File:DistrPolytopeR2.pdf
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Summary
[edit]| Description |
English: Two-dimensional example of a en:distributive polytope. The polygon (1,1) / (2,5) / (3,6) / (7,7) / (6,3) / (2,2) / (1,1) is not convex, but satisfies the definition from Felsner.Knauer.2019[1] p.45.
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| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions |
Nonconvex: File:DistrPolytopeR2.pdf - File:DistrPolytopeR2 svg.svg Convex: File:convexDistrPolytopeR2.pdf - File:convexDistrPolytopeR2 svg.svg |
LaTeX source
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\documentclass[12pt]{article}
\usepackage[pdftex]{color}
\usepackage[paperwidth=85mm,paperheight=85mm]{geometry}
\usepackage{amssymb}
\usepackage{amsmath}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{85mm}
\setlength{\textheight}{85mm}
\setlength{\oddsidemargin}{-2.5cm}
\setlength{\parindent}{0cm}
\setlength{\unitlength}{1mm}
% colors
\definecolor{bAllowed} {rgb}{0.90,0.99,0.90}
\definecolor{bForbidden} {rgb}{0.99,0.90,0.90}
\definecolor{fCross} {rgb}{0.99,0.99,0.99}
\definecolor{fConn} {rgb}{0.80,0.80,0.80}
\definecolor{fRect} {rgb}{0.99,0.80,0.80}
\definecolor{fAxis} {rgb}{0.00,0.00,0.99}
\newcommand{\cross}[2]{%
\textcolor{bAllowed}{\put(#1,#2){\makebox(0,0)[tr]{\rule{2mm}{2mm}}}}%
\textcolor{bAllowed}{\put(#1,#2){\makebox(0,0)[bl]{\rule{2mm}{2mm}}}}%
\textcolor{bForbidden}{\put(#1,#2){\makebox(0,0)[br]{\rule{2mm}{2mm}}}}%
\textcolor{bForbidden}{\put(#1,#2){\makebox(0,0)[tl]{\rule{2mm}{2mm}}}}%
\textcolor{fCross}{\put(#1,#2){\put(-3,0){\line(1,0){6}}}}%
\textcolor{fCross}{\put(#1,#2){\put(0,-3){\line(0,1){6}}}}%
}
\begin{document}
\begin{picture}(80,80)
% horizontal axis
\textcolor{fAxis}{\put(5,5){\vector(1,0){75}}}%
\textcolor{fAxis}{\multiput(5,5)(10,0){8}{\line(0,-1){1}}}%
\textcolor{fAxis}{\put( 5,3){\makebox(0,0)[t]{$\scriptstyle 0$}}}%
\textcolor{fAxis}{\put(15,3){\makebox(0,0)[t]{$\scriptstyle 1$}}}%
\textcolor{fAxis}{\put(25,3){\makebox(0,0)[t]{$\scriptstyle 2$}}}%
\textcolor{fAxis}{\put(35,3){\makebox(0,0)[t]{$\scriptstyle 3$}}}%
\textcolor{fAxis}{\put(45,3){\makebox(0,0)[t]{$\scriptstyle 4$}}}%
\textcolor{fAxis}{\put(55,3){\makebox(0,0)[t]{$\scriptstyle 5$}}}%
\textcolor{fAxis}{\put(65,3){\makebox(0,0)[t]{$\scriptstyle 6$}}}%
\textcolor{fAxis}{\put(75,3){\makebox(0,0)[t]{$\scriptstyle 7$}}}%
% vertical axis
\textcolor{fAxis}{\put(5,5){\vector(0,1){75}}}%
\textcolor{fAxis}{\multiput(5,5)(0,10){8}{\line(-1,0){1}}}%
\textcolor{fAxis}{\put(3, 5){\makebox(0,0)[r]{$\scriptstyle 0$}}}%
\textcolor{fAxis}{\put(3,15){\makebox(0,0)[r]{$\scriptstyle 1$}}}%
\textcolor{fAxis}{\put(3,25){\makebox(0,0)[r]{$\scriptstyle 2$}}}%
\textcolor{fAxis}{\put(3,35){\makebox(0,0)[r]{$\scriptstyle 3$}}}%
\textcolor{fAxis}{\put(3,45){\makebox(0,0)[r]{$\scriptstyle 4$}}}%
\textcolor{fAxis}{\put(3,55){\makebox(0,0)[r]{$\scriptstyle 5$}}}%
\textcolor{fAxis}{\put(3,65){\makebox(0,0)[r]{$\scriptstyle 6$}}}%
\textcolor{fAxis}{\put(3,75){\makebox(0,0)[r]{$\scriptstyle 7$}}}%
% allowed/forbidden direction indicators
\cross{15}{15}%
\cross{25}{55}%
\cross{35}{65}%
\cross{75}{75}%
\cross{65}{35}%
\cross{25}{25}%
% worst-case rectangles wrt. interior connections
\textcolor{fRect}{\put(25.000,55.000){\line(1,0){40.000}}}%
\textcolor{fRect}{\put(25.000,55.000){\line(0,-1){20.000}}}%
\textcolor{fRect}{\put(65.000,35.000){\line(-1,0){40.000}}}%
%
\textcolor{fRect}{\put(35.000,65.000){\line(1,0){30.000}}}%
\textcolor{fRect}{\put(35.000,65.000){\line(0,-1){30.000}}}%
\textcolor{fRect}{\put(65.000,35.000){\line(0,1){30.000}}}%
% interior connections
\textcolor{fConn}{\put(15.000,15.000){\line(2,5){20.000}}}%
\textcolor{fConn}{\put(25.000,25.000){\line(1,1){50.000}}}%
\textcolor{fConn}{\put(15.000,15.000){\line(5,2){50.000}}}%
%
\textcolor{fConn}{\put(25.000,55.000){\line(5,2){50.000}}}%
\textcolor{fConn}{\put(25.000,55.000){\line(2,-1){40.000}}}%
\textcolor{fConn}{\put(25.000,55.000){\line(0,-1){30.000}}}%
%
\textcolor{fConn}{\put(35.000,65.000){\line(1,-1){30.000}}}%
\textcolor{fConn}{\put(35.000,65.000){\line(-1,-4){10.000}}}%
% polygon
\thicklines
\put(15.000,15.000){\circle*{1.000}}%
\put(15.000,15.000){\line(1,4){10.000}}%
\put(25.000,55.000){\circle*{1.000}}%
\put(25.000,55.000){\line(1,1){10.000}}%
\put(35.000,65.000){\circle*{1.000}}%
\put(35.000,65.000){\line(4,1){40.000}}%
\put(75.000,75.000){\circle*{1.000}}%
\put(75.000,75.000){\line(-1,-4){10.000}}%
\put(65.000,35.000){\circle*{1.000}}%
\put(65.000,35.000){\line(-4,-1){40.000}}%
\put(25.000,25.000){\circle*{1.000}}%
\put(25.000,25.000){\line(-1,-1){10.000}}%
\end{picture}
\end{document}
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[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 12:11, 14 November 2019 |  | 500 × 500 (24 KB) | Jochen Burghardt (talk | contribs) | User created page with UploadWizard |
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