Maple 2019 includes a couple new plotting utilities for drawing mathematical shapes
Polygons by Name
Improved Visualization of Graphs
Animations in the Plot Builder
The new command plottools,polygonbyname draws shapes in plots. It knows about many mathematical shapes and has many options for creating them exactly as desired. This command is very useful for annotating other plots or building more complex 2-D visualizations. For example, it is used by GraphTheory,DrawGraph to render custom vertex shapes in Graph visualizations.
withplots: withplottools: setoptions axes=none, scaling=constrained, size=400,400
The size of shapes is primarily controlled by defining the dimensions of a box that should fit entirely inside the shape. Here is a parallelogram that fits a 16x9 box.
displaypolygonbynameparallelogram, inbox=16,9, color=Red, axes=boxed
Regular polygons with an arbitrary number of sides can be specified by just a number for the name, or as "n-gon", or common name like "hexagon". Here is an animation of calling polygonbyname on the integers 3-36.
inscribedCircle ≔ displaypolygonbynamecircle, radius=1, color=Blue, style=line:displayseqdisplayinscribedCircle,polygonbynamei, radius=1, style=line, i=3..36, insequence;
In addition to being able to specify the size of the polygon, you can specify its position with the center option and its orientation with the rotation option.
display polygonbynameinvtriangle, center=−3,0, polygonbynametriangle, center=0,0, polygonbynametriangle, center=3,0, rotation=−90 degrees,size=600,200, style=line, linestyle=dash;
There many other ways to modify the shape with command options: irregular, reuleaux, rounded, star, and wide. Not all options, or combinations of options, are supported for every shape. See the help page for details.
inscribedCircle ≔ displaypolygonbynamecircle, color=Blue, style=line:inscribedBox≔displaypolygonbyname⁡rectangle,color=Red,style=line:
displayinscribedBox,inscribedCircle, polygonbynameoctagon, star, color=Linen ;
display polygonbynamehexagon, color=Linen, rounded
display polygonbynamereuleaux hexagon, color=Linen
displaypolygonbyname7gon, wide, color=Linen
Most of these command options can also be specified as part of the name. Here is a wide irregular 9 pointed star.
displaypolygonbynamewide irregular 9-star, color=Linen
Many shapes commonly used in diagrams are known by name.
plots:-displaymaps→displaypolygonbynames, color=Linen,title=s, Array1..4,1..5,circle, semicircle, ellipse, star, stadium, half stadium, indent stadium, superellipse, supercircle, rectangle, square, parallelogram, trapezoid, rectangle, diamond, kite, invkite, dart, rhombus,triangle;
The plottools,ellipse and plottools,ellipticArc commands now have a super option that creates superellipses and generalized superellipses or arcs thereof. A generalized superellipse is the locus of points [x,y] satisfying the equation
for center [x0,y0], radial distances a and b, and super elliptic parameters m1 and m2. If m1≠m2 the curve is a generalized superellipse, and just a superellipse otherwise.
ms ≔ 15,13,12,23, 1, 32, 2, 3, 5:display(seq(ellipse(super=msi, legend=catm=,msi, color=Niagara ∥i), i=1..nopsms), scaling=constrained, size=600,600);
Generalized superellipses have different shapes in the x and y directions. This is most obvious when one of the parameters is less than 1 and the other is greater.
display ellipsesuper=1/5,3,color=DarkRed, ellipsesuper=2,5,color=DarkBlue,scaling=constrained, size=600,600
Many improvements have been made to the rendering of graphs with the DrawGraph command. As well, many new option have been added to customize the style of graphs. For full details see the GraphTheory updates page.
restart;withGraphTheory:GV1 ≔Graph1,2,1, 2,3,2, 3,4,3, 4,5,4, 5,1,5;
GV1≔Graph 1: a directed weighted graph with 5 vertices and 5 arc(s)
DrawGraphGV1, stylesheet=vertexshape=squircle,edgethickness=3, vertexcolor=Red, arrowpos=0.1,arrowsize=25,weightfontsize=25,vertexfontsize=25
The Correlogram command in the Statistics package computes autocorrelations of a data set and displays the result as a column plot with dashed lines indicating the 95% confidence band. AutoCorrelationPlot is an alias for the Correlogram command.
You can now build animations interactively through the Plot Builder.
From the Context Panel for an expression, select Plot Builder.
Select the animation toggle button to create an animation.
Specify options as desired in the panel.
Click build animation.
To play the animation, use the animation toolbar.
Note: If you are animating a plot with more than one parameterized variable, you can change the sequence order of these variables using the options in the context panel:
It is now possible to export plots to the Scalable Vector Graphics (SVG) file format.
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