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Need code to calculate the Lower Envelope for a set of (non collinear) points.
*To*: mathgroup at smc.vnet.net
*Subject*: [mg51409] Need code to calculate the Lower Envelope for a set of (non collinear) points.
*From*: gilmar.rodriguez at nwfwmd.state.fl.us (Gilmar Rodr?guez Pierluissi)
*Date*: Sat, 16 Oct 2004 04:20:45 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Dear Mathematica Solver Group:
I'm looking for a program to calculate the Lower Envelope
("LE" for short)for a set of (non-collinear) points on the
plane. Please download the following file containing an
arbitrary set of such points(which I'm calling "A") by
double-clicking the following shortcut:
http://gilmarlily.netfirms.com/download/A.txt
You can also down load:
http://gilmarlily.netfirms.com/download/Lower Envelope.nb
to evaluate the following steps using Mathematica (version 5):
If your define your working directory as C:\Temporary, then kindly
evaluate the following Mathematica commands:
In[1]: A = ReadList["C:\\Temporary\\A.txt", {Number, Number}];
Next, plot the set A:
In[2]: plt1 = ListPlot[A, PlotJoined -> True, PlotStyle -> {Hue[.7]}]
I can manipulate the program ConvexHull to find the Lower Envelope
for the set A as follows:
In[3]: << DiscreteMath`ComputationalGeometry`
In[4]: convexhull = ConvexHull[A]
The following input gives a picture of the Convex Hull:
In[5]: plt2 = ListPlot[Table[A[[convexhull[[i]]]], {i,
1, Length[convexhull]}], PlotJoined -> True, PlotStyle -> {Hue[.6]}]
Modifying the starting value of index i in In[5] above
(starting at i=96 instead of i=1) gives a picture of the
Lower Envelope of A:
In[6]:plt3 = ListPlot[Table[A[[convexhull[[i]]]], {i,
96, Length[convexhull]}], PlotJoined -> True, PlotStyle -> {Hue[.6]}]
In[7]: Show[plt1, plt3]
The Lower Envelope of A ("LEA" for short) is given by:
In[8]: LEA = Table[A[[convexhull[[i]]]], {i, 96, Length[convexhull]}]
So my question is: How can the code of the ConvexHull program be modified,
to get a program that calculates the LE of a set?
The following (clumsy)alternative attempt:
In[9]: LE[B_] := Module[{M}, {L = Length[B]; M = {};
AppendTo[M, B[[L]]]; {Xg, Yg} = B[[L]]; Do[If[B[[
L - i + 1]][[2]] < Yg, {{Xg, Yg} = B[[L -
i + 1]], AppendTo[M, B[[L - i + 1]]]}], {i, 1, L - 1}]}; Sort[M]]
In[10]: LE[A]
In[11]: plt4 = ListPlot[LE[A], PlotJoined -> True, PlotStyle -> {Hue[.1]}]
In[12]: Show[plt1, plt4]
gives me something that is "not even close, and no cigar".
What I need is an algorithm that gives me the Lower Envelope E of A
as shown in In[8] above. Thank you for your help!
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