2D polygons

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plot::Polygon2d([pt2d1, pt2d2, …], <a = amin .. amax>, options)
plot::Polygon2d(M2d, <a = amin .. amax>, options)


plot::Polygon2d defines polygons in 2D by a given list of vertex points. A polygon consists of points and edges. The edges are made up of the lines traversing from the first to the second point, the second to the third point, and so on. The last point is automatically connected with the first point if the attribute Closed = TRUE is specified.

Points and lines can be hidden via PointsVisible = FALSE and LinesVisible = FALSE. By default, the vertex points are hidden, and the edges are visible.

All points as a whole can be manipulated via PointStyle and PointSize. The attribute LineColor sets the color for all points and all lines. Likewise all lines can be manipulated via LineStyle and LineWidth.

You can vary the color of all lines and points via LineColorType. The default value is Flat. Specifying the values Dichromatic or Rainbow lets you set the second color LineColor2. With Functional, the colors are taken from a custom LineColorFunction.

The area of any closed 2D polygon can be filled by specifying Filled = TRUE. The filled area is defined by connecting the last and the first vertex. This additional edge itself, however, is only displayed if Closed = TRUE is set. A fill color and a fill pattern can be chosen by FillColor and FillPattern.

In case of a self-intersecting polygon, a FillStyle can be selected. See Example 2.


AttributePurposeDefault Value
AffectViewingBoxinfluence of objects on the ViewingBox of a sceneTRUE
AntiAliasedantialiased lines and points?TRUE
Closedopen or closed polygonsFALSE
Colorthe main colorRGB::Blue
Filledfilled or transparent areas and surfacesFALSE
FillColorcolor of areas and surfacesRGB::Red
FillStyledefinition of inside/outsideEvenOdd
FillPatterntype of area fillingDiagonalLines
Framesthe number of frames in an animation50
Legendmakes a legend entry 
LegendTextshort explanatory text for legend 
LegendEntryadd this object to the legend?FALSE
LineColorcolor of linesRGB::Blue
LineWidthwidth of lines0.35
LineColor2color of linesRGB::DeepPink
LineStylesolid, dashed or dotted lines?Solid
LinesVisiblevisibility of linesTRUE
LineColorTypeline coloring typesFlat
LineColorFunctionfunctional line coloring 
LineColorDirectionthe direction of color transitions on lines[0, 1]
LineColorDirectionXx-component of the direction of color transitions on lines0
LineColorDirectionYy-component of the direction of color transitions on lines1
Namethe name of a plot object (for browser and legend) 
ParameterEndend value of the animation parameter 
ParameterNamename of the animation parameter 
ParameterBegininitial value of the animation parameter 
ParameterRangerange of the animation parameter 
Points2dlist of 2D points 
PointSizethe size of points1.5
PointStylethe presentation style of pointsFilledCircles
PointsVisiblevisibility of mesh pointsFALSE
TimeEndend time of the animation10.0
TimeBeginstart time of the animation0.0
TimeRangethe real time span of an animation0.0 .. 10.0
Titleobject title 
TitleFontfont of object titles[" sans-serif ", 11]
TitlePositionposition of object titles 
TitleAlignmenthorizontal alignment of titles w.r.t. their coordinatesCenter
TitlePositionXposition of object titles, x component 
TitlePositionYposition of object titles, y component 
VisibleAfterobject visible after this time value 
VisibleBeforeobject visible until this time value 
VisibleFromToobject visible during this time range 
VisibleAfterEndobject visible after its animation time ended?TRUE
VisibleBeforeBeginobject visible before its animation time starts?TRUE


Example 1

Create a polygon with vertices located at the 5 complex 5th roots of 1. The polygon consists of the 4 lines joining the 5 points in the order given:

p := plot::Polygon2d(
       [[cos(2*PI*k/5), sin(2*PI*k/5)] $ k = 0..4]):
plot(p, plot::Circle2d(1, [0, 0])):

In order to include the line connecting the last with the first point, pass the attribute Closed to the polygon:

p::Closed := TRUE:
plot(p, plot::Circle2d(1, [0, 0])):

delete p

Example 2

Plot a closed 2D polygon and fill the area inside. In fact, there are two possible interpretations of what “inside” really means. In the first plot, the complement of the unbound component of the complement of the polygon is filled. In the second plot only that area is filled that contains points with nonzero winding number with respect to the polygon. See FillStyle for a detailed discussion.

p := plot::Polygon2d(
      [[cos(PI*k/3), sin(PI*k/3)] $k = 1..6,
       [cos(PI*k/3 + PI/6)/2, sin(PI*k/3 + PI/6)/2] $k = 1..6
      ], Closed = TRUE):
S1 := plot::Scene2d(p, Filled = TRUE):
S2 := plot::Scene2d(p, Filled = TRUE, FillStyle = Winding):
plot(S1, S2, Layout = Horizontal, Axes = Frame,
     Scaling = Constrained)

delete p, S1, S2:


pt2d1, pt2d2, …

The 2D vertices. These must not be of type plot::Point2d, but lists of two numerical real values or arithmetical expressions of the animation parameter a (the coordinates).

pt2d1, pt2d2, … is equivalent to the attribute Points2d.


An array or a matrix with 2 columns. Each row provides the coordinates of one point.

M2d is equivalent to the attribute Points2d.


Animation parameter, specified as a = amin..amax, where amin is the initial parameter value, and amax is the final parameter value.

See Also

MuPAD Functions

MuPAD Graphical Primitives