# How to express PSTricks point in terms of a shifted variable and function?

For a trivial example, suppose that \f(x) is a quadratic curve defined as follows

\def\f(#1){-#1*(#1-8)/4}


For each element \ix in {0,1,2,3,4,5,6,7,8} there is a point (\ix,\f(\ix)) that will be the center of a square of 1 cm square.

How to express the bottom-left & top-right points of \psframe in terms of \ix and \f(\ix)?

NOTE: Please don't suggest other simpler solutions such as using \rput to put the squares because I am interested in PSTricks point expression. RPN notation should be avoided if it is possible.

I give you the skeleton (not working) as below to save your time.

\documentclass[pstricks,border=12pt]{standalone}

\begin{document}

\def\f(#1){-#1*(#1-8)/4}

\begin{pspicture}
\multido{\ix=0+1}{9}{
% the following expression is wrong!
\psframe[dimen=middle](*\ix-0.5 {\f(x)-0.5})(*\ix+0.5 {\f(x)+0.5})
}
\psplot[algebraic]{0}{8}{\f(x)}
\end{pspicture}

\end{document}


The output I want to get is as follows:

-

\listfiles
\documentclass{article}
\usepackage{pst-plot}
\SpecialCoor
\begin{document}

\def\f(#1){-#1*(#1-8)/4}

\begin{pspicture}(-1,-2)(10,5)
\psforeach{\ix}{0,1,..,9}{%
\rput(*\ix\space {\f(x)}){\psframe[dimen=middle](-0.5,-0.5)(0.5,0.5)}}
\psplot[algebraic]{0}{8}{\f(x)}
\end{pspicture}

\begin{pspicture}(-1,-2)(10,5)
\psforeach{\ix}{0,1,..,9}{%
\psframe[dimen=middle](*{\ix\space 0.5 sub}  {\f(\ix)-0.5})
\psplot[algebraic]{0}{8}{ \f(x) }
\end{pspicture}

\end{document}

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You know how to make it look easy... – Werner Dec 13 '11 at 16:46
@Herbert and @ CounterTerrorist: Just replace \f(x) with \f(\ix). – Werner Dec 13 '11 at 16:49
For what it's worth, @CounterTerrorist requested a no-\rput solution, even though it may be simpler. Your previous solution worked fine in that regard. – Werner Dec 13 '11 at 16:54
that was in pstricks-add and then moved into the core, but the documentation hasn't yet updated (> 400 pages!). The syntax ist for the * version is simple: (*<x value> {<f(x)>}), where f(x) must be described in algebraic notation, e.g. {sin(x)+cos(2*x)/2} – Herbert Dec 13 '11 at 17:17
See pst-news08.pdf (section 2.12 Special coordinates, p 19). – Werner Dec 13 '11 at 17:19

Use a postscript formulation of your algebraic function, and then reference the coordinates using the "raw PS" notation:

\documentclass{article}
\usepackage{pst-plot}% http://ctan.org/pkg/pst-plot
% The following package (multido) is loaded by pst-plot
%\usepackage{multido}% http://ctan.org/pkg/multido
\begin{document}

\def\f(#1){-#1*(#1-8)/4}% function f(x)=-x*(x-8)/4
% PS definition of f(x): x neg x 8 sub 4 div mul
\def\halfsize{0.5\space}% Modify this for smaller squares

\begin{pspicture}
\multido{\ix=0+1}{9}{%
\psframe[linewidth=0.5pt,linecolor=red!50]% Red squares
(!\ix\space \halfsize sub \ix\space neg \ix\space 8 sub 4 div mul \halfsize sub)% bottom left
(!\ix\space \halfsize add \ix\space neg \ix\space 8 sub 4 div mul \halfsize add)% upper right
}
\psplot[algebraic]{0}{8}{\f(x)}% Plot function
\end{pspicture}

\end{document}


The postscript formulation of \f(x)=-x*(x-8)/4 is

x neg x 8 sub 4 div mul


Now you can specify the node positions using postscript notation/coordinates (!<x> <y>) (excuse the ASCII art):

         (     x - 0.5     ,      - x    *      (x - 8) / 4          - 0.5 )

|     x - 0.5     |      - x    *      (x - 8) / 4          - 0.5 |
|     x - 0.5     |      - x    *      (x - 8) / 4        |0.5| - |
|     x - 0.5     |      - x    |      (x - 8) / 4        |0.5| - |
|     x - 0.5     |      - x    |      x - 8    |         |0.5| - |
|    x    |0.5| - |    x    | - |    x    |8| - |4| / | * |0.5| - |
(x,y) ~ (!\ix\space 0.5 sub \ix\space neg \ix\space 8 sub 4 div mul 0.5 sub)


It is required that you use \space after control sequences to introduce a space, otherwise elements are concatenated, leading to incorrect output (or sometimes input that doesn't compile). Also, note that there's no comma , separating the coordinates <x> and <y>; they are merely placed on a stack - first <x> and then <y>.

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