Services & Resources / Wolfram Forums
MathGroup Archive
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

RE: Color Fill areas in 2D graphic

  • To: mathgroup at
  • Subject: [mg23387] RE: [mg23354] Color Fill areas in 2D graphic
  • From: "David Park" <djmp at>
  • Date: Fri, 5 May 2000 02:07:22 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

> Hi,
> I want combine several ParametricPlot Images. After this is done, how
> can I fill areas within the image with a specific color ?
> thanks
> Roland Pabel

Hi Roland,

If you wish to try out my DrawingPaper routines, which are available at my
web site below, then the attached Mathematica notebook, ColoredArea.nb,
shows how to fill in areas with color. (MathGroup readers may contact me for
a copy of the notebook.)

If you have a closed curve defined by a parametric expression, then all you
have to do is convert the Line primitive to a Polygon primitive and supply a

If the area is defined by the combination of several parametric arcs, then
DrawingPaper has a routine, StitchLineSegments which will stitch the arcs
together into one line which can then be converted to a Polygon.

Of course, the standard way to color the area between two curves is to use
FilledPlot, but this requires the first curve to always be above the second
curve. Sometimes this does not happen in the x-y plane but does happen in a
different coordinate system. In those cases the DrawingPaper routine
DrawingTransform can convert a FilledPlot back to x-y coordinates. For
example, the area outside a unit circle but inside a cardioid can be filled
with FilledPlot in a theta-r representation and then transformed to a x-y

The notebook has examples of coloring in a tilted ellipse, coloring in the
area bounded by two intersecting parabolas with their axes in the y and -y
direction, and the circle-cardioid example mentioned above.

The packages you will need for the notebook from my web site are
DrawingPaper.m and FilledDrawing.m. The packages should be put in the
AddOns/ExtraPackages/Graphics folder. There are also other Drawing packages
and a tutorial.

David Park
djmp at


                    Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 4.0,
MathReader 4.0, or any compatible application. The data for the notebook 

starts with the line containing stars above.

To get the notebook into a Mathematica-compatible application, do one of 

the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing the
word CacheID, otherwise Mathematica-compatible applications may try to
use invalid cache data.

For more information on notebooks and Mathematica-compatible
applications, contact Wolfram Research:
  email: info at
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from
Wolfram Research.

(*CacheID: 232*)

(*NotebookOptionsPosition[      8299,        242]*)
(*NotebookOutlinePosition[      8952,        265]*)
(*  CellTagsIndexPosition[      8908,        261]*)


Cell["Filling Areas with Color", "Title"],

David Park
djmp at\
\>", "Subtitle"],

  "The Graphics`DrawingPaper` packages can be downloaded from my web 
site. It \
should be placed in the AddOns/ExtraPackages/Graphics directory. It can 
then \
be used just like the standard packages. Here is a click-on link to the 
web \
  ButtonBox[" ",
      URL[ " "], None},
  " "
}], "Text"],

    \(Needs["\<Graphics`DrawingPaper`\>"]\), "\[IndentingNewLine]",
    \(Needs["\<Graphics`FilledDrawing`\>"]\), "\[IndentingNewLine]",
    \(Needs["\<Geometry`Rotations`\>"]\)}], "Input"],


Cell["For a closed curve", "Section"],

This is the parametric representation of an ellipse with 7:3 axes ratio 
and \
rotated an an angle \[Theta].\
\>", "Text"],

    \(ellipse[\[Theta]_, t_] :=
      RotationMatrix2D[\(-\[Theta]\)] . {7  Cos[t], 3  Sin[t]}\)], 

We set the color to be LightBlue (DrawingPaper automatically loads in \
Graphics`Colors`), parametrically draw the curve, save it, convert the 
Line \
to a Polygon, change the color to Black and display the curve.\
\>", "Text"],

        Graphics[\n\t\t{LightBlue, \((curve 
                    Evaluate[ellipse[\[Pi]/4, t]], {t, 0, 2  \[Pi]}])\) 
              Line \[Rule] Polygon, Black, curve}], \n\n
        AspectRatio \[Rule] Automatic,
        PlotRange \[Rule] {{\(-10\), 10}, {\(-10\), 10}},
        Background \[Rule] Linen, \n{}];\)\)], "Input",
}, Closed]],


Cell["For a region defined by several arcs", "Section"],

Here are two parabolas with their axes in the y and -y directions. (If 
they \
were in the x direction we could use FilledPlot or FilledDraw.)\
\>", "Text"],

    \(\(par1[t_] := {\(-3\) + t\^2, t};\)\), "\[IndentingNewLine]",
    \(par2[t_] := {3 - t\^2, t}\)}], "Input"],

Cell["This finds their points of intersection.", "Text"],


    \(Solve[par1[t] \[Equal] par2[t]]\)], "Input"],

    \({{t \[Rule] \(-\ at 3\)}, {t \[Rule] \ at 3}}\)], "Output"]
}, Open  ]],

Cell["This plots the two curves to show the area we wish to color.", 

              Evaluate[{par1[t], par2[t]}], {t, \(-\ at 3\), \ at 3}]}], \n\n
        AspectRatio \[Rule] Automatic,
        PlotRange \[Rule] {{\(-10\), 10}, {\(-10\), 10}}/2,
        Background \[Rule] Linen, \n{}];\)\)], "Input",

We want to define a curve by stitching the two arc segments together. 
Then \
all we have to do is convert the Line to a Polygon. DrawingPaper 
contains a \
routine for stitching together arcs. The only thing we have to be 
careful \
about is stitching them end to end in the correct order. Since the 
plotting \
iterators always run from the minimum value to the maximum value (no 
matter \
what order we put them), we will often have to reverse the order of the 
points in some of the line segments.\
\>", "Text"],


    \(\(?StitchLineSegments\)\)], "Input"],

    \("StitchLineSegments[segs_List] will stitch together a list of line 
segments into one line segment. One must be careful with the order of 
the \
segments and the order of the points within each segment. The segs list 
is \
Flattened as the first step."\)], "Print"]
}, Open  ]],

So here we assemble our curve by drawing the two line segments 
separately and \
stitching them together.\
\>", "Text"],

              par1[t] // Evaluate, {t, \(-\ at 3\), \ at 3}],
            ParametricDraw[par2[t] // Evaluate, {t, \(-\ at 3\), \ at 3}] /.
              Line[a_] \[RuleDelayed] Line[Reverse[a]]}];\)\)], 

Now it is a simple matter to draw the colored area and outline it in 
\>", "Text"],

        Graphics[\n\t\t{LightBlue, curve /. Line \[Rule] Polygon, Black, 

            curve}], \n\nAspectRatio \[Rule] Automatic,
        PlotRange \[Rule] {{\(-10\), 10}, {\(-10\), 10}}/2,
        Background \[Rule] Linen, \n{}];\)\)], "Input",
}, Closed]],


For a region where FilledPlot can be used in a different coordinate 
\>", "Section"],

Sometimes we can use a different coordinate system where FilledPlot will 
work \
for the filling of the areas between two  curve. For example, to color 
the \
area inside of a cardioid, but outside a unit circle, we can do a 
FilledDraw \
in the \[Theta]-r plane. Then we can use the DrawingTransform routine 
from \
DrawingPaper to transform to an x-y representation.\
\>", "Text"],


    \(\(?DrawingTransform\)\)], "Input"],

    \("DrawingTransform[f1, f2], where f1 and f2 are function names, is 
a \
rule which applies the following transformation to all points in the 
graphics \
object: {x_?NumberQ, y_?NumberQ} \[Rule] {f1[x, y], f2[x, y]}."\)], 
}, Open  ]],

  "This shows how ",
  " can often be used to simplify the filling of areas. We make an 
\[Theta]-r \
plot and then transform to rectangular coordinates. Don't mix up the 
order of \
\[Theta] and r! DrawPolarR is the DrawingPaper version of PolarPlot and 
is \
used to outline the regions."
}], "Text"],

                  1 + Cos[\[Theta]]}, {\[Theta], \(-\[Pi]\)/2, \[Pi]/2}, 

                Fills \[Rule] LightSteelBlue, \ Curves \[Rule] None,
                PlotPoints \[Rule] 31] /.
              DrawingTransform[Function[{\[Theta], r}, r\ 
                Function[{\[Theta], r}, r\ Sin[\[Theta]]]], 
              1 + Cos[\[Theta]], {\[Theta], 0, 2  \[Pi]},
              PlotPoints \[Rule] 31], \n\t\tDrawPolarR[
              1, {\[Theta], 0, 2  \[Pi]}]}], \n\n
        AspectRatio \[Rule] Automatic,
        PlotRange \[Rule] {{\(-1.501\), 2.5}, {\(-2\), 2}},
        Background \[Rule] Linen, \n{Frame \[Rule] True,
          FrameLabel \[Rule] {x, y}}];\)\)], "Input"]
}, Closed]]
}, Open  ]]
FrontEndVersion->"4.0 for Microsoft Windows",
ScreenRectangle->{{0, 1280}, {0, 943}},
WindowSize->{660, 763},
WindowMargins->{{0, Automatic}, {Automatic, 0}}

Cached data follows.  If you edit this Notebook file directly, not using
Mathematica, you must remove the line containing CacheID at the top of
the file.  The cache data will then be recreated when you save this file 

from within Mathematica.




Cell[1739, 51, 41, 0, 115, "Title"],
Cell[1783, 53, 90, 4, 122, "Subtitle"],
Cell[1876, 59, 434, 10, 71, "Text"],
Cell[2313, 71, 206, 3, 70, "Input"],

Cell[2544, 78, 37, 0, 59, "Section"],
Cell[2584, 80, 131, 3, 33, "Text"],
Cell[2718, 85, 122, 2, 30, "Input"],
Cell[2843, 89, 236, 4, 52, "Text"],
Cell[3082, 95, 420, 9, 150, "Input"]
}, Closed]],

Cell[3539, 109, 55, 0, 39, "Section"],
Cell[3597, 111, 165, 3, 52, "Text"],
Cell[3765, 116, 129, 2, 52, "Input"],
Cell[3897, 120, 56, 0, 33, "Text"],

Cell[3978, 124, 64, 1, 30, "Input"],
Cell[4045, 127, 73, 1, 32, "Output"]
}, Open  ]],
Cell[4133, 131, 76, 0, 33, "Text"],
Cell[4212, 133, 320, 7, 135, "Input"],
Cell[4535, 142, 521, 8, 109, "Text"],

Cell[5081, 154, 56, 1, 30, "Input"],
Cell[5140, 157, 284, 4, 82, "Print"]
}, Open  ]],
Cell[5439, 164, 128, 3, 33, "Text"],
Cell[5570, 169, 276, 5, 77, "Input"],
Cell[5849, 176, 99, 2, 33, "Text"],
Cell[5951, 180, 299, 6, 130, "Input"]
}, Closed]],

Cell[6287, 191, 101, 2, 39, "Section"],
Cell[6391, 195, 388, 6, 71, "Text"],

Cell[6804, 205, 54, 1, 30, "Input"],
Cell[6861, 208, 246, 3, 63, "Print"]
}, Open  ]],
Cell[7122, 214, 361, 8, 71, "Text"],
Cell[7486, 224, 785, 14, 190, "Input"]
}, Closed]]
}, Open  ]]

End of Mathematica Notebook file.

  • Prev by Date: Re: Random Geometric (long)
  • Next by Date: matrices, dot products and convergents of continued fractions
  • Previous by thread: Color Fill areas in 2D graphic
  • Next by thread: Re: Color Fill areas in 2D graphic