plot::easy

plot::easy tries to transform all given data and expressions into valid graphical objects and attributes:

plot::easy(sin(x), [PI/2,1])

Since the function plot calls the function plot::easy for preprocessing its input data, scenes like above can directly be plotted using plot :

plot(sin(x), [PI/2,1], #x=PI/2, #y=1)

MuPAD graphics

Now, it is only a small step to animate this scene:

plot(sin(x), {[x,sin(x)], #Points}, #x=x, #y=sin(x))

MuPAD graphics

Note: Graphical objects and attributes, as well as data that plot::easy cannot transform, are returned unchanged:

plot::easy(x, plot::Point2d(1,1), LineStyle=Dashed, "UnknownObject")

This is why plot returns the following error message when it is executed with the above arguments:

plot(x, plot::Point2d(1,1), LineStyle=Dashed, "UnknownObject");

Error: unexpected arguments: "UnknownObject" [plot::Canvas::new]

Points can be entered as lists with two or three values. Alternatively, a corresponding column vector in combination with the option #Points (alias #P , see example� 18 ) can be used.

Note that for plotting animated points the option #Points is required. Otherwise a curve (when entered a list) or an arrow (when entered a vector) is plotted:

plot([0,1], [s,s^2], {[s,s^2], #Points}, s=-2.. 2,

matrix([t,t^2]), {matrix([t,t^2]), #Points}, t= 2..-2

)

MuPAD graphics

Arrows can be specified as column vectors with two or three elements. Alternatively, a list in combination with the option #Arrows (alias #A , see example� 13 ) can be used:

plot(matrix([0,1]), matrix([s,s^2]), s=2..-2,

[t,t^2], {[t,t^2], #Arrows}, t=-2..2

)

MuPAD graphics

If an arrow should start at coordinates other than (0,0) or (0,0,0), respectively, then a list of two column vectors or a corresponding list of lists in combination with the option #Arrows (alias #A , see example� 13 ) can be used:

u:= matrix([3,2]):

v:= matrix([1,4]):

w:= (1-a)*u + a*v:

u, v, w;

plot(u, v, [u,w], a=0.1..1, #Arrows)

MuPAD graphics

delete u, v, w:

Polygons can be specified as lists, tables or matrices. In the following example, polygons are plotted using different input styles. The option #Origin (alias #O , see example� 17 ) ensures that the origin of the coordinate system is visible in the scene as well:

plot([[1,3],[2,5],[3,3],[4,8]],

table(1=4,2=6,3=4,4=9),

[matrix([1,5]),matrix([2,7]),matrix([3,5]),matrix([4,10])],

matrix([[1,6],[2,8],[3,6],[4,11]]),

#Origin)

MuPAD graphics

Note that polygons are displayed as points when option #Points (alias #P , see example� 18 ) is used:

plot([[1,3],[2,5],[3,3],[4,8]],

table(1=4,2=6,3=4,4=9),

[matrix([1,5]),matrix([2,7]),matrix([3,5]),matrix([4,10])],

matrix([[1,6],[2,8],[3,6],[4,11]]),

#Points, #Origin)

MuPAD graphics

Note that the following polygons with two elements are displayed as arrows when option #Arrows (alias #A , see example� 13 ) is used:

plot([[1,4],[2,6]],

[matrix([1,5]),matrix([2,7])],

matrix([[1,6],[2,8]]),

#Arrows, #Origin)

MuPAD graphics

Point lists can be specified as lists, tables or matrices. For each point an RGBa color has to be specified. In the following example, point lists are plotted using different input styles. The option #Origin (alias #O , see example� 17 ) ensures that the origin of the coordinate system is visible in the scene as well:

plot([[1,2,RGB::Red], [2,4,[0,1,0]], [3,3,[0,0,1,0.5]]],

[matrix([1,3,RGB::Red]),matrix([2,5,[0,1,0]]),matrix([3,4,[0,0,1,0.5]])],

matrix([[1,4,RGB::Red], [2,6,[0,1,0]], [3,5,[0,0,1,0.5]]]),

table(1=[5,RGB::Red], 2=[7,[0,1,0]], 3=[6,[0,0,1,0.5]]),

#Origin)

MuPAD graphics

Note that the following point lists are displayed as arrows when option #Arrows (alias #A , see example� 13 ) is used:

plot([[1,2,RGB::Red], [2,4,[0,1,0]] ,[3,3,[0,0,1,0.5]]],

[matrix([1,3,RGB::Red]),matrix([2,5,[0,1,0]]),matrix([3,4,[0,0,1,0.5]])],

matrix([[1,4,RGB::Red], [2,6,[0,1,0]], [3,5,[0,0,1,0.5]]]),

table(1=[5,RGB::Red], 2=[7,[0,1,0]] ,3=[6,[0,0,1,0.5]]),

#Arrows, #Origin)

MuPAD graphics

For drawing horizontal and vertical infinite lines, the short syntax and with e is a real expression, can be used:

plot(sin(x), [PI/2,1], #x=PI/2, #y=1, #Legend)

MuPAD graphics

For drawing horizontal and vertical infinite planes, the short syntax , and , with e is a real expression, can be used.

Both, lines and planes can also be animated:

plot([t,0,t^2], {[t,0,t^2], #Points}, #x=t, #z=t^2, #Legend)

MuPAD graphics

See also: plot::Text2d , plot::Text3d .

Usually plot::easy creates a 2D scene, unless one of the arguments is a 3D object or can only be transformed to a 3D object or the option #3D is used.

plot(sin(x), #3)

MuPAD graphics

However, the option #3D is only a hint. It is ignored if the current scene can only be a 2D scene. In the following example, the 2D point determines the dimension of the scene:

plot([PI/2,1], sin(x), #3)

MuPAD graphics

In the following example, the 3D point determines the dimension of the scene. There is no need to use option #3D in order to create a 3d scene:

plot([PI/2,1,0], sin(x))

MuPAD graphics

With option #Arrows , arrows instead of points or curves are created. When used within a {...}-group, it affects the elements of this group or scene only.

plot({{ [-5,25], [5,25], [x,x^2] }},

{{ [-5,25], [5,25], [x,x^2], #A }})

MuPAD graphics

Option #Constrained creates a coordinate system with constrained scaled axes. This is a shortcut for Scaling = Constrained .

plot({{ x^2 }}, {{ x^2, #C }})

MuPAD graphics

Option #Grid creates a coordinate system with grid lines. This is a shortcut for GridVisible = TRUE .

plot({{ x^2 }}, {{ x^2, #G }})

MuPAD graphics

Option #Legend creates a legend. This is a shortcut for LegendVisible = TRUE in combination with LegendEntry = TRUE . Note that plot::easy explicitly sets a legend text for each graphical object it creates.

plot([0,-6], x^2-5, [t,t^2], #L)

MuPAD graphics

Option #Origin includes the coordinates (0,0) or (0,0,0), respectively, into the viewing box of the current scene.

plot({{[2,2], [3,3]}}, {{[2,2], [3,3], #O}})

MuPAD graphics

Using option #Points , points instead of arrows or curves are created. Furthermore, this option sets the attributes PointsVisible =TRUE and LinesVisible =FALSE . When used within a {...}-group, it affects the elements of this group or scene only.

plot({[-5,25], [x,x^2], #Gray}, {matrix([5,25]), [x,x^2], #P})

MuPAD graphics

#X / #Y / #Z = a..b sets the x- / y- / z-range of the viewing box of the scene to a..b . This is a shortcut for ViewingBoxXRange / ViewingBoxYRange / ViewingBoxZRange = a..b .

plot({{x^2, sin(x)}}, {{x^2, sin(x), #Y=0..4}})

MuPAD graphics

We draw a 3D scene with a restricted viewing box. Therefore, only a quater of the shere is visible:

plot({{plot::Sphere(1)}},

{{plot::Sphere(1), #X=0..1, #Y=0..1, #Z=0..1}})

MuPAD graphics

plot::easy automatically carries out the following transformations:

Graphical object	Data or mathematical expression
plot::Point2d :	[c 1 , c 2 ], {[, ], #Points }, {matrix ([, ]), #Points }.
plot::Point3d :	[c 1 , c 2 , c 3 ], {[, , ], #Points }, {matrix ([, , ]), #Points }.
plot::Arrow2d :	matrix ([c 1 , c 2 ]), {[c 1 , c 2 ], #Arrows }, {[matrix ([, ]), matrix ([, ])], #Arrows }, {matrix ([[, ], [, ]]), #Arrows }, {[[, ], [, ]], #Arrows }.
plot::Arrow3d :	matrix ([c 1 , c 2 , c 3 ]), {[c 1 , c 2 , c 3 ], #Arrows }, {[matrix ([, , ]), matrix ([, , ])], #Arrows }, {matrix ([[, , ], [, , ]]), #Arrows }, {[[, , ], [, , ]], #Arrows }.
plot::Polygon2d :	[[, ],...], [matrix ([, ]),...], matrix ([[, ],...]), table (=,...).
plot::Polygon3d :	[[, , ],...], [matrix ([, , ]),...], matrix ([[, , ],...]). table (=[, ],...).
plot::PointList2d :	[[, , RGBa ],...], [matrix ([, , RGBa ]),...], matrix ([[, , RGBa ],...]), table (=[, RGBa ],...).
plot::PointList3d :	[[, , , RGBa ],...], [matrix ([, , , RGBa ]),...], matrix ([[, , , RGBa ],...]). table (=[, , RGBa ],...).
plot::Line2d :	#x=, #y=.
plot::Plane :	#z=, {#x=, #3D}, {#y=, #3D}, {#z=, #3D}.
plot::Curve2d :	[, ].
plot::Curve3d :	[, , ].
plot::Function2d :	, , , [,...].
plot::Function3d :	, , [,...], {, #3D }, {, #3D }.
plot::Implicit2d :	=.
plot::Implicit3d :	=, {=, #3D }.
plot::Inequality :	, , , , [<, >, =,...].
plot::Text2d :	[, ]=text , matrix ([, ])=text , [, ]=procedure , matrix ([, ])=procedure .
plot::Text3d :	[, , ]=text , matrix ([, , ])=text , [, , ]=procedure , matrix ([, , ])=procedure .

#3D :	alias #3 . Creates a 3D instead of a 2D scene, if possible. Usually, a 2D scene is created unless one of the arguments is a 3D object or can only be transformed into one.
#Arrows :	alias #A . Creates arrows instead of points. When used within a {...}-group, it affects the elements of this group or scene only.
#Constrained :	alias #C . Creates a coordinate system with axes having the same scaling. This is a shortcut for Scaling =Constrained .
#Grid :	alias #G . Creates a coordinate system with grid lines. This is a shortcut for GridVisible =TRUE .
#Legend :	alias #L . Creates a legend. This is a shortcut for LegendEntry =TRUE and LegendVisible =TRUE . When used within a {...}-group, it affects the elements of this group or scene only. Note that plot::easy explicitly sets a legend text for each graphical object it creates.
#Origin :	alias #O . Includes the coordinates (0,0) or (0,0,0), respectively, into the viewing box of the current scene.
#Points :	alias #P . Creates points instead arrows or curves. Furthermore, it sets the attributes PointsVisible =TRUE and LinesVisible =FALSE . When used within a {...}-group, it affects the elements of this group or scene only.
#XRange = a .. b :	alias #X = a .. b . Sets the x-range of the viewing box of the scene to a..b . This is a shortcut for ViewingBoxXRange =a..b .
#YRange = a .. b :	alias #Y = a .. b . Sets the y-range of the viewing box of the scene to a..b . This is a shortcut for ViewingBoxYRange =a..b .
#ZRange = a .. b :	alias #Z = a .. b . Sets the z-range of the viewing box of the scene to a..b . This is a shortcut for ViewingBoxZRange =a..b .
#<Colorname>:	If, and only if, RGB ::<Colorname> is a valid color name in MuPAD , #<Colorname> is transformed to: Color =RGB ::<Colorname>, LineColorType =Flat and for 3D objects additionally FillColorType =Flat . Transparent RGBa colors can be specified as #<Colorname>.[t], with t is in 0..1. When used within a {...}-group, it affects the elements of this group or scene only.
#<Colorname1> .. #<Colorname2>:	If, and only if, RGB ::<Colorname1> and RGB ::<Colorname2> are valid color names in MuPAD , this option is transformed to: Color =RGB ::<Colorname1>, LineColorType =Dichromatic , LineColor2 =RGB ::<Colorname2> in 2D scenes and to: Color =RGB ::<Colorname1>, FillColorType =Dichromatic , FillColor2 =RGB ::<Colorname2> in 3D scenes. Transparent RGBa colors can be specified as #<Colorname>.[t], with t is in 0..1. When used within a {...}-group, it affects the elements of this group or scene only.