‣ LaTeXDrawProjPicture( A[, DrawOptions] ) | ( function ) |
Returns: A string.
Generates LaTeX tikz-code for a nice projective picture of the real 3-arrangement. If x,y,z are the coordinates, by default, this is the 2-dim affine arrangement obtained by intersecting A with the plane z=1.
In the optional parameters DrawOptions, a record, the following parameters can be chosen
scale, a positive rational scaling factor,
isecps intersection points are drawn, true or false,
Hind labels for the hyperplanes are added, true or false,
deconeH a vector giving the normal of the plane (=1) with which to intersect A,
MarkHs a list of indices of hyperplanes of A, these are drawn in another color.
gap> A:=AGpql(2,2,3); <HyperplaneArrangement: 6 hyperplanes in 3-space> gap> Print(LaTeXDrawProjPicture(A)); \begin{tikzpicture}[scale=1.0] \draw (-2.83,2.83) -- (2.83,-2.83); % H_1 \draw (2.83,2.83) -- (-2.83,-2.83); % H_2 \draw (-1.,3.87) -- (-1.,-3.87); % H_3 \draw (1.,3.87) -- (1.,-3.87); % H_4 \draw (3.87,-1.) -- (-3.87,-1.); % H_5 \draw (3.87,1.) -- (-3.87,1.); % H_6 \end{tikzpicture} gap> DrawOpts:=rec(scale:=1/2,isecps:=true,Hind:=true, > deconeH:=[1,1,1],MarkHs:=[1,2]);; gap> Print(LaTeXDrawProjPicture(AGpql(2,2,3),DrawOpts)); \begin{tikzpicture}[scale=1.0] \draw[color=red] (-3.56,1.83) -- (1.83,-3.56); % H_1 \node at (1.97,-3.71) {\small $1$}; \draw[color=red] (2.83,2.83) -- (-2.83,-2.83); % H_2 \node at (-2.97,-2.97) {\small $2$}; \draw (3.35,2.16) -- (-4.,0.20); % H_3 \node at (-4.20,0.14) {\small $3$}; \draw (-1.04,3.85) -- (1.04,-3.85); % H_4 \node at (1.09,-4.06) {\small $4$}; \draw (2.16,3.35) -- (0.20,-4.); % H_5 \node at (0.14,-4.20) {\small $5$}; \draw (-3.85,1.04) -- (3.85,-1.04); % H_6 \node at (4.06,-1.09) {\small $6$}; \fill[red] (-0.87,-0.87) circle[radius=2pt]; % P[ 1, 2 ] \fill[red] (-2.37,0.63) circle[radius=2pt]; % P[ 1, 3, 6 ] \fill[red] (1.73,1.73) circle[radius=2pt]; % P[ 2, 3, 5 ] \fill[red] (0.63,-2.37) circle[radius=2pt]; % P[ 1, 4, 5 ] \fill[red] (0.0,0.0) circle[radius=2pt]; % P[ 2, 4, 6 ] \fill[red] (-0.32,1.17) circle[radius=2pt]; % P[ 3, 4 ] \fill[red] (1.17,-0.32) circle[radius=2pt]; % P[ 5, 6 ] \end{tikzpicture}
The preceding example will look as follows
‣ LaTeXDrawSpherePicture( A ) | ( function ) |
Returns: A string.
Generates LaTeX tikz-code for the intersection of a real 3-arrangement with the unit sphere. To compile the LaTeX-code the .sty-file "graphonsphere.sty" (from /doc/LaTeX_Examples) needs to be in the same folder and added via "\usepackage{graphonsphere}".
gap> A:=AGpql(2,2,3); <HyperplaneArrangement: 6 hyperplanes in 3-space> gap> Print(LaTeXDrawSpherePicture(A)); \tdplotsetmaincoords{63}{63} \begin{tikzpicture}[scale=3,tdplot_main_coords] \draw[ball color = gray!40, opacity = 0.2] (0,0,0) circle (1cm); \def\OMcolor{black} {\color{\OMcolor} % the vertices of the OM-cpx \foreach \i/\vx/\vy/\vz in { 1/0./0./1., 2/-0.57/0.57/0.57, 3/-0.57/-0.57/0.57, 4/0.57/-0.57/0.57, 5/0.57/0.57/0.57, 6/0./1./0., 7/1./0./0., 8/0./0./-1., 9/0.57/-0.57/-0.57, 10/0.57/0.57/-0.57, 11/-0.57/0.57/-0.57, 12/-0.57/-0.57/-0.57, 13/0./-1./0., 14/-1./0./0. }{ \node (\i) at (\vx,\vy,\vz) {}; \POnSfb{\vx}{\vy}{\vz}{} } % % the edges of the OM-cpx \foreach \ax/\ay/\az/\bx/\by/\bz in { 0./0./1./ -0.57/0.57/0.57, %[ 1, 2 ] 0./0./1./ -0.57/-0.57/0.57, %[ 1, 3 ] 0./0./1./ 0.57/-0.57/0.57, %[ 1, 4 ] 0./0./1./ 0.57/0.57/0.57, %[ 1, 5 ] -0.57/0.57/0.57/ -0.57/-0.57/0.57, %[ 2, 3 ] -0.57/0.57/0.57/ 0.57/0.57/0.57, %[ 2, 5 ] -0.57/0.57/0.57/ 0./1./0., %[ 2, 6 ] -0.57/0.57/0.57/ -0.57/0.57/-0.57, %[ 2, 11 ] -0.57/0.57/0.57/ -1./0./0., %[ 2, 14 ] -0.57/-0.57/0.57/ 0.57/-0.57/0.57, %[ 3, 4 ] -0.57/-0.57/0.57/ -0.57/-0.57/-0.57, %[ 3, 12 ] -0.57/-0.57/0.57/ 0./-1./0., %[ 3, 13 ] -0.57/-0.57/0.57/ -1./0./0., %[ 3, 14 ] 0.57/-0.57/0.57/ 0.57/0.57/0.57, %[ 4, 5 ] 0.57/-0.57/0.57/ 1./0./0., %[ 4, 7 ] 0.57/-0.57/0.57/ 0.57/-0.57/-0.57, %[ 4, 9 ] 0.57/-0.57/0.57/ 0./-1./0., %[ 4, 13 ] 0.57/0.57/0.57/ 0./1./0., %[ 5, 6 ] 0.57/0.57/0.57/ 1./0./0., %[ 5, 7 ] 0.57/0.57/0.57/ 0.57/0.57/-0.57, %[ 5, 10 ] 0./1./0./ 0.57/0.57/-0.57, %[ 6, 10 ] 0./1./0./ -0.57/0.57/-0.57, %[ 6, 11 ] 1./0./0./ 0.57/-0.57/-0.57, %[ 7, 9 ] 1./0./0./ 0.57/0.57/-0.57, %[ 7, 10 ] 0./0./-1./ 0.57/-0.57/-0.57, %[ 8, 9 ] 0./0./-1./ 0.57/0.57/-0.57, %[ 8, 10 ] 0./0./-1./ -0.57/0.57/-0.57, %[ 8, 11 ] 0./0./-1./ -0.57/-0.57/-0.57, %[ 8, 12 ] 0.57/-0.57/-0.57/ 0.57/0.57/-0.57, %[ 9, 10 ] 0.57/-0.57/-0.57/ -0.57/-0.57/-0.57, %[ 9, 12 ] 0.57/-0.57/-0.57/ 0./-1./0., %[ 9, 13 ] 0.57/0.57/-0.57/ -0.57/0.57/-0.57, %[ 10, 11 ] -0.57/0.57/-0.57/ -0.57/-0.57/-0.57, %[ 11, 12 ] -0.57/0.57/-0.57/ -1./0./0., %[ 11, 14 ] -0.57/-0.57/-0.57/ 0./-1./0., %[ 12, 13 ] -0.57/-0.57/-0.57/ -1./0./0. %[ 12, 14 ] }{ \GCArcABfb{\ax}{\ay}{\az}{\bx}{\by}{\bz}{color=\OMcolor} } } \end{tikzpicture}
The preceding example will look as follows
‣ LaTeXDrawTopeGraph( A ) | ( function ) |
Returns: A string.
Generates LaTeX tikz-code for the tope graph of a real 3-arrangement on the unit sphere. To compile the LaTeX-code the .sty-file "graphonsphere.sty" (from /doc/LaTeX_Examples) needs to be in the same folder and added via "\usepackage{graphonsphere}".
gap> A:=AGpql(2,2,3); <HyperplaneArrangement: 6 hyperplanes in 3-space> gap> Print(LaTeXDrawTopeGraph(A)); \tdplotsetmaincoords{63}{63} \begin{tikzpicture}[scale=3,tdplot_main_coords] \draw[ball color = gray!40, opacity = 0.2] (0,0,0) circle (1cm); \def\OMcolor{blue!70!black} {\color{\OMcolor} % the vertices of the OM-cpx \foreach \i/\vx/\vy/\vz in { 1/-0.88/-0.47/0., 2/0.88/0.47/0., 3/-0.88/0./-0.47, 4/0.88/0./0.47, 5/-0.88/0./0.47, 6/0.88/0./-0.47, 7/-0.88/0.47/0., 8/0.88/-0.47/0., 9/-0.47/0./-0.88, 10/0.47/0./0.88, 11/-0.47/0./0.88, 12/0.47/0./-0.88, 13/-0.47/-0.88/0., 14/0.47/0.88/0., 15/0./-0.47/-0.88, 16/0./0.47/0.88, 17/0./-0.47/0.88, 18/0./0.47/-0.88, 19/0./-0.88/-0.47, 20/0./0.88/0.47, 21/0./-0.88/0.47, 22/0./0.88/-0.47, 23/0.47/-0.88/0., 24/-0.47/0.88/0. }{ \node (\i) at (\vx,\vy,\vz) {}; \POnSfb{\vx}{\vy}{\vz}{} } % % the edges of the OM-cpx \foreach \ax/\ay/\az/\bx/\by/\bz in { -0.88/-0.47/0./ -0.88/0./-0.47, %[ 1, 3 ] -0.88/-0.47/0./ -0.88/0./0.47, %[ 1, 5 ] -0.88/-0.47/0./ -0.47/-0.88/0., %[ 1, 13 ] 0.88/0.47/0./ 0.88/0./0.47, %[ 2, 4 ] 0.88/0.47/0./ 0.88/0./-0.47, %[ 2, 6 ] 0.88/0.47/0./ 0.47/0.88/0., %[ 2, 14 ] -0.88/0./-0.47/ -0.88/0.47/0., %[ 3, 7 ] -0.88/0./-0.47/ -0.47/0./-0.88, %[ 3, 9 ] 0.88/0./0.47/ 0.88/-0.47/0., %[ 4, 8 ] 0.88/0./0.47/ 0.47/0./0.88, %[ 4, 10 ] -0.88/0./0.47/ -0.88/0.47/0., %[ 5, 7 ] -0.88/0./0.47/ -0.47/0./0.88, %[ 5, 11 ] 0.88/0./-0.47/ 0.88/-0.47/0., %[ 6, 8 ] 0.88/0./-0.47/ 0.47/0./-0.88, %[ 6, 12 ] -0.88/0.47/0./ -0.47/0.88/0., %[ 7, 24 ] 0.88/-0.47/0./ 0.47/-0.88/0., %[ 8, 23 ] -0.47/0./-0.88/ 0./-0.47/-0.88, %[ 9, 15 ] -0.47/0./-0.88/ 0./0.47/-0.88, %[ 9, 18 ] 0.47/0./0.88/ 0./0.47/0.88, %[ 10, 16 ] 0.47/0./0.88/ 0./-0.47/0.88, %[ 10, 17 ] -0.47/0./0.88/ 0./0.47/0.88, %[ 11, 16 ] -0.47/0./0.88/ 0./-0.47/0.88, %[ 11, 17 ] 0.47/0./-0.88/ 0./-0.47/-0.88, %[ 12, 15 ] 0.47/0./-0.88/ 0./0.47/-0.88, %[ 12, 18 ] -0.47/-0.88/0./ 0./-0.88/-0.47, %[ 13, 19 ] -0.47/-0.88/0./ 0./-0.88/0.47, %[ 13, 21 ] 0.47/0.88/0./ 0./0.88/0.47, %[ 14, 20 ] 0.47/0.88/0./ 0./0.88/-0.47, %[ 14, 22 ] 0./-0.47/-0.88/ 0./-0.88/-0.47, %[ 15, 19 ] 0./0.47/0.88/ 0./0.88/0.47, %[ 16, 20 ] 0./-0.47/0.88/ 0./-0.88/0.47, %[ 17, 21 ] 0./0.47/-0.88/ 0./0.88/-0.47, %[ 18, 22 ] 0./-0.88/-0.47/ 0.47/-0.88/0., %[ 19, 23 ] 0./0.88/0.47/ -0.47/0.88/0., %[ 20, 24 ] 0./-0.88/0.47/ 0.47/-0.88/0., %[ 21, 23 ] 0./0.88/-0.47/ -0.47/0.88/0. %[ 22, 24 ] }{ \GCArcABfb{\ax}{\ay}{\az}{\bx}{\by}{\bz}{color=\OMcolor} } } \end{tikzpicture}
The preceding example will look as follows
Both functions LaTexDrawSpherePicture and LaTeXDrawTopeGraph combined can be used to draw nice pictures of oriented matroid complexes and their duals.
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