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139 lines
5.1 KiB
139 lines
5.1 KiB
% Codi per a plans
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% De http://tex.stackexchange.com/questions/19972/draw-a-plane-in-space-and-a-coordinate-system-using-tikz
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\makeatletter
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% Set some defaults
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\tikzset{
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plane max x/.initial=2,
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plane max y/.initial=2,
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plane max z/.initial=2
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}
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\tikzset{plane/.style={fill opacity=0.5}}
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% Define a plane.
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% #1 = name of the plane
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% #2*x + #3*y + #4*z = #5 is the equation of the plane
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\newcommand*\definePlaneByEquation[5]{
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\expandafter\gdef\csname tsx@plane@#1\endcsname{
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\def\tsx@plane@xcoeff{#2}
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\def\tsx@plane@ycoeff{#3}
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\def\tsx@plane@zcoeff{#4}
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\def\tsx@plane@scalar{#5}
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}
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}
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% Draw a plane.
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% The optional first argument is passed as options to TikZ.
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% The mandatory second argument is the name of the plane.
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\newcommand\drawPlane[2][]{
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\tikzset{plane max x/.get=\tsx@plane@maxx}
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\tikzset{plane max y/.get=\tsx@plane@maxy}
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\tikzset{plane max z/.get=\tsx@plane@maxz}
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\csname tsx@plane@#2\endcsname
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\ifdim\tsx@plane@xcoeff pt=0pt
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\ifdim\tsx@plane@ycoeff pt=0pt
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\ifdim\tsx@plane@zcoeff pt=0pt
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%invalid plane
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\else % x=0, y=0
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\filldraw[plane,#1,shift={(0,0,\tsx@plane@scalar/\tsx@plane@zcoeff)}]
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(0,0,0) --
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(\tsx@plane@maxx,0,0) --
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(\tsx@plane@maxx,\tsx@plane@maxy,0) --
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(0,\tsx@plane@maxy,0) --
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cycle;
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\fi
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\else % x=0, y != 0
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\ifdim\tsx@plane@zcoeff pt=0pt % x=0, z=0
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\filldraw[plane,#1,shift={(0,\tsx@plane@scalar/\tsx@plane@ycoeff,0)}]
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(0,0,0) --
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(\tsx@plane@maxx,0,0) --
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(\tsx@plane@maxx,0,\tsx@plane@maxz) --
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(0,0,\tsx@plane@maxz) --
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cycle;
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\else % x=0
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\filldraw[plane,#1]
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(0,\tsx@plane@scalar/\tsx@plane@ycoeff,0) --
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(0,0,\tsx@plane@scalar/\tsx@plane@zcoeff) --
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(\tsx@plane@maxx,0,\tsx@plane@scalar/\tsx@plane@zcoeff) --
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(\tsx@plane@maxx,\tsx@plane@scalar/\tsx@plane@ycoeff,0) --
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cycle;
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\fi
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\fi
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\else % x!=0
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\ifdim\tsx@plane@ycoeff pt=0pt % x!=0,y=0
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\ifdim\tsx@plane@zcoeff pt=0pt % x!=0,y=0,z=0
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\filldraw[plane,#1,shift={(\tsx@plane@scalar/\tsx@plane@xcoeff,0,0)}]
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(0,0,0) --
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(0,0,\tsx@plane@maxz) --
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(0,\tsx@plane@maxy,\tsx@plane@maxz) --
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(0,\tsx@plane@maxy,0) --
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cycle;
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\else % x!=0,y=0,z!=0
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\filldraw[plane,#1]
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(\tsx@plane@scalar/\tsx@plane@xcoeff,0) --
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(0,0,\tsx@plane@scalar/\tsx@plane@zcoeff) --
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(0,\tsx@plane@maxy,\tsx@plane@scalar/\tsx@plane@zcoeff) --
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(\tsx@plane@scalar/\tsx@plane@xcoeff,\tsx@plane@maxy,0) --
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cycle;
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\fi
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\else % x!=0,y!=0
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\ifdim\tsx@plane@zcoeff pt=0pt % x!=0,y!=0,z=0
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\filldraw[plane,#1]
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(\tsx@plane@scalar/\tsx@plane@xcoeff,0) --
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(0,\tsx@plane@scalar/\tsx@plane@ycoeff,0) --
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(0,\tsx@plane@scalar/\tsx@plane@ycoeff,\tsx@plane@maxz) --
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(\tsx@plane@scalar/\tsx@plane@xcoeff,0,\tsx@plane@maxz) --
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cycle;
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\else % x!=0,y!=0,z!=0
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\filldraw[plane,#1]
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(\tsx@plane@scalar/\tsx@plane@xcoeff,0,0) --
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(0,\tsx@plane@scalar/\tsx@plane@ycoeff,0) --
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(0,0,\tsx@plane@scalar/\tsx@plane@zcoeff) --
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cycle;
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\fi
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\fi
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\fi
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}
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% Define a point.
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% #1 = name of the point
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% (#2,#3,#4) is the location.
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% Also creates a coordinate node of name #1 at the location.
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\newcommand\definePointByXYZ[4]{
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\coordinate (#1) at (#2,#3,#4);
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\expandafter\gdef\csname tsx@point@#1\endcsname{
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\def\tsx@point@x{#2}
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\def\tsx@point@y{#3}
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\def\tsx@point@z{#4}
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}
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}
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% Project a point to a plane.
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% #1 = name of the new point
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% #2 = name of old point
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% #3 = name of plane
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\newcommand\projectPointToPlane[3]{{
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\csname tsx@point@#2\endcsname
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\csname tsx@plane@#3\endcsname
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% square of norm of the normal vector
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\pgfmathparse{\tsx@plane@xcoeff*\tsx@plane@xcoeff + \tsx@plane@ycoeff*\tsx@plane@ycoeff + \tsx@plane@zcoeff*\tsx@plane@zcoeff}
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\let\nnormsq\pgfmathresult
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% Calculate distance in terms of the (non-normalized) normal vector
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\pgfmathparse{(\tsx@point@x*\tsx@plane@xcoeff + \tsx@point@y*\tsx@plane@ycoeff + \tsx@point@z*\tsx@plane@zcoeff - \tsx@plane@scalar) / \nnormsq}
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\let\distance\pgfmathresult
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% Calculate point
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\pgfmathparse{\tsx@point@x - \distance*\tsx@plane@xcoeff}
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\let\x\pgfmathresult
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\pgfmathparse{\tsx@point@y - \distance*\tsx@plane@ycoeff}
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\let\y\pgfmathresult
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\pgfmathparse{\tsx@point@z - \distance*\tsx@plane@zcoeff}
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\let\z\pgfmathresult
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\definePointByXYZ{#1}{\x}{\y}{\z}
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}}
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\makeatother
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