Graphics Improvements in Maple 15 - Maple Programming Help

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Graphics Improvements in Maple 15

  

Maple 15 includes many improvements in plotting. These are summarized below.

 

Plotting Trigonometric Functions

Improved Captions for Plots and Tutors

Extracting Data from Plots

More Control over Plots of 3-D Solutions to a System of DEs

Improved Options for Animations

Plotting Trigonometric Functions

• 

Tickmarks in multiples of π are now added to plots generated by the plot and plot3d commands when π is detected in the range arguments.

plot3d(cos(x)*sin(y), x=-Pi..Pi, y=-Pi..Pi, 'axes'='boxed');

• 

The range argument for the plot command is optional. When this is omitted, the default range is now set to -2*Pi..2*Pi instead of -10..10 when a trigonometric function is detected in the expression to be plotted.

plot([cos(x), sin(x)]);

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Plots created using the Plot Builder or through the context menu also set the default range to -2*Pi..2*Pi when a trigonometric function is detected.

• 

When specifying π tickmarks with the tickmarks or axis option, you can now use the name piticks instead of the spacing suboption. Similarly, if you want to remove π tickmarks that were automatically added, you can use the decimalticks value for the tickmarks option.

plot(sin(x), x = 0 .. 2*Pi, tickmarks = [decimalticks, piticks]);

Improved Captions for Plots and Tutors

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Visualization plots and tutors in the Student packages have improved captions, including formatted 2-D mathematics describing the graph.

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For an introduction to these visualizations, see the Calculus1Visualization, MultivariateCalculus, LinearAlgebraVisualization, and StudentVectorCalculus example worksheets.

Extracting Data from Plots

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The new getdata command in the plottools package retrieves data from a 2-D or 3-D plot and returns it in the form of a Matrix or Array, along with the ranges of the data. More details are available in the plottools[getdata] help page.

plottools[getdata](plot([sin(x), x^2-2*x], x = -2 .. 2));

curve,2...2.,0.999972563137118797..0.999980362556832647, 200 x 2 MatrixData Type: float8Storage: rectangularOrder: Fortran_order,curve,2...2.,0.999981268221130759..8., 200 x 2 MatrixData Type: float8Storage: rectangularOrder: Fortran_order

(1)

More Control over Plots of 3-D Solutions to a System of DEs

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The DEplot3d command in the DEtools package has been enhanced, with the addition of 3-d field arrows, and the ability to animate either curves, arrows, or both.

  

Example of a command to plot field arrows:

with(DEtools,DEplot3d):

DEplot3d({diff(x(t),t)=y(t),diff(y(t),t)=-sin(x(t))},[x(t),y(t)],t=0..10,
[[x(0)=0,y(0)=.5],[x(0)=0,y(0)=1],[x(0)=0,y(0)=1.8],[x(0)=-2*Pi,y(0)=1],
[x(0)=2*Pi,y(0)=.5],[x(0)=-2*Pi,y(0)=2.1],[x(0)=2*Pi,y(0)=-2.1]],
orientation=[-5,85],linecolor=sin(t)-t,arrows=cheap);

  

Same system animating the solution curves:

DEplot3d({diff(x(t),t)=y(t),diff(y(t),t)=-sin(x(t))},[x(t),y(t)],t=0..10,
[[x(0)=0,y(0)=.5],[x(0)=0,y(0)=1],[x(0)=0,y(0)=1.8],[x(0)=-2*Pi,y(0)=1],
[x(0)=2*Pi,y(0)=.5],[x(0)=-2*Pi,y(0)=2.1],[x(0)=2*Pi,y(0)=-2.1]],
orientation=[-5,85],linecolor=sin(t)-t,animate=true);

• 

See DEtools[DEplot3d] for more information.

Improved Options for Animations

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The background and trace options for the animate command in the plots package have been improved. For more information, see the plots[animate] help page.

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The background option now accepts a list of plots in addition to a single plot. The plots are automatically combined with the plots[display] command to form a single background plot.

  

Note: To run animations, right-click ( Command-click, Macintosh) the plot, and select Animation > Play.

plots[animate](plot, [t*x^2, x=-1..1], t=0..1, 'background'=[plot(.5, -1..1, 'color'="Blue"), plots[pointplot]([0, 0], 'symbol'='solidbox', 'color'="Green", 'symbolsize'=30)]);

• 

The trace option now allows you to specify a list of the frames to be traced during the animation, as an alternative to having a number of equally spaced frames.

plots[animate](plot, [t*x^2, x = -1..1], t=0..1, 'trace'=[1, 2, 3, 23, 24, 25]);

See Also

Index of New Maple 15 Features