Displaying parts of \draw command sequentially

Question

I would like to display parts of a one \draw command sequentially. Using the following code I would like to display the axes only on the first slide, then the axes and the blue line only on the second slide, then the axes and the red line with the blue line on the third slide.

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\begin{frame}[fragile,t]
\frametitle{}
\begin{tikzpicture}[scale=.9, transform shape]
\draw [thick,-latex](0,0) -- (8,0);
\draw [thick,-latex](0,0) -- (0,8.);
\draw [very thick,blue] (4.,4.) +(-45:4cm) node [black, xshift=.24cm, yshift=-.05cm] {$D$} -- +(135:4cm) +(45:4cm) node [black, xshift=0cm, yshift=.05cm] {$S$} edge[very thick, red] ++(-135:4cm);
\end{tikzpicture}
\end{frame}
\end{document}

Answer 1

Till Tantau being the creator of BEAMER and Tikz-PGF the overlay work with tikz. Just add the overlay specification after the command name.

For example, here to make the transparency visible on the second and all subsequent images: draw<2->(0,0)--(2,0);

Edit 2: Beamer manual p 85:

9.6.1 Making Commands and Environments Overlay Specification-Aware

beamer extends the syntax of LaTeX's standard command \newcommand:

\newcommand<>{< command name>}[< argument number>][< default optional value>]{< text>}

[...]

The additionally allowed argument is the overlay specification

Till Tantau wrote all Tikz commands in this way. It is therefore essential that the overlay follows the name of the command. So we can't trace a path in sequence. It is necessary to write several paths, each written with a given overlay.

Then, it's not possible to display parts of the \draw command in sequence. It is mandatory to write as many \draw commands as sequences.

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\begin{frame}[fragile,t]
\frametitle{}
\begin{tikzpicture}[scale=.9, transform shape]
\useasboundingbox(0,0)rectangle(8,8);
\draw [thick,-latex](0,0) -- (8,0)(0,0) -- (0,8.);
\draw<2-> [very thick,blue] (4.,4.) +(-45:4cm) node [black, xshift=.24cm, yshift=-.05cm] {$D$} -- +(135:4cm) +(40:4cm) node [black, xshift=0cm, yshift=.05cm] {$S$} edge[very thick, purple!90!black, solid] ++(-140:4cm);
\draw<3-> [thick, black, densely dashed] (0,4.) node [black, xshift=-.28cm, yshift=-.05cm] {$P_0$} -- ++(0:4.) node [circle, draw, solid, black, fill=black, scale=0.2, xshift=0cm, yshift=0cm]{} -- +(-90:4.);
\end{tikzpicture}
\end{frame}
\end{document}

Note: instead of writing two \draw commands:

 \draw [thick,-latex](0,0) -- (8,0);
 \draw [thick,-latex](0,0) -- (0,8.);

you can write only one draw command

\draw [thick,-latex](0,0) -- (8,0)(0,0) -- (0,8.);

Answer 2

Do you want to have this three graphics?

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usepackage{pgfplots}
\newcommand{\achses}{\draw [thick,-latex](0,0) -- (8,0);\draw [thick,-latex](0,0) -- (0,8.);}
\newcommand{\blueline}{\draw [very thick,blue] (4.,4.) +(-45:4cm) node [black, xshift=.24cm, yshift=-.05cm] {$D$} -- +(135:4cm) +(45:4cm);}
\newcommand{\redline}{\draw [very thick,blue] (4.,4.) +(-45:4cm) node [black, xshift=.24cm, yshift=-.05cm] {$D$} -- +(135:4cm) +(45:4cm) node [black, xshift=0cm, yshift=.05cm] {$S$} edge[very thick, red] ++(-135:4cm);
}% needs removal of blueline!
\newcommand{\myframe}[2]{\frametitle{#1}\begin{tikzpicture}[scale=.9, transform shape]#2\end{tikzpicture}}
\begin{document}
\begin{frame}[fragile,t]\myframe{}{\achses}
\end{frame}
\newpage
\begin{frame}[fragile,t]\myframe{}{\achses\blueline}
\end{frame}
\newpage
\begin{frame}[fragile,t]\myframe{}{\achses\blueline\redline}
\end{frame}
\end{document}

From \redline the code for the blue line should be removed (otherwise the blue line is plotted twice).

First argument of \myframe is the argumet to \frametitle, which was empty in the minimal example.

Using the \pause command (see https://tex.stackexchange.com/a/9160/6865, thanks to Bobyandbob for pointing this out) it would also be possible:

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\begin{frame}[fragile,t]
\frametitle{}
\begin{tikzpicture}[scale=.9, transform shape]
\draw [thick,-latex](0,0) -- (8,0);
\draw [thick,-latex](0,0) -- (0,8.);\pause
\draw [very thick,blue] (4.,4.) +(-45:4cm) node [black, xshift=.24cm, yshift=-.05cm] {$D$} -- +(135:4cm) +(45:4cm);\pause
\draw [very thick,blue] (4.,4.) +(-45:4cm) node [black, xshift=.24cm, yshift=-.05cm] {$D$} -- +(135:4cm) +(45:4cm) node [black, xshift=0cm, yshift=.05cm] {$S$} edge[very thick, red] ++(-135:4cm);
\end{tikzpicture}
\end{frame}
\end{document}