. In particular, the coordinateview option can be used to restrict the view in the polar coordinate system.

The style of the coordinate axes (either polar or cartesian) can be changed with the axiscoordinates option. This option is available for 2-D plots in general and is not restricted to the polarplot command.

The section Colors describes the use of the plots:-setcolors commands to set the default curve colors for 2-D plots. More general commands for setting options for all 2-D and 3-D plotting commands are plots:-setoptions and plots:-setoptions3d.

The plots:-setoptions command allows you to specify options that are applied to all 2-D plots created in the same Maple session. The plots:-setoptions3d command performs a similar function for 3-D plots. These settings are recognized by the plot, plot3d, and plots:-display commands, as well as a number of other plotting commands in Maple.

In the following example, the default symbol for point plots is set to solidcircle with a symbol size of 20.

The default value is overridden in the following example, which provides the symbol option explicitly in a command.

The plots:-display command can be used to build an animation. The calling sequence is

where L is a list of plot structures, all 2-D or all 3-D. An animation will be created in which the plots in L appear in sequence, one in each frame.

The plots:-animate command can be used to create an animation from a single command with one varying parameter. Any Maple plotting command that produces a 2-D or 3-D plot, including ones in packages not primarily intended for plotting, can be used.

The following example shows how to create an animation with the plots:-spacecurve command. The first argument to animate is the procedure name. The second argument is the list of arguments to be passed the the given procedure. This list contains a parameter whose range, over which the animation will vary, is given in the final argument to animate.

You can animate a custom procedure instead of a Maple library command.

An animation can be generated from any static 3-D plot with the viewpoint option. This option allows you to create the animation by varying the viewpoint through the plot, as if a camera were flying through the space. The position, direction, and orientation of the camera can be varied.

There are several ways to create the animation, which are all described on the plot3d/viewpoint help page. The simplest way is to use one of the standard viewpoint paths, such as circleleft.

Another way is to provide a parametrically defined path.

There are a number of other commands in Maple for creating animations, such as plots:-animatecurve (for visualizing the drawing of a curve) and ones for specific applications such as those in the Student package.

Animations, like other plots, can be combined using the plots:-display command and put into arrays of plots. You can display an entire animation, frame by frame, in a table by passing it directly to the plots:-display command.

If you specify the insequence option to plots:-display, then it is displayed as a regular animation. (Output is suppressed here; to produce the plot change the colon to a semicolon.)

The Maple standard worksheet interface provides all of the functionality for plotting described in this chapter. If you are using another interface, then some of the plotting features will not be available. For more details about the differences, refer to the plot/interface help page.

With any of these interfaces, you can redirect plotting output to an alternative device. The devices available are listed in the plot/device help page and include common graphics formats such as JPEG and PostScript®.

Plot output is controlled by a number of interface variables such as plotdevice (the name of the plotting device) and plotoutput (the name of an output file). These are described in the interface help page. The plotsetup command provides a simpler way to set up these interface variables, without having to use the interface command directly.

For example, the following command specifies that all subsequent plot output be in PostScript format and be saved in a file called plot.ps. Furthermore, the PostScript driver will use a portrait orientation with no border. The plotsetup(default) command restores the default output options.

If the first argument to a plotting command is an expression in the plotting variable, these same plotting variables must appear in the range arguments. A common mistake is to omit the plotting variable in the ranges or to use a different variable name accidentally. It is also a mistake to provide a procedure as the first argument but then to use variable names in the subsequent range arguments.

Another common mistake is to use the expression form when you mean to provide an operator. A typical example is the following:

The correct way to plot this procedure over the range -1 to 1 is the use operator form.

If you attempt to use expression form, then p(x) is evaluated immediately, the value 0 is passed to the plot command as the first argument, and the resulting plot is a horizontal line.

Most of the Maple plotting commands are meant to work with real-valued functions, though specialized commands such as plots[complexplot] are available for plotting complex-valued functions. Generally, when evaluation of the input expression or procedure results in a complex value, the value is replaced by an undefined value. Many plotting commands check for numbers with very small imaginary parts and will convert these numbers to real numbers, with the criteria for dropping an imaginary part depending on the Digits environment variable and on its relative size compared to the real part. This procedure helps to avoid problems caused by round-off errors during the computation. However, it is advisable to ensure that the input expression or procedure always evaluates to a numeric value.

In the first example below, the ragged edge is caused by the fact that some of the values are undefined. The second example, which has the range of t going from 0 to s instead of 0 to 1, produces a more accurate plot.

Non-numeric data can also be produced as the result of mistyping a variable name. In the example below, the second argument mistakenly contains the variable z instead of x. Consequently, when a numeric value in the range 0..Pi is substituted for the variable z in the expression sin(x), the result remains the algebraic expression sin(x), which is non-numeric. This leads to a warning from Maple and an empty plot.