tikz-comandes.tex

   1 % Codi per a plans
   2 % De http://tex.stackexchange.com/questions/19972/draw-a-plane-in-space-and-a-coordinate-system-using-tikz
   3 \makeatletter
   4
   5 % Set some defaults
   6 \tikzset{
   7     plane max x/.initial=2,
   8     plane max y/.initial=2,
   9     plane max z/.initial=2
  10 }
  11
  12 \tikzset{plane/.style={fill opacity=0.5}}
  13
  14 % Define a plane.
  15 % #1 = name of the plane
  16 % #2*x + #3*y + #4*z = #5 is the equation of the plane
  17 \newcommand*\definePlaneByEquation[5]{
  18     \expandafter\gdef\csname tsx@plane@#1\endcsname{
  19         \def\tsx@plane@xcoeff{#2}
  20         \def\tsx@plane@ycoeff{#3}
  21         \def\tsx@plane@zcoeff{#4}
  22         \def\tsx@plane@scalar{#5}
  23     }
  24 }
  25
  26 % Draw a plane.
  27 % The optional first argument is passed as options to TikZ.
  28 % The mandatory second argument is the name of the plane.
  29 \newcommand\drawPlane[2][]{
  30     \tikzset{plane max x/.get=\tsx@plane@maxx}
  31     \tikzset{plane max y/.get=\tsx@plane@maxy}
  32     \tikzset{plane max z/.get=\tsx@plane@maxz}
  33     \csname tsx@plane@#2\endcsname
  34
  35     \ifdim\tsx@plane@xcoeff pt=0pt
  36         \ifdim\tsx@plane@ycoeff pt=0pt
  37             \ifdim\tsx@plane@zcoeff pt=0pt
  38                 %invalid plane
  39             \else % x=0, y=0
  40                 \filldraw[plane,#1,shift={(0,0,\tsx@plane@scalar/\tsx@plane@zcoeff)}]
  41                     (0,0,0) --
  42                     (\tsx@plane@maxx,0,0) --
  43                     (\tsx@plane@maxx,\tsx@plane@maxy,0) --
  44                     (0,\tsx@plane@maxy,0) --
  45                     cycle;
  46             \fi
  47         \else % x=0, y != 0
  48             \ifdim\tsx@plane@zcoeff pt=0pt % x=0, z=0
  49                 \filldraw[plane,#1,shift={(0,\tsx@plane@scalar/\tsx@plane@ycoeff,0)}]
  50                     (0,0,0) --
  51                     (\tsx@plane@maxx,0,0) --
  52                     (\tsx@plane@maxx,0,\tsx@plane@maxz) --
  53                     (0,0,\tsx@plane@maxz) --
  54                     cycle;
  55             \else % x=0
  56                 \filldraw[plane,#1]
  57                     (0,\tsx@plane@scalar/\tsx@plane@ycoeff,0) --
  58                     (0,0,\tsx@plane@scalar/\tsx@plane@zcoeff) --
  59                     (\tsx@plane@maxx,0,\tsx@plane@scalar/\tsx@plane@zcoeff) --
  60                     (\tsx@plane@maxx,\tsx@plane@scalar/\tsx@plane@ycoeff,0) --
  61                     cycle;
  62             \fi
  63         \fi
  64     \else % x!=0
  65         \ifdim\tsx@plane@ycoeff pt=0pt % x!=0,y=0
  66             \ifdim\tsx@plane@zcoeff pt=0pt % x!=0,y=0,z=0
  67                 \filldraw[plane,#1,shift={(\tsx@plane@scalar/\tsx@plane@xcoeff,0,0)}]
  68                     (0,0,0) --
  69                     (0,0,\tsx@plane@maxz) --
  70                     (0,\tsx@plane@maxy,\tsx@plane@maxz) --
  71                     (0,\tsx@plane@maxy,0) --
  72                     cycle;
  73             \else % x!=0,y=0,z!=0
  74                 \filldraw[plane,#1]
  75                     (\tsx@plane@scalar/\tsx@plane@xcoeff,0) --
  76                     (0,0,\tsx@plane@scalar/\tsx@plane@zcoeff) --
  77                     (0,\tsx@plane@maxy,\tsx@plane@scalar/\tsx@plane@zcoeff) --
  78                     (\tsx@plane@scalar/\tsx@plane@xcoeff,\tsx@plane@maxy,0) --
  79                     cycle;
  80             \fi
  81         \else % x!=0,y!=0
  82             \ifdim\tsx@plane@zcoeff pt=0pt % x!=0,y!=0,z=0
  83                 \filldraw[plane,#1]
  84                     (\tsx@plane@scalar/\tsx@plane@xcoeff,0) --
  85                     (0,\tsx@plane@scalar/\tsx@plane@ycoeff,0) --
  86                     (0,\tsx@plane@scalar/\tsx@plane@ycoeff,\tsx@plane@maxz) --
  87                     (\tsx@plane@scalar/\tsx@plane@xcoeff,0,\tsx@plane@maxz) --
  88                     cycle;
  89             \else % x!=0,y!=0,z!=0
  90                 \filldraw[plane,#1]
  91                     (\tsx@plane@scalar/\tsx@plane@xcoeff,0,0) --
  92                     (0,\tsx@plane@scalar/\tsx@plane@ycoeff,0) --
  93                     (0,0,\tsx@plane@scalar/\tsx@plane@zcoeff) --
  94                     cycle;
  95             \fi
  96         \fi
  97     \fi
  98 }
  99
 100 % Define a point.
 101 % #1 = name of the point
 102 % (#2,#3,#4) is the location.
 103 % Also creates a coordinate node of name #1 at the location.
 104 \newcommand\definePointByXYZ[4]{
 105     \coordinate (#1) at (#2,#3,#4);
 106     \expandafter\gdef\csname tsx@point@#1\endcsname{
 107         \def\tsx@point@x{#2}
 108         \def\tsx@point@y{#3}
 109         \def\tsx@point@z{#4}
 110     }
 111 }
 112
 113 % Project a point to a plane.
 114 % #1 = name of the new point
 115 % #2 = name of old point
 116 % #3 = name of plane
 117 \newcommand\projectPointToPlane[3]{{
 118     \csname tsx@point@#2\endcsname
 119     \csname tsx@plane@#3\endcsname
 120
 121     % square of norm of the normal vector
 122     \pgfmathparse{\tsx@plane@xcoeff*\tsx@plane@xcoeff + \tsx@plane@ycoeff*\tsx@plane@ycoeff + \tsx@plane@zcoeff*\tsx@plane@zcoeff}
 123     \let\nnormsq\pgfmathresult
 124
 125     % Calculate distance in terms of the (non-normalized) normal vector
 126     \pgfmathparse{(\tsx@point@x*\tsx@plane@xcoeff + \tsx@point@y*\tsx@plane@ycoeff + \tsx@point@z*\tsx@plane@zcoeff - \tsx@plane@scalar) / \nnormsq}
 127     \let\distance\pgfmathresult
 128
 129     % Calculate point
 130     \pgfmathparse{\tsx@point@x - \distance*\tsx@plane@xcoeff}
 131     \let\x\pgfmathresult
 132     \pgfmathparse{\tsx@point@y - \distance*\tsx@plane@ycoeff}
 133     \let\y\pgfmathresult
 134     \pgfmathparse{\tsx@point@z - \distance*\tsx@plane@zcoeff}
 135     \let\z\pgfmathresult
 136
 137     \definePointByXYZ{#1}{\x}{\y}{\z}
 138 }}
 139 \makeatother