tkf on 04/13/08

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# PSTrick: Manifold and Tangent Space

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\documentclass[12pt]{article}\usepackage{pstricks} % To use the standard "xcolor" package with PSTricks%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Draw manifold and tangent sapce %%%%%%%%%%%\newcommand{\ManAndTan}[6]{% \rput(#1){% % Manifold ã¨ Tangent Space ã¯ãã‚Œãžã‚ŒäºŒå›žæç”»ã—ã¦ã‚‹ã®ã§å¤‰æ›´ã®æ™‚ã¯æ³¨æ„   % Manifold   \psccurve[framearc=0.3,             fillstyle=solid,             fillcolor=lightgray]%èƒŒæ™¯è‰²	     (-1,-1)(0,-1.5)(2,-1.2)(2.6,-0.4)(1,2)(-1,1)   % Tangent Space   \pspolygon[fillstyle=solid,              fillcolor=white,%èƒŒæ™¯è‰²	      linestyle=none]	      (-1,0)(0,-1)(2.5,1.5)(1.5,2.5)   % Draw curve on the manifold   \begin{psclip}{% No background and no line    \psccurve[framearc=0.3,               linestyle=none]              (-1,-1)(0,-1.5)(2,-1.2)(2.6,-0.4)(1,2)(-1,1)    }    \psbezier[linecolor=gray](-1,-1)(0,0)(2,2)(2,-2)% cliped curve   \end{psclip}   % Tangent Space   \pspolygon(-1,0)(0,-1)(2.5,1.5)(1.5,2.5)   % Tangent Vector   \psline[linewidth=2pt]{*->}(0,0)(1.5,1.5)   % æ–‡å­—   \rput(-0.8, 1.7){#2}% M   \rput( 2.5, 2.2){#3}% T_m M   \rput( 1  , 1.4){#4}% v   \rput( 1.6,-0.5){#5}% c(t)   \rput(-0.4, 0  ){#6}% m }}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Draw chat on Euclid space %%%%%%%%%%%%%%%%%\newcommand{\EuclidSpace}[4]{% \rput(#1){%  \psline{->}(-1,0)(2,0)  \psline{->}(0,-1)(0,2)   \begin{psclip}{% No background and no line    \psccurve[framearc=0.3](-0.5,-0.5)(0.5,-0.8)(1.5,0)(1.1,1.4)(-0.5,1)    }    \psbezier[linecolor=lightgray](-1,-1)(0,0)(2,2)(2,-2)% cliped curve   \end{psclip}  \rput(0.4,2.2){#2}  \rput(1.5,1.5){#3}  \rput(0.7,0.7){#4} }}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\pagestyle{empty}\begin{document} \psset{linewidth=1pt,arrowsize=0.2}%,showpoints=true} \begin{pspicture}*(-2,-2)(11,11) % TM \ManAndTan{0,3}{$M$}{$T_m M$}{$v$}{$c(t)$}{$m$} \ManAndTan{5,7}{$N$}{$T_n N$}{$w$}{$f \circ c(t)$}{$n$} \ManAndTan{8,3}{$P$}{$T_p P$}{}{$g \circ f \circ c(t)$}{$p$} % R^m \EuclidSpace{0,8}{$R^m$}{$U$}{$\varphi(c(t))$} % R \psline{->}(-1,0)(2,0) \rput(2.2,0.3){$t \in R$} % ç·šç¨®ã‚’dashedã«è¨­å®š. ä»¥ä¸‹ã§æãçŸ¢å°ã«é©ç”¨ \psset{linestyle=dashed} % -> \phi \pscurve{->}(0,3)(-0.5,5.5)(0,8) \rput(-0.2,6){$\varphi$} % c(t) \pscurve{->}(0,0)(-0.2,1)(0,3) \rput(0.1,1){$c$} % f \pscurve{->}(0,3)(4,4)(5,7) \pscurve{->}(5,7)(6.5,5)(8,3) \rput(4,3.5){$f$} \rput(6.5,4.6){$g$} % g \pscurve{->}(1,4)(3,7)(6,8) \pscurve{->}(6,8)(8.4,6.5)(9,4) \rput(2.3,7){$T_m f$} \rput(8.2,6){$T_n g$} % ã‚°ãƒªãƒƒãƒ‰ã‚’æã %\psgrid(0,0)(-2,-2)(11,11)\end{pspicture} \end{document}