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.

We are going to remove the margin (white space) around a figure in input.pdf. We do this in Linux (I do not find free tools in Windows yet). We need

1. input.pdf a single-page image file
2. pdfcrop executable (get from http://sourceforge.net/projects/pdfcrop/)
3. pdf2eps script (get from http://tex.stackexchange.com/questions/20883/how-to-convert-pdf-to-eps)

I saved a copy of items 2 and 3 here. Of course, you need to put them in the search path and apply “chmod a+x” to them.

Then run the following

  $ pdfcrop --verbose input.pdf output.pdf
  $ pdf2eps 1 output

The second line will generate output.eps.

If we need to impose the same bounding box on more than one files, read the output of

  $ pdfcrop --verbose input1.pdf output1.pdf
  $ pdfcrop --verbose input2.pdf output2.pdf
  ...
  $ pdfcrop --verbose inputn.pdf outputn.pdf

Figure out the largest bounding box <left> <top> <right> <bottom>, and run

  $ pdfcrop --bbox "<left> <top> <right> <bottom>" input1.pdf output1.pdf
  $ pdfcrop --bbox "<left> <top> <right> <bottom>" input2.pdf output2.pdf
  ...
  $ pdfcrop --bbox "<left> <top> <right> <bottom>" inputn.pdf outputn.pdf

[Download m-file]

function myprint(name, h)
% This code will produce eps and pdf files out of a MATLAB figure with no
% change. What you see will be what you get.
%
% Example:
%
%   h = figure(1);
%   ...(your plotting code) ...
%   myprint('filename', h);
%
% Your will get filename.eps and filename.pdf.
% -----------------
% Wotao Yin (2011).

if ~ischar(name)
    error('Input 1 must be char');
end

if ~exist('h','var') || isempty(h)
    h = gcf;
end

ppos = get(h,'Position'); ppos(1:2)=0; psize = ppos(3:4);
dpi = get(0,'ScreenPixelsPerInch');
set(gcf, 'PaperPositionMode', 'manual');
set(gcf, 'PaperUnits', 'inches');
set(gcf, 'PaperSize', psize/dpi);
set(gcf, 'PaperPosition', ppos/dpi);

print('-painters','-depsc2','-r0',name);
print('-painters','-dpdf','-r0',name);

end