[Tex/LaTex] TikZ: How to draw an helicoid and fill area below curve

intersectionstikz-pgf

I am trying to draw an helicoid and to fill the area below the curve. Since the aim of the figure is just to "give an idea", I would prefer to keep it simple and to avoid using PGFplots and GNUplot — with which I am not familiar.

Referring to the MWE below, I drew the curve and the shading, but the latter does not seem right for negative values of x, i.e. the horizontal direction. Thus I am asking how to make it right.

Moreover, I would like to draw lines starting from the axis of the helicoid, i.e. the z axis in TikZ coordinate system, to the corresponding point on the helicoid itself. The piece of code I commented out should serve this purpose, but it does not work as it is now.

Can someone help me?

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}
  \draw [name path=E-wave] [red,thick,->] plot [domain=0:13,samples=100] ({sin(\x r)},{cos(\x r)},\x);
  \fill [red,fill opacity=0.2] (0,0,0) -- plot [domain=0:13,samples=100] ({sin(\x r)},{cos(\x r)},\x) -- (0,0,13) -- cycle;
  %\foreach [evaluate={\xpos=1.1*sin(\zpos*180/pi);\ypos=1.1*cos(\zpos*180/pi);}] \zpos in {0,0.25*pi,...,4*pi} {
  %  \path [name path=mgntd] (0,0,\zpos) --  (\xpos,\ypos,\zpos);
  %  \draw [name intersections={of=E-wave and mgntd,by={isect\zpos}}] (0,0,\zpos) -- (isect\zpos);
  %}
  \draw [->] (0,0,0) -- (0,0,14.5);
\end{tikzpicture}
\end{document}

enter image description here

Best Answer

The main problem was that step was too small to be recognized by the intersections library (some ideas are written in the comment section). We also needed to correct a coefficient of 1.1 to get arrowheads back on the curve. The presented layout is in a way similar to this one, http://i.stack.imgur.com/mcmob.png.

%! *latex mal-helicoid.tex
\documentclass[a4paper]{article}
\pagestyle{empty}
\usepackage{tikz}
\usetikzlibrary{intersections}
\pagecolor{white}

\begin{document}
\tikzset{malstyle/.style={->,>=stealth, line width=0.2pt},
  malarrow/.style={->, >=stealth}}

\begin{tikzpicture}
% The curve drawing and filling...
\draw [name path=Ewave] [red, thick, ->, fill, fill opacity=0.2] (0,0,0) -- plot [domain=0:12.5664, samples=100] ({sin(\x r)}, {cos(\x r)}, \x) -- (0,0,12.5664) --cycle;
%\fill [red, fill opacity=0.2] (0,0,0) -- plot [domain=0:12.5664, samples=100] ({sin(\x r)},{cos(\x r)},\x) -- (0,0,12.5664) -- cycle;

% Adding all kind of arrows...
\foreach [ evaluate={\xpos=sin(\zpos*180/pi); \ypos=cos(\zpos*180/pi);} ]
   \zpos in {0, 0.2618, ..., 12.5664} 
  {% Beginning of \foreach...
  \draw[malstyle, black] (0,0,\zpos) -- (\xpos, \ypos, \zpos);
  \draw[malstyle, black!40] (0,0,0) --  (\xpos, \ypos, 0);
  \draw[malstyle, green] (0,0,\zpos) --  (\xpos, 0, \zpos);
  \draw[malstyle, blue] (0,0,\zpos) --  (0, \ypos, \zpos);
  }% End of \foreach...

% Drawing the axis... (positive and negative values)
% positive
\draw [malarrow] (0,0,0) -- (0,0,14.5) node[xshift=5, yshift=15] {$z$};
\draw [malarrow] (0,0,0) -- (0,2,0) node[xshift=-5, yshift=-10] {$y$};
\draw [malarrow] (0,0,0) -- (2,0,0) node[xshift=-10, yshift=-5] {$x$};
% negative
\draw[dashed] (0,0,0)--(-2,0,0)  (0,0,0)--(0,-2,0)  (0,0,0)--(0,0,-4);
\end{tikzpicture}

\end{document}

mwe, my fifth and hopefully the last attempt :-)

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[Tex/LaTex] Numerical conditional within tikz keys

I am definitely unfamiliar with both beamer and tikz (do not quite get what the \only are supposed to do) but perhaps this could go in the direction you want:

\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{chains}
\newcounter{count}

% helper macro:
\long\def\GobToSemiColon #1;{}

\newcommand\myPicture{
\begin{tikzpicture}
  \begin{scope}[start chain = going below]
  \ifnum\value{count}<1 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>3 \expandafter\GobToSemiColon\fi
  \node[draw, rectangle, on chain] {display only when counter is between
    1 and 3};

  \ifnum\value{count}>-1 \expandafter\GobToSemiColon\fi
  \node[draw, rectangle, on chain] {display only when counter is
    negative}; 

  \ifnum\value{count}<100 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>200 \expandafter\GobToSemiColon\fi  
  \node[draw, rectangle, on chain] {display only if counter is between
    100 and 200};

  \ifnum\value{count}<3 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>20 \expandafter\GobToSemiColon\fi
  \node[draw, circle, on chain] {only when counter is in the range 3 to 20};
  \end{scope}
\end{tikzpicture}
}

\begin{document}
\begin{frame}
\only{\setcounter{count}{-3}\myPicture}
\only{\setcounter{count}{105}\myPicture}
\only{\setcounter{count}{39}\myPicture}
\only{\setcounter{count}{2}\myPicture}
\only{\setcounter{count}{5}\myPicture}
\end{frame}
\end{document}

beamer

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

Best Answer

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[Tex/LaTex] Numerical conditional within tikz keys

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

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