Posted By

tkf on 04/13/08


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PSTrick: Manifold and Tangent Space


 / Published in: LaTeX
 

URL: http://arataka.wordpress.com/2008/04/13/pstrick%e3%81%a7%e5%a4%9a%e6%a7%98%e4%bd%93%e3%81%ae%e5%9b%b3/

PSTrickで書いた多様体の図

  1. \documentclass[12pt]{article}
  2. \usepackage{pstricks} % To use the standard "xcolor" package with PSTricks
  3. %
  4. %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Draw manifold and tangent sapce %%%%%%%%%%%
  5. \newcommand{\ManAndTan}[6]{%
  6. \rput(#1){%
  7. % Manifold と Tangent Space はそれぞれ二回描画してるので変更の時は注意
  8. % Manifold
  9. \psccurve[framearc=0.3,
  10. fillstyle=solid,
  11. fillcolor=lightgray]%背景色
  12. (-1,-1)(0,-1.5)(2,-1.2)(2.6,-0.4)(1,2)(-1,1)
  13. % Tangent Space
  14. \pspolygon[fillstyle=solid,
  15. fillcolor=white,%背景色
  16. linestyle=none]
  17. (-1,0)(0,-1)(2.5,1.5)(1.5,2.5)
  18. % Draw curve on the manifold
  19. \begin{psclip}{% No background and no line
  20. \psccurve[framearc=0.3,
  21. linestyle=none]
  22. (-1,-1)(0,-1.5)(2,-1.2)(2.6,-0.4)(1,2)(-1,1)
  23. }
  24. \psbezier[linecolor=gray](-1,-1)(0,0)(2,2)(2,-2)% cliped curve
  25. \end{psclip}
  26. % Tangent Space
  27. \pspolygon(-1,0)(0,-1)(2.5,1.5)(1.5,2.5)
  28. % Tangent Vector
  29. \psline[linewidth=2pt]{*->}(0,0)(1.5,1.5)
  30. % 文字
  31. \rput(-0.8, 1.7){#2}% M
  32. \rput( 2.5, 2.2){#3}% T_m M
  33. \rput( 1 , 1.4){#4}% v
  34. \rput( 1.6,-0.5){#5}% c(t)
  35. \rput(-0.4, 0 ){#6}% m
  36. }
  37. }%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  38. %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Draw chat on Euclid space %%%%%%%%%%%%%%%%%
  39. \newcommand{\EuclidSpace}[4]{%
  40. \rput(#1){%
  41. \psline{->}(-1,0)(2,0)
  42. \psline{->}(0,-1)(0,2)
  43. \begin{psclip}{% No background and no line
  44. \psccurve[framearc=0.3](-0.5,-0.5)(0.5,-0.8)(1.5,0)(1.1,1.4)(-0.5,1)
  45. }
  46. \psbezier[linecolor=lightgray](-1,-1)(0,0)(2,2)(2,-2)% cliped curve
  47. \end{psclip}
  48. \rput(0.4,2.2){#2}
  49. \rput(1.5,1.5){#3}
  50. \rput(0.7,0.7){#4}
  51. }
  52. }%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  53. \pagestyle{empty}
  54. \begin{document}
  55.  
  56. \psset{linewidth=1pt,arrowsize=0.2}%,showpoints=true}
  57.  
  58. \begin{pspicture}*(-2,-2)(11,11)
  59. % TM
  60. \ManAndTan{0,3}{$M$}{$T_m M$}{$v$}{$c(t)$}{$m$}
  61. \ManAndTan{5,7}{$N$}{$T_n N$}{$w$}{$f \circ c(t)$}{$n$}
  62. \ManAndTan{8,3}{$P$}{$T_p P$}{}{$g \circ f \circ c(t)$}{$p$}
  63. % R^m
  64. \EuclidSpace{0,8}{$R^m$}{$U$}{$\varphi(c(t))$}
  65. % R
  66. \psline{->}(-1,0)(2,0)
  67. \rput(2.2,0.3){$t \in R$}
  68. % 線種をdashedに設定. 以下で描く矢印に適用
  69. \psset{linestyle=dashed}
  70. % -> \phi
  71. \pscurve{->}(0,3)(-0.5,5.5)(0,8)
  72. \rput(-0.2,6){$\varphi$}
  73. % c(t)
  74. \pscurve{->}(0,0)(-0.2,1)(0,3)
  75. \rput(0.1,1){$c$}
  76. % f
  77. \pscurve{->}(0,3)(4,4)(5,7)
  78. \pscurve{->}(5,7)(6.5,5)(8,3)
  79. \rput(4,3.5){$f$}
  80. \rput(6.5,4.6){$g$}
  81. % g
  82. \pscurve{->}(1,4)(3,7)(6,8)
  83. \pscurve{->}(6,8)(8.4,6.5)(9,4)
  84. \rput(2.3,7){$T_m f$}
  85. \rput(8.2,6){$T_n g$}
  86. % グリッドを描く
  87. %\psgrid(0,0)(-2,-2)(11,11)
  88. \end{pspicture}
  89.  
  90. \end{document}

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