The following images were generated by tikz and pgfplots scripts in latex.

The Latex source file is:

\documentclass{article}

\usepackage{tikz, pgfplots}
\usepgfplotslibrary{external}
\tikzexternalize[prefix=figures/]

\begin{document}

\thispagestyle{empty}

\tikzsetnextfilename{L1_ball_fig} % general PDF image L1_ball_fig.pdf
\begin{tikzpicture}[scale=0.5]
   \begin{axis}[hide axis, view={125}{25}, axis equal=true]

        % 3 axes
        \addplot3[thin,dotted,->] coordinates {(-2.4,0,0) (3.0,0,0)};
        \addplot3[thin,dotted,->] coordinates {(0,-2.4,0) (0,3.0,0)};
        \addplot3[thin,dotted,->] coordinates {(0,0,-2.4) (0,0,3.0)};

        % L1 ball boundaries
        \addplot3[thin,domain=0:4/3, samples y=0] (x,0,4/3-x);
        \addplot3[thin,domain=0:4/3, samples y=0] (x,0,x-4/3);

        \addplot3[domain=0:4/3, samples y=0] (0,x,4/3-x);
        \addplot3[domain=0:4/3, samples y=0] (0,x,x-4/3);

        \addplot3[domain=-4/3:0, samples y=0] (x,0,4/3+x);
        \addplot3[dashed, domain=-4/3:0, samples y=0] (x,0,-x-4/3);

        \addplot3[domain=-4/3:0, samples y=0] (0,x,4/3+x);
        \addplot3[dashed, domain=-4/3:0, samples y=0] (0,x,-x-4/3);

        % horizontal lines
        \addplot3[domain=0:4/3, samples y=0] (4/3-x,x,0);
        \addplot3[domain=0:4/3, samples y=0] (x-4/3,x,0);
        \addplot3[dashed, domain=-4/3:0, samples y=0] (-4/3-x,x,0);
        \addplot3[domain=-4/3:0, samples y=0] (4/3+x,x,0);

        % Ax = b
        \addplot3[red,domain=-1.6:3.0, samples y=0] ({(2-x)*1/3},{-(2-x)*1/3},x);

    	% intersection points
    	\addplot3[only marks, mark size=2pt, blue] coordinates{(0,0,2)} node [left] {$\mathbf{x}^o$};
    	\addplot3[only marks, mark size=2pt] coordinates{(2/3,-2/3,0)};
   \end{axis}
\end{tikzpicture}

\tikzsetnextfilename{L05_ball_fig} % general PDF image L05_ball_fig.pdf
\begin{tikzpicture}[scale=0.5]
%   \begin{axis}[xmin=-2, xmax=3, ymin=-2, ymax=3, zmin=-2, zmax=3, hide axis, view={135}{35}, plot box ratio=1 1 2]
   \begin{axis}[hide axis, view={125}{25}, axis equal=true]

        % 3 axes
        \addplot3[thin,dotted,->] coordinates {(-2.2,0,0) (2.8,0,0)};
        \addplot3[thin,dotted,->] coordinates {(0,-2.2,0) (0,2.8,0)};
        \addplot3[thin,dotted,->] coordinates {(0,0,-2.2) (0,0,2.8)};

        % Ax = b
        \addplot3[red,domain=-1.6:3.0, samples y=0] ({(2-x)*1/3},{-(2-x)*1/3},x);

        % L_1/2 ball boundaries
        \addplot3[domain=0:4/2, samples y=0] (x,0,{(sqrt(4/2)-sqrt(x))^2});
        \addplot3[domain=0:4/2, samples y=0] (x,0,-{(sqrt(4/2)-sqrt(x))^2});

        \addplot3[domain=0:4/2, samples y=0] (0,x,{(sqrt(4/2)-sqrt(x))^2});
        \addplot3[domain=0:4/2, samples y=0] (0,x,-{(sqrt(4/2)-sqrt(x))^2});

        \addplot3[domain=-4/2:0, samples y=0] (x,0,{(sqrt(4/2)-sqrt(-x))^2});
        \addplot3[dashed, domain=-4/2:0, samples y=0] (x,0,-{(sqrt(4/2)-sqrt(-x))^2});

        \addplot3[domain=-4/2:0, samples y=0] (0,x,{(sqrt(4/2)-sqrt(-x))^2});
        \addplot3[dashed, domain=-4/2:0, samples y=0] (0,x,-{(sqrt(4/2)-sqrt(-x))^2});

        % connection lines
        \addplot3[domain=0:4/2, samples y=0] ({(sqrt(4/2)-sqrt(x))^2},x,0);
        \addplot3[domain=0:4/2, samples y=0] (-{(sqrt(4/2)-sqrt(x))^2},x,0);
        \addplot3[dashed, domain=-4/2:0, samples y=0] (-{(sqrt(4/2)-sqrt(-x))^2},x,0);
        \addplot3[domain=-4/2:0, samples y=0] ({(sqrt(4/2)-sqrt(-x))^2},x,0);

    	% intersection points
    	\addplot3[only marks, mark size=2pt, blue] coordinates{(0,0,2)} node [left] {$\mathbf{x}^o$};

   \end{axis}
\end{tikzpicture}

\end{document}

To typeset this latex, I used pdflatex with the switch -shell-escape (or -enable-write18 in MikTex). I also used the tools in this blog to crop the white space around the plots.

This entry was posted on Sunday, August 26th, 2012 at 3:56 pm and is filed under Talks. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.