[Date Index]
[Thread Index]
[Author Index]
Re: hatched regions, shading, and fills
*To*: mathgroup at smc.vnet.net
*Subject*: [mg124317] Re: hatched regions, shading, and fills
*From*: Chris Young <cy56 at comcast.net>
*Date*: Mon, 16 Jan 2012 17:15:44 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <j0trq5$d2s$1@smc.vnet.net>
On 2011-07-29 08:42:45 +0000, Sam McDermott said:
> Hi,
>
> After looking over some old threads, it looks like there is no elegant
> way to add hatch marked regions in the interior of a graphic. This is
> regrettable, because it would really simplify things for my particular
> task right now.
>
> However, are there other easily accessed directives that might give a
> similar result? For instance, filling in a region with polka dots?
> Adding diagonal lines? Filling with a very simple texture?
>
> Any help is much appreciated,
> Thanks,
> Sam
The following will at least fill a triangle with hatch lines, green if
the orientation is positive, red if negative.
The mesh lines are plotted parallel to the first side. A better way
might be to plot them perpendicular to an angle bisector of the
triangle.
It's a little slow, and it needs to have the hatch lines have the same
spacings no matter how the vertices of the triangle are moved around.
A notebook and screen shots are at:
http://home.comcast.net/~cy56/HatchLines.nb
http://home.comcast.net/~cy56/HatchLines1.png
http://home.comcast.net/~cy56/HatchLines2.png
Module[
{
x1, y1, x2, y2, x3, y3,
orient
},
Manipulate[
x1 = P[[1, 1]]; y1 = P[[1, 2]];
x2 = P[[2, 1]]; y2 = P[[2, 2]];
x3 = P[[3, 1]]; y3 = P[[3, 2]];
orient = Sign[Chop[Det[\!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"x1", "y1", "1"},
{"x2", "y2", "1"},
{"x3", "y3", "1"}
},
GridBoxAlignment->{
"Columns" -> {{Center}}, "ColumnsIndexed" -> {},
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}], "", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]\)]]];
Show[
Graphics[
{
FaceForm[], EdgeForm[], Polygon[P],
Blue, Line[{P[[1]], P[[2]]}],
Red, Line[{P[[2]], P[[3]]}],
Darker[Yellow, 0.3], Line[{P[[3]], P[[1]]}]
}
],
RegionPlot[
And @@ (If[orient > 0, Positive, Negative] /@ {Det[( {
{x1, x2, x},
{y1, y2, y},
{1, 1, 1}
} )], Det[( {
{x2, x3, x},
{y2, y3, y},
{1, 1, 1}
} )], Det[( {
{x3, x1, x},
{y3, y1, y},
{1, 1, 1}
} )] }),
{x, -2, 2}, {y, -2, 2},
ColorFunction -> (White &),
BoundaryStyle -> None,
Mesh -> Round[20 Norm[P[[2]] - P[[1]]], 1],
MeshStyle -> (Green // If[orient > 0, #, Red] &),
MeshFunctions -> {{x, y} \[Function] Det[( {
{x2, x3, x},
{y2, y3, y},
{1, 1, 1}
} )]},
PlotPoints -> 50
],
PlotRange -> 2,
Axes -> True,
GridLines -> Automatic
],
{{P, {{0, 0}, {1, 0}, {1, 1}}}, Locator}
]
]
Prev by Date:
**Re: How to check whether an infinite set is closed under addition?**
Next by Date:
**Re: How to check whether an infinite set is closed under addition?**
Previous by thread:
**Re: hatched regions, shading, and fills**
Next by thread:
**Re: without individual scaling?**
| |