plot
::Implicit2d
Contour lines of a function from R^2 to R
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plot::Implicit2d(f
, x = x_{min} .. x_{max}
, y = y_{min} .. y_{max}
, <a = a_{min} .. a_{max}
>, options
)
plot::Implicit2d(f(x, y), x = x_{min}..x_{max} ,
y = y_{min}..y_{max} )
plots
the curves where the smooth function f
is zero.
plot::Implicit2d(f, x = x_{min}..x_{max} ,
y = y_{min}..y_{max} )
plots
the zeroes of f in
the given range, i.e., the set .
plot::Implicit2d
assumes that f is regular
almost everywhere on this curve, which means that f must
be differentiable and at least one of its partial derivatives must
be nonzero.
To plot other contours than zeroes, use the option Contours
.
Attribute  Purpose  Default Value 

AffectViewingBox  influence of objects on the ViewingBox of
a scene  TRUE 
AntiAliased  antialiased lines and points?  TRUE 
Color  the main color  RGB::Blue 
Contours  the contours of an implicit function  [0 ] 
Frames  the number of frames in an animation  50 
Function  function expression or procedure  
Legend  makes a legend entry  
LegendText  short explanatory text for legend  
LegendEntry  add this object to the legend?  TRUE 
LineColor  color of lines  RGB::Blue 
LineWidth  width of lines  0.35 
LineColor2  color of lines  RGB::DeepPink 
LineStyle  solid, dashed or dotted lines?  Solid 
LinesVisible  visibility of lines  TRUE 
LineColorType  line coloring types  Flat 
LineColorFunction  functional line coloring  
LineColorDirection  the direction of color transitions on lines  [0 , 1 ] 
LineColorDirectionX  xcomponent of the direction of color transitions on lines  0 
LineColorDirectionY  ycomponent of the direction of color transitions on lines  1 
Mesh  number of sample points  [11 , 11 ] 
Name  the name of a plot object (for browser and legend)  
ParameterEnd  end value of the animation parameter  
ParameterName  name of the animation parameter  
ParameterBegin  initial value of the animation parameter  
ParameterRange  range of the animation parameter  
TimeEnd  end time of the animation  10.0 
TimeBegin  start time of the animation  0.0 
TimeRange  the real time span of an animation  0.0 .. 10.0 
Title  object title  
TitleFont  font of object titles  [" sansserif " , 11 ] 
TitlePosition  position of object titles  
TitleAlignment  horizontal alignment of titles w.r.t. their coordinates  Center 
TitlePositionX  position of object titles, x component  
TitlePositionY  position of object titles, y component  
Visible  visibility  TRUE 
VisibleAfter  object visible after this time value  
VisibleBefore  object visible until this time value  
VisibleFromTo  object visible during this time range  
VisibleAfterEnd  object visible after its animation time ended?  TRUE 
VisibleBeforeBegin  object visible before its animation time starts?  TRUE 
XMax  final value of parameter “x”  
XMesh  number of sample points for parameter “x”  11 
XMin  initial value of parameter “x”  
XName  name of parameter “x”  
XRange  range of parameter “x”  
YMax  final value of parameter “y”  
YMesh  number of sample points for parameter “y”  11 
YMin  initial value of parameter “y”  
YName  name of parameter “y”  
YRange  range of parameter “y” 
It is wellknown that a circle can be described as :
plot(plot::Implicit2d(x^2+y^21, x = 1..1, y = 1..1))
Note that plot::Implicit2d
uses the given
range completely, even if there is nothing to plot at a border:
plot(plot::Implicit2d(x^2+y^21, x = 2..2, y = 2..2))
plot::Implicit2d
handles functions which
are not regular at isolated points on the contours:
plot(plot::Implicit2d((xy)*(x+y), x = 1..1, y = 1..1))
However, it fails if the function is singular on more than isolated points:
plot(plot::Implicit2d(0, x = 1..1, y = 1..1))
We plot some of the elliptic curves y^{2} = x^{3} + 4 x + c:
plot(plot::Implicit2d(y^2  x^3 + 4*x, x = 3..3, y = 4..4, Contours = [c $ c = 3..6]))
Like most graphical objects, plot::Implicit2d
can
be animated easily:
plot(plot::Implicit2d(x^2  y^2 = (x  a*y)*(x^2 + y^2), x = 2..2, y = 2..2, a = 2..2))

A realvalued expression or an equation in

 

Realvalued expressions, possibly in the animation parameter.
The image is plotted with


Animation parameter, specified as 
plot::Implicit2d
uses a curve tracking method:
It first generates starting points on the curve and then uses a predictorcorrector
method to follow the curve thus found in both directions, using the
implicit function theorem.