Graphics Improvements in Maple 11
Maple 11 includes many improvements in plotting. These are summarized below.
To View Plots from this Help Page
Highlights of Improvements
General Improvements to 2-D Plots
New and Updated Plotting Commands
New and Updated Options
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The following list highlights major improvements in Maple plotting documented in this help page. Detailed information and links to relevant help pages are provided in the sections below.
Look and Performance of 2-D Plots - The look of 2-D plots has been improved significantly. 2-D plots render faster and use less memory.
Arrays of Plots - Arrays of plots created with the plots[display] command are now displayed as a table giving you greater control over the individual plots. You can display both 2-D and 3-D plots in a single array.
Typesetting in Plots - You can display typeset text and mathematical expressions in 2-D plots.
Internationalization - You can display any international alphabet/character in a 2-D plot, provided the appropriate font is installed.
Intersection Plotter - The plots[intersectplot] command has been added for plotting the 3-D intersection of surfaces.
2-D Implicit Plotter - The plots[implicitplot] command for plotting 2-D implicit curves has been improved significantly and new options have been added.
Density Plotter - The plots[densityplot] command has been improved significantly and new options have been added.
2-D Differential Equation System Plotter - The DEtools[DEplot] command has new options for animation and for visualizing the direction field.
New Options - New options are available for adding captions and changing the location of legends.
Updated Options - New line styles and symbols for plotting curves and points have been added, and you have better control over the placement of tickmarks.
Extended Color Names - The list of named colors understood by Maple has been extended. A new command, plots[setcolors], allows you to change the default colors assigned to 2-D curves.
Drawing Tools - Maple allows you to sketch an idea in a canvas, draw on plots, or even draw on images. For details, see worksheet/documenting/drawingtools.
This section describes general improvements to the look and performance of 2-D plots in Maple 11.
Speed and Layout of Plots - Plots are rendered faster and use less memory.
Tickmarks - Tickmark generation has been improved for 2-D plots. A new algorithm is used to determine the optimal placement of tickmarks given the layout constraints. You can control tickmark spacing and generation of subticks.
Typesetting in Plots - Typeset text and mathematics can now appear anywhere where text is normally allowed. This includes text provided through the plots[textplot] command and the following options: caption, labels, legend, tickmarks, and title.
plot(x^2/(x+5), x=1..5, caption=typeset("A plot of ", x^2/(x+5), "."));
Internationalization - You can display any international alphabet/character in a 2-D plot where text is normally allowed.
Fonts - You can use a wider range of fonts within plots, depending on the fonts available. The family name of any font supported by the display can be used in place of the existing options.
Highlighting - Highlighting has changed significantly, both for rollover and selection. Selection is indicated by translucent highlighting of the object selected. Rollover highlighting is indicated by symbols drawn at the object vertices.
Note that rollover highlighting must be enabled. From the main menu, select Tools>Options and then the Display tab. Select the Enable rollover highlighting in plots check box.
Export to Windows(R) Meta Files - When 2-D plots are exported to Windows Meta Files (WMF format), they are written as vectors, allowing them to be scaled indefinitely.
Context Menus - The menu format has been enhanced. The Axis Properties dialog has been redesigned.
Legends - You can use long legend strings. Also, formatting of multiple legends has been enhanced.
Numeric Range - The numeric range for a 2-D plot has greatly increased. Values of 10^+200 and 10^-200 are now correctly represented. Variations of +/- 10^-9 about 1.0 are displayed correctly.
Pan and Scale - The pan and scale features of the plot (controlled with the mouse) no longer move and resize the plot within its surrounding area. Instead, they change the view ranges of the plot.
Zoom Factor - Text in plots now takes account of the Zoom factor.
This section describes the new commands, plots[intersectplot] and plots[setcolors], as well as major updates to several existing commands in the plots package.
A := Array(1..2, 1..2):
A[1,1] := plot(sin(x), x=-Pi..Pi, axes=framed):
A[1,2] := plot(cos(x), x=-Pi..Pi, axes=boxed, style=point):
A[2,1] := plot3d((1.5)^x*sin(y), x=-3..3, y=-3..3, axes=boxed):
A[2,2] := plot3d((1.3)^x*sin(y), x=-1..2*Pi, y=0..Pi, coords=spherical,
3-D Surface Intersection Plotter - The new plots[intersectplot] command allows you to plot the intersection of any combination of two explicit, parametric or implicit surfaces. For example, to plot the intersection of 2 spheres, one implicit, one parametric:
Implicit Plotter - New options for the plots[implicitplot] command have been added and significant efficiency improvements made. You can use the new options to efficiently refine an implicit plot, compute a direct implicit plot as the resultant of two expressions polynomial in the elimination variable, better interpolate curves that represent singularities in the plot, and reduce the number of points used for the plot without reducing the detail level.
Direct plotting of a resultant:
[x^2+y^2+z^2=1, (x+z/2)^2/(5/4)+y^2=1/3, z],
x=-1..1, y=-1..1, gridrefine=2, scaling=constrained);
High detail, small size plot of 4 concentric circles:
fn := (x^2+y^2-1)*(x^2+y^2-0.73)*(x^2+y^2-0.5)*(x^2+y^2-0.31):
plots[implicitplot](fn, x=-1.2..1.2, y=-1.2..1.2, grid=[51,51],
gridrefine=2, crossingrefine=2, resolution=1000);
Density Plotter - The plots[densityplot] command has been improved significantly and new options have been added. They include brightness, contrast, and scaletorange.
plots[densityplot](x*(x^2-y^2)/(x^2+y^2)^2, x=-0.1 .. 0.1, y=-0.1 .. 0.1,
grid=[64,64], style=patchnogrid, brightness=0.7, contrast=0.7);
3-D Conformal Plotter - The new spherecolor option for the plots[conformal3d] command allows you to specify the color of the sphere.
Default Curve Colors - You can set the default colors for curves in 2-D plots with the new plots[setcolors] command.
Animations - The new trace option for the plots[animate] command allows you to create a trace of n frames to be displayed in an animated plot.
This section describes changes to general plotting options that can be used with 2-D and 3-D plots. For more information, see the plot/option and plot3d/option help pages.
Captions - You can add a caption underneath a 2-D or 3-D plot using the new caption option.
Legend Style - You can specify a legend's location (right, left, top or bottom of a 2-D plot) and its font using the new legendstyle option.
Axes - A tickmarks suboption has been added to the axis option. Tickmarks can still be controlled using the regular tickmarks=[m, n] option. For details, see plot/axis.
Tickmarks - You can specify the gap between tickmarks and gridlines using the new spacing structure. The gap may be given in terms of Pi or other constants and the tickmark labels will be typeset when possible. For details, see plot/tickmarks.
plot(cos(x), x=-2*Pi..2*Pi, tickmarks=[spacing(Pi/2), default]);
Line Styles - New linestyle options values are available: longdash, spacedash, and spacedot.
Symbols - New symbol options values are available for 2-D plots: asterisk, diagonalcross, solidbox, solidcircle and soliddiamond. For 3-D plots, the new values are: asterisk, diagonalcross, sphere and solidsphere.
plots[pointplot]([[0,1], [1,-1], [3,0], [4,-3]], axes=boxed,
Colors - Maple supports many new color names. For more information, see Plot Color Names.
Filled Regions - The filled option for the implicit and contour plotting commands in the plots package has been changed to filledregions, to distinguish it from the general filled option for 2-D and 3-D plotting. The contour-plotting commands will still accept the old filled option name. For a filled surface, use plot3d and style=contour.
The new plot/computation help page provides details about how numeric computation is performed and gives suggestions on how to obtain the best performance from the plotting commands.
Index of New Maple 11 Features
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