AmatureQ: clipping graphics? Small .nb attached

• To: mathgroup at smc.vnet.net
• Subject: [mg22869] AmatureQ: clipping graphics? Small .nb attached
• From: "Steven T. Hatton" <hattons at cpkwebser5.ncr.disa.mil>
• Date: Sun, 2 Apr 2000 15:33:38 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Note: Please don't flame me if I did a no-no by attaching a notebook.  I
looked on the Mathematica site for pointers on how to send notebooks, and they
suggested attachments to mail.  If this is undesirable, I will
discontinue this practice.

The listing below generates a manifold of square parallel pipettes.  I
would like to know if there is a way to "clip the wings" on this thing.
That is, can I restrict the range of the ParametricPlot3D so that the
internal plane segments do not protrude from the surface of the largest
square?  I attempted to use notation such as, "/;  j -size  -1 <= x <=
size + 1 -j, to restrict the range of evaluation on the chamber
formula.  I couldn't get it to work.  If anybody has an answer to this
specific question I would be grateful if you would share it.

If you know of a more eloquent way of generating this whole thing, that
would also be appreciated.  Sorry if my Mathematica code looks like my little
sister's preschool scribble.  I am just an armchair mathematician.

TIA,

Steve

Clear[x, size, ySize, layers, distort, \[Alpha], n, flip, dispUp,
dispDown, \
foundation, sign, position, j, chamber, hive]
size = 6;
ySize = \[Pi] size;
\[Alpha] = .2;
n = 1;
layers = 6;

distort[n_, \[Theta]_, \[Alpha]_] := \[Alpha]  Sin[n \[Theta]];

flip[x_] := 0  /; x < 0;
flip[x_] := 1 /; x >= 0;
dispUp[x_, n_, \[Theta]_, \[Alpha]_] =
flip[x] distort[n, \[Theta], \[Alpha]];

unFlip[x_] := 1 /; x < 0;
unFlip[x_] := 0 /; x >= 0;
dispDown[x_, n_, \[Theta]_, \[Alpha]_] =
unFlip[x] distort[n, \[Theta], \[Alpha]];

SetOptions[ParametricPlot3D, PlotPoints -> {11, 11}];

foundation[sign_, x_, n_, y_, \[Alpha]_, position_] :=
sign  Abs[x] + dispUp[x, n, y, \[Alpha]] +
dispDown[x, n, y, \[Alpha]] +
position;

chamber[x_, n_, y_, \[Alpha]_, j_] := If[ OddQ[j],
{x, y, foundation[1, x, n, y, \[Alpha], j - 1]},
{x, y, foundation[-1, x, n, y, \[Alpha], j ]}]

hive[x_, n_, y_, \[Alpha]_] =
Table[chamber[x, n, y, \[Alpha], j], {j, 1, 2 size}]

hiveG = Graphics3D[
{
(*EdgeForm[], *)
First[ParametricPlot3D[
Evaluate[hive[x, n, y, \[Alpha]]],
{x, -size, size},
{y, 0, ySize} ,
BoxRatios -> {1, 1, 1},
DisplayFunction -> Identity]
]
}
];
Show[ hiveG]

(***********************************************************************

Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 4.0,
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***********************************************************************)

(*CacheID: 232*)

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(*WindowFrame->Normal*)

Notebook[{
Cell[BoxData[{
\(Clear[x, size, ySize, layers, distort, \[Alpha], n, flip, dispUp,
dispDown, foundation, sign, position, j, chamber,
hive]\), "\[IndentingNewLine]",
\(\(size\  = 6;\)\), "\n",
\(\(ySize = \ \[Pi]\ size;\)\), "\n",
\(\(\[Alpha]\  = \  .2;\)\), "\n",
\(\(n\  = \ 1;\)\), "\[IndentingNewLine]",
\(\(layers = 6;\)\n\), "\n",
\(\(distort[
n_, \[Theta]_, \[Alpha]_]\  := \ \[Alpha]\ \ Sin[
n\ \[Theta]];\)\[IndentingNewLine]\), "\n",
\(\(flip[x_] := 0\ \  /; x < 0;\)\), "\n",
\(\(flip[x_] := \ 1\  /; x\  \[GreaterEqual] \ 0;\)\), "\n",
\(\(dispUp[x_, n_, \ \[Theta]_, \ \[Alpha]_]\  = \
flip[x]\ distort[
n, \ \[Theta], \ \[Alpha]];\)\ \[IndentingNewLine]\), "\n",
\(\(unFlip[x_] := 1\  /; x < 0;\)\), "\n",
\(\(unFlip[x_] := \ 0\  /; x\  \[GreaterEqual] \ 0;\)\), "\n",
\(\(dispDown[x_, n_, \ \[Theta]_, \ \[Alpha]_]\  =
unFlip[x]\ distort[
n, \ \[Theta], \ \[Alpha]];\)\[IndentingNewLine]\
\[IndentingNewLine]\), "\n",
\(\(SetOptions[ParametricPlot3D,
PlotPoints \[Rule] {11, 11}];\)\n\), "\[IndentingNewLine]",
\(\(foundation[sign_, x_, n_, y_, \[Alpha]_, \
position_]\  := \ \[IndentingNewLine]sign\ \ Abs[x]\  + \
dispUp[x, n, y, \[Alpha]]\  + \ \[IndentingNewLine]dispDown[x, n,
y, \[Alpha]]\  + \ \[IndentingNewLine]position;\)\
\[IndentingNewLine]\[IndentingNewLine]\), "\[IndentingNewLine]",
\(chamber[x_, n_, y_, \[Alpha]_, j_]\  :=
If[\ OddQ[j], \ \[IndentingNewLine]{x, \ y,
foundation[1, x, n, y, \[Alpha], \
j - 1]}, \[IndentingNewLine]{x, \ y,
foundation[\(-1\), x, n, y, \[Alpha], \
j\ ]}]\[IndentingNewLine]\[IndentingNewLine]\), "\
\[IndentingNewLine]",
\(hive[x_, n_, y_, \[Alpha]_]\  = \
Table[chamber[x, n, y, \[Alpha], j], \ {j, 1,
2\ size}]\[IndentingNewLine]\[IndentingNewLine]\), "\n",
\(\(hiveG\  =
Graphics3D[\[IndentingNewLine]{\ \[IndentingNewLine] (*\(EdgeForm[]\)\
\(,\)\ *) \[IndentingNewLine]First[
ParametricPlot3D[\[IndentingNewLine]Evaluate[
hive[x, n, y, \[Alpha]]], \[IndentingNewLine]{x, \(-size\),
size}, \[IndentingNewLine]{y, 0,
ySize}\ , \[IndentingNewLine]BoxRatios \[Rule] {1, 1,
1}, \[IndentingNewLine]DisplayFunction\  \[Rule] \
Identity]\[IndentingNewLine]]\[IndentingNewLine]}\
\[IndentingNewLine]];\)\), "\n",
\(Show[\ hiveG]\)}], "Input"]
},
FrontEndVersion->"4.0 for X",
ScreenRectangle->{{0, 1600}, {0, 1200}},
WindowSize->{520, 600},
WindowMargins->{{414, Automatic}, {Automatic, 202}}
]

(***********************************************************************
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.
***********************************************************************)

(*CellTagsOutline
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(*CellTagsIndex
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Notebook[{
Cell[1717, 49, 2609, 50, 795, "Input"]
}
]
*)

(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)

--------------E76D2AEC5FC69C18E68400A2
filename="boxample.nb"

(***********************************************************************

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.

applications, contact Wolfram Research:
web: http://www.wolfram.com
email: info at wolfram.com
phone: +1-217-398-0700 (U.S.)

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

(*CacheID: 232*)

(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[      4330,        101]*)
(*NotebookOutlinePosition[      4972,        124]*)
(*  CellTagsIndexPosition[      4928,        120]*)
(*WindowFrame->Normal*)

Notebook[{
Cell[BoxData[{
\(Clear[x, size, ySize, layers, distort, \[Alpha], n, flip, dispUp,
dispDown, foundation, sign, position, j, chamber,
hive]\), "\[IndentingNewLine]",
\(\(size\  = 6;\)\), "\n",
\(\(ySize = \ \[Pi]\ size;\)\), "\n",
\(\(\[Alpha]\  = \  .2;\)\), "\n",
\(\(n\  = \ 1;\)\), "\[IndentingNewLine]",
\(\(layers = 6;\)\n\), "\n",
\(\(distort[
n_, \[Theta]_, \[Alpha]_]\  := \ \[Alpha]\ \ Sin[
n\ \[Theta]];\)\[IndentingNewLine]\), "\n",
\(\(flip[x_] := 0\ \  /; x < 0;\)\), "\n",
\(\(flip[x_] := \ 1\  /; x\  \[GreaterEqual] \ 0;\)\), "\n",
\(\(dispUp[x_, n_, \ \[Theta]_, \ \[Alpha]_]\  = \
flip[x]\ distort[
n, \ \[Theta], \ \[Alpha]];\)\ \[IndentingNewLine]\), "\n",
\(\(unFlip[x_] := 1\  /; x < 0;\)\), "\n",
\(\(unFlip[x_] := \ 0\  /; x\  \[GreaterEqual] \ 0;\)\), "\n",
\(\(dispDown[x_, n_, \ \[Theta]_, \ \[Alpha]_]\  =
unFlip[x]\ distort[
n, \ \[Theta], \ \[Alpha]];\)\[IndentingNewLine]\
\[IndentingNewLine]\), "\n",
\(\(SetOptions[ParametricPlot3D,
PlotPoints \[Rule] {11, 11}];\)\n\), "\[IndentingNewLine]",
\(\(foundation[sign_, x_, n_, y_, \[Alpha]_, \
position_]\  := \ \[IndentingNewLine]sign\ \ Abs[x]\  + \
dispUp[x, n, y, \[Alpha]]\  + \ \[IndentingNewLine]dispDown[x, n,
y, \[Alpha]]\  + \ \[IndentingNewLine]position;\)\
\[IndentingNewLine]\[IndentingNewLine]\), "\[IndentingNewLine]",
\(chamber[x_, n_, y_, \[Alpha]_, j_]\  :=
If[\ OddQ[j], \ \[IndentingNewLine]{x, \ y,
foundation[1, x, n, y, \[Alpha], \
j - 1]}, \[IndentingNewLine]{x, \ y,
foundation[\(-1\), x, n, y, \[Alpha], \
j\ ]}]\[IndentingNewLine]\[IndentingNewLine]\), "\
\[IndentingNewLine]",
\(hive[x_, n_, y_, \[Alpha]_]\  = \
Table[chamber[x, n, y, \[Alpha], j], \ {j, 1,
2\ size}]\[IndentingNewLine]\[IndentingNewLine]\), "\n",
\(\(hiveG\  =
Graphics3D[\[IndentingNewLine]{\ \[IndentingNewLine] (*\(EdgeForm[]\)\
\(,\)\ *) \[IndentingNewLine]First[
ParametricPlot3D[\[IndentingNewLine]Evaluate[
hive[x, n, y, \[Alpha]]], \[IndentingNewLine]{x, \(-size\),
size}, \[IndentingNewLine]{y, 0,
ySize}\ , \[IndentingNewLine]BoxRatios \[Rule] {1, 1,
1}, \[IndentingNewLine]DisplayFunction\  \[Rule] \
Identity]\[IndentingNewLine]]\[IndentingNewLine]}\
\[IndentingNewLine]];\)\), "\n",
\(Show[\ hiveG]\)}], "Input"]
},
FrontEndVersion->"4.0 for X",
ScreenRectangle->{{0, 1600}, {0, 1200}},
WindowSize->{520, 600},
WindowMargins->{{414, Automatic}, {Automatic, 202}}
]

(***********************************************************************
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.
***********************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
*)

(*NotebookFileOutline
Notebook[{
Cell[1717, 49, 2609, 50, 795, "Input"]
}
]
*)

(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)

--------------E76D2AEC5FC69C18E68400A2--

```

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