plotting multiple polygons

[Xiangdong Liu]

Hi again!

I have a set of points in ASCII file as follows:

x11 y11
x12 y12
....
x1n1 y1n1
x11 y11

x21 y21
x22 y22
....
x2n2 y2n2
x21 y21

x31 y31
x32 y32
....
x3n3 y3n3
x31 y31

....

Basically, there are multiple (and many many) groups of consecutive
lines of x and y coordinates of points, each group representing a
polygon and each group is separated by an empty line from other
groups.

I need to make one plot that shows all the polygons, unconnected one
another.

If I do the following, I would get a plot that shows all the polygons
connected one another.

In[1]:= polygons = ReadList["asciiFile",Table[Number,{2}]];
In[2]:= ListPlot[polygons, PlotJoined->True];

Any simple way to draw standalone polygons in one plot?

Thanks,

Xiangdong Liu

[Tom Burton]

Hi,

Consider a file temp.txt:

1 1
2 1
1 2
1 1

3 1
4 1
3 2
3 1

The first issue is to get Mathematica to include the blank lines in the processed input. I could not quickly get Mathematica to do this with Number, so I used Word instead and them converted the words to expressions:

In[27]:=
data1 = Map[ToExpression, ReadList["temp.txt",
Word, NullRecords -> True, RecordLists ->
True], {2}]

{{1, 1}, {2, 1}, {1, 2}, {1, 1}, {}, {3, 1},
{4, 1}, {3, 2}, {3, 1}, {}}

The next thing to do is to split the list into sublists, breaking at the empty lists:

In[28]:=
data2 = Split[data1, #1 != {} & ]

{{{1, 1}, {2, 1}, {1, 2}, {1, 1}, {}},
{{3, 1}, {4, 1}, {3, 2}, {3, 1}, {}}}

In[29]:=
data3 = (DeleteCases[#1, {}] & ) /@ data2

{{{1, 1}, {2, 1}, {1, 2}, {1, 1}},
{{3, 1}, {4, 1}, {3, 2}, {3, 1}}}

The Polygon[__] pattern does not include the repeated first point, so if you want to use Polygon, drop the first (or last) point from each sublist:

In[30]:=
data4 = Rest/@data3

{{{2, 1}, {1, 2}, {1, 1}}, {{4, 1}, {3, 2},
{3, 1}}}

Then to show filled polygons:

In[31]:=
Show[Graphics[Polygon /@ data4]];

To show unfilled polygons, you can use the low-level form

In[32]:=
Show[Graphics[Line /@ data3]];

The easiest high-level command to use is probably MultipleListPlot

In[33]:=
Needs["Graphics`MultipleListPlot`"]

I needed the PlotStyle Command to prevent MultipleListPlot from assigning various styles to the various polygons:

In[34]:=
MultipleListPlot[Sequence @@ data3,
PlotJoined -> True, PlotStyle -> Dashing[{}]];

Tom Burton

------

Tom