File:DistrPolytopeR2.pdf
Summary
| 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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