Intersection of two tkz-fct funktions

Question

Is it possible to mark the intersection point of two tkz-fct functions and print it's coordinates?

For example in this case:

\documentclass{article}


\usepackage{tkz-fct}
\begin{document}
\begin{tikzpicture}
\tkzInit[ymax=15,xmax=4,ystep=5]
\tkzAxeXY
\tkzFct[color=red,domain=0:4]{2*x**2+5}
\tkzFct[color=blue,domain=0:4]{-x**3+15}
\end{tikzpicture}
\end{document}

Answer 1

No there is nothing specific in tkz-fct. You need to use TikZ to do that. With simple functions like in your example, you can use fp.

I think when you have complex functions , it's better to get the intersection with a real mathematics soft.

Actually tkz-fct works only with gnuplot and perhaps it's possible to use tables created by gnuplot to find an approximation of the intersection.

Now perhaps with lua, it's possible to find a fine method.

Update

But I find a solution ! I modified my package but I don't know if there are bad effects:

I used id for 'name path' and I modified \def\tkz@fct

\documentclass{article}
\usepackage{tkz-fct}
\usetikzlibrary{%
  arrows,
  calc,intersections
} 

\makeatletter
\def\tkz@fct[#1]#2{%
\pgfkeys{/tkzfct/.cd,
domain      = \tkz@dmin:\tkz@dmax,
samples     = 200,
fp          = true,
id          = tkzfct}
\pgfqkeys{/tkzfct}{#1}%
\iftkz@init@NO%
  \FPdiv{\tkz@x@delta}{\tkz@init@xorigine}{\tkz@init@xstep}%
  \FPdiv{\tkz@y@delta}{\tkz@init@yorigine}{\tkz@init@ystep}%
\else
  \FPset{\tkz@x@delta}{0}%
  \FPset{\tkz@y@delta}{0}%
\fi% 
% stockage
\advance\tkz@tkzf@fct by  1 %
\FPdiv\tkz@ba{\tkz@min}{\tkz@init@xstep}%
\FPdiv\tkz@bb{\tkz@max}{\tkz@init@xstep}%
\def\x{(x*\tkz@init@xstep)}%
\expandafter\edef\csname tkzFctgnu\@alph\tkz@tkzf@fct \endcsname{#2}%
\expandafter\edef\csname tkzFctgnuLast\endcsname{#2}     
 \clip (\tkz@xa,\tkz@ya) rectangle (\tkz@xb,\tkz@yb);
 \draw[name path =\tkz@fct@id,xshift  = -\tkz@x@delta cm,yshift  = -\tkz@y@delta cm,/tkzfct/.cd,#1 ]%
 plot[id=\tkz@fct@id,domain= \tkz@ba:\tkz@bb,samples    = \tkz@fct@samples]%
 function{(#2)/\tkz@init@ystep};%
%\end{scope} 
   \let\tkz@tmp@xstep\tkz@init@xstep
   \def\tkz@init@xstep{1}
\iftkz@fp%       
   \ReplaceSubStrings{\tkz@tempa}{#2}{log}{ln}
   \ReplaceSubStrings{\tkz@tempb}{\tkz@tempa}{**}{^}
   \ReplaceSubStrings{\tkz@tempa}{\tkz@tempb}{\x}{x}
   \ReplaceSubStrings{\tkz@tempb}{\tkz@tempa}{asin}{arcsin}
   \ReplaceSubStrings{\tkz@tempa}{\tkz@tempb}{acos}{arccos}
   \ReplaceSubStrings{\tkz@tempb}{\tkz@tempa}{atan}{arctan} 
  \expandafter\edef\csname tkzFct\@alph\tkz@tkzf@fct\endcsname{\tkz@tempb}%
  \expandafter\edef\csname tkzFctLast\endcsname{\tkz@tempb}%
 \fi
  \let\tkz@init@xstep\tkz@tmp@xstep 
 \catcode`\:=\tkzTWOPTCode\relax   
}%


\makeatother

\begin{document}
\begin{tikzpicture}
\tkzInit[ymax=15,xmax=4,ystep=5]
\tkzAxeXY
\tkzFct[id=f,color=red,domain=0:4]{2*x**2+5}
\tkzFct[id=g,color=blue,domain=0:4]{-x**3+15}
 \fill [red, opacity=0.5, name intersections={of=f and g}]
    (intersection-1) circle (2pt) node {};
\end{tikzpicture}
\end{document}  

todo

With some calculations you can get the coordinate system values like Jakes writes. I need to create a specific macro because sometimes the system is translate and the units can change with xstep and ystep.

Here a solution before a new macro

\begin{document}
\begin{tikzpicture}
\tkzInit[ymax=15,xmax=4,ystep=5]
\tkzAxeXY
\tkzFct[id=f,color=red,domain=0:4]{2*x**2+5}
\tkzFct[id=g,color=blue,domain=0:4]{-x**3+15}
 \makeatletter   
    \draw [name intersections={of=f and g, by=fxg}] let \p1=(fxg) in
   (fxg) circle (1pt) \pgfextra{\pgfmathsetmacro\xc{\x1/28.45}\pgfmathsetmacro\yc{\y1/28.45*\tkz@init@ystep}} node [right,align=left] {a=\xc\\ b=\yc};
\end{tikzpicture} 

Answer 2

It is possible if you use TikZ directly to plot and combine it with the intersections library.

\documentclass{article}

\usepackage{tkz-fct}
\usetikzlibrary{intersections}

\tikzset{
   name plot/.style={every path/.style={name path global=#1}}
}

\begin{document}
\begin{tikzpicture}
\tkzInit[ymax=15,xmax=4,ystep=5]
\tkzAxeXY
%
\tkzFct[name plot=A,color=red,domain=0:4]{2*x**2+5}
%
\tkzFct[name plot=B,color=blue,domain=0:4]{-x**3+15}
%
\draw [name intersections={of=A and B, by=AxB}] (AxB) circle (2pt);
\end{tikzpicture}
\end{document}

With the following line you can read out the absolute coordinates of the intersection point as it is placed in the resulting picture. With some calculations you can get the coordinate system values I guess …

\draw [name intersections={of=A and B, by=AxB}] let \p1=(AxB) in
   (AxB) circle (1pt) node [right] {\x1,\y1};

---

File list

 *File List*
 article.cls    2007/10/19 v1.4h Standard LaTeX document class
  size10.clo    2007/10/19 v1.4h Standard LaTeX file (size option)
 tkz-fct.sty    2011/06/01 1.16 c function 
tkz-base.sty    2011/06/01 1.16 c tkz-base
    etex.sty    1998/03/26 v2.0 eTeX basic definition package (PEB)
    tikz.sty    2010/10/13 v2.10 (rcs-revision 1.76)
     pgf.sty    2008/01/15 v2.10 (rcs-revision 1.12)
  pgfrcs.sty    2010/10/25 v2.10 (rcs-revision 1.24)
everyshi.sty    2001/05/15 v3.00 EveryShipout Package (MS)
  pgfrcs.code.tex
 pgfcore.sty    2010/04/11 v2.10 (rcs-revision 1.7)
graphicx.sty    1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)
  keyval.sty    1999/03/16 v1.13 key=value parser (DPC)
graphics.sty    2009/02/05 v1.0o Standard LaTeX Graphics (DPC,SPQR)
    trig.sty    1999/03/16 v1.09 sin cos tan (DPC)
graphics.cfg    2010/04/23 v1.9 graphics configuration of TeX Live
  pdftex.def    2011/05/27 v0.06d Graphics/color for pdfTeX
infwarerr.sty    2010/04/08 v1.3 Providing info/warning/message (HO)
 ltxcmds.sty    2011/04/18 v1.20 LaTeX kernel commands for general use (HO)
  pgfsys.sty    2010/06/30 v2.10 (rcs-revision 1.37)
  pgfsys.code.tex
pgfsyssoftpath.code.tex    2008/07/18  (rcs-revision 1.7)
pgfsysprotocol.code.tex    2006/10/16  (rcs-revision 1.4)
  xcolor.sty    2007/01/21 v2.11 LaTeX color extensions (UK)
   color.cfg    2007/01/18 v1.5 color configuration of teTeX/TeXLive
 pgfcore.code.tex
pgfcomp-version-0-65.sty    2007/07/03 v2.10 (rcs-revision 1.7)
pgfcomp-version-1-18.sty    2007/07/23 v2.10 (rcs-revision 1.1)
  pgffor.sty    2010/03/23 v2.10 (rcs-revision 1.18)
 pgfkeys.sty    
 pgfkeys.code.tex
  pgffor.code.tex
    tikz.code.tex
numprint.sty    2008/02/17 v1.38 Print numbers (HH)
   array.sty    2008/09/09 v2.4c Tabular extension package (FMi)
      fp.sty    1995/04/02
defpattern.sty    1994/10/12
fp-basic.sty    1996/05/13
fp-addons.sty    1995/03/15
 fp-snap.sty    1995/04/05
  fp-exp.sty    1995/04/03
fp-trigo.sty    1995/04/14
  fp-pas.sty    1994/08/29
fp-random.sty    1995/02/23
  fp-eqn.sty    1995/04/03
  fp-upn.sty    1996/10/21
 fp-eval.sty    1995/04/03
tkz-tools-utilities.tex
tkz-tools-arith.tex
tkz-tools-base.tex
tkz-tools-misc.tex
tkz-tools-math.tex
tkz-obj-points.tex
tkz-obj-segments.tex
tkz-obj-marks.tex
supp-pdf.mkii
pdftexcmds.sty    2011/04/22 v0.16 Utilities of pdfTeX for LuaTeX (HO)
ifluatex.sty    2010/03/01 v1.3 Provides the ifluatex switch (HO)
   ifpdf.sty    2011/01/30 v2.3 Provides the ifpdf switch (HO)
epstopdf-base.sty    2010/02/09 v2.5 Base part for package epstopdf
  grfext.sty    2010/08/19 v1.1 Managing graphics extensions (HO)
kvdefinekeys.sty    2011/04/07 v1.3 Defining keys (HO)
kvoptions.sty    2010/12/23 v3.10 Keyval support for LaTeX options (HO)
kvsetkeys.sty    2011/04/07 v1.13 Key value parser (HO)
etexcmds.sty    2011/02/16 v1.5 Prefix for e-TeX command names (HO)
epstopdf-sys.cfg    2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live
 ***********