## sâmbătă, 31 august 2013

### Some random examples with PGF/TikZ

July 2013, the lucky month when a student of mine whom I was advising on his undergraduate thesis, finally successfully finished it. It happened that I only now have the time to write about this event. I was much busy before.
The title of the thesis was "Computer Technologies for Visualization of Mathematical Objects"  (the original title, in Romanian, sounds like: "Tehnologii de vizualizare a obiectelor matematice prin utilizarea calculatorului").
We both had been working hard to get it well done. And the fruitful result of the months of hard work that we had spent is, on my side, some good experience of working with LaTeX, PGF/TikZ, appreciation of the work from my colleagues, on the student's side, the highest score for this work and,  on the committee's side, the pleasant experience of viewing some fresh ideas, powerful technologies, a well-structured and understandable content of the work.

I will present some of the things that the thesis was about in the paragraphs below.

\begin{figure}[!hb]
\tikzset{external/force remake}
\centering%
\begin{tikzpicture}
\begin{axis}[xlabel=$x$,ylabel=$y$,zlabel=$z$]
\begin{scope}[every node/.style={circle,inner sep=1.5pt,fill=black}]
\node[pin=50:\footnotesize{saddle point}] at (axis cs:0,0,0) {};
\end{scope}
\end{axis}
\end{tikzpicture}
\caption{Saddle point of function $f(x,y)=x^2-y^2$}
\end{figure}


\begin{figure}[!hb]
\begin{tikzpicture}
\begin{axis}[xlabel=$x$,ylabel=$y$,zlabel=$z$,view/az=225,view/h=165]

\begin{scope}[every node/.style={circle,inner sep=1.5pt,fill=black}]
\node[pin=140:\footnotesize{minimum}] at (axis cs:1,2,-17) {};
\node[pin=140:\footnotesize{maximum}] at (axis cs:-1,-2,19) {};
\node[pin=140:\footnotesize{saddle}] at (axis cs:1,-2,15) {};
\node[pin=140:\footnotesize{saddle}] at (axis cs:-1,2,-13) {};
\end{scope}
\end{axis}
\end{tikzpicture}
\caption{Critical points of function $f(x,y)=x^3+y^3-3x-12y+1$}
\end{figure}


\begin{figure}[!hb]
\begin{tikzpicture}
\begin{axis}[xlabel=$x$,ylabel=$y$,zlabel=$z$,view/az=75]
\caption{Critical points of function $f(x,y)=x^3+y^3-3x-12y+1$ (different view)}