[Tex/LaTex] Intersecting planes not shown correctly with TikZ

3dMATLABpgfplotstikz-pgf

I made a plot in MATLAB of a deformed and an undeformed model. I converted the figure to TikZ using matlab2tikz and added it to my .tex file. I then noticed that the two configurations, which are intersecting, are not displayed correctly. To illustrate what I mean, I've stripped down the TikZ code to make to rectangles cross in a 3D space:

\begin{tikzpicture}
\begin{axis}[%
    width=5cm,height=5cm,
    view={-37.5}{45},
    scale only axis,
    xmin=-3, xmax=23,
    ymin=0, ymax=20,
    zmin=-5, zmax=5,
    hide axis]
    \addplot3 [fill=white!80!red,opacity=0.5,draw=black] table[row sep=crcr]{
    20 0 0\\
    20 20 0\\
    0 20 0\\
    0 0 0\\
    };

    \addplot3 [fill=white!80!blue,opacity=0.8,draw=black] table[row sep=crcr]{
    15 5 -4\\
    15 15 0\\
    5 15 4\\
    5 5 0\\
    };
\end{axis}
\end{tikzpicture}

The result looks like this:

Two crossing planes

As can be seen one plane lies entirely on top of the other, while in fact they intersect (i.e. about half of the blue plane lies 'underneath' the red plane).
With my minimum TikZ knowledge I was hoping someone here could help me fix this problem, such that the planes indeed intersect.

Best Answer

Unfortunately, this doesn't seem possible in the current version of pgfplots. From the manual (Section 4.5.1):

pgfplots supports z buffering techniques up to a certain extent. It works pretty well for single scatter plots (z buffer=sort), mesh or surface plots (z buffer=auto) or parametric mesh and surface plots (z buffer=sort). However, it can’t combine different \addplot commands, those will be drawn in the order of appearance. You may encounter the limitations sometimes. Maybe it will be improved in future versions.

Related Solutions

[Tex/LaTex] plotting two time series with bounds

This happens because PGFPlots only uses one "stack" per axis: You're stacking the second confidence interval on top of the first. The easiest way to fix this is probably to use the approach described in "Is there an easy way of using line thickness as error indicator in a plot?": After plotting the first confidence interval, stack the upper bound on top again, using stack dir=minus. That way, the stack will be reset to zero, and you can draw the second confidence interval in the same fashion as the first:

\documentclass{standalone}
\usepackage{pgfplots, tikz}

\usepackage{pgfplotstable}

\pgfplotstableread{
temps   y_h y_h__inf    y_h__sup    y_f y_f__inf    y_f__sup    

1   0.237340    0.135170    0.339511    0.237653    0.135482    0.339823    
2   0.561320    0.422007    0.700633    0.165871    0.026558    0.305184    
3   0.694760    0.534205    0.855314    0.074856    -0.085698   0.235411    
4   0.728306    0.560179    0.896432    0.003361    -0.164765   0.171487    
5   0.711710    0.544944    0.878477    -0.044582   -0.211349   0.122184    
6   0.671241    0.511191    0.831291    -0.073347   -0.233397   0.086703    
7   0.621177    0.471219    0.771135    -0.088418   -0.238376   0.061540    
8   0.569354    0.431826    0.706882    -0.094382   -0.231910   0.043146    
9   0.519973    0.396571    0.643376    -0.094619   -0.218022   0.028783    
10  0.475121    0.366990    0.583251    -0.091467   -0.199598   0.016664    
}{\table}

\begin{document}
\begin{tikzpicture}

    \begin{axis}
    % y_h confidence interval
    \addplot [stack plots=y, fill=none, draw=none, forget plot]   table [x=temps, y=y_h__inf]   {\table} \closedcycle;
    \addplot [stack plots=y, fill=gray!50, opacity=0.4, draw opacity=0, area legend]   table [x=temps, y expr=\thisrow{y_h__sup}-\thisrow{y_h__inf}]   {\table} \closedcycle;
    % subtract the upper bound so our stack is back at zero
    \addplot [stack plots=y, stack dir=minus, forget plot, draw=none] table [x=temps, y=y_h__sup] {\table};

    % y_f confidence interval
    \addplot [stack plots=y, fill=none, draw=none, forget plot]   table [x=temps, y=y_f__inf]   {\table} \closedcycle;
    \addplot [stack plots=y, fill=gray!50, opacity=0.4, draw opacity=0, area legend]   table [x=temps, y expr=\thisrow{y_f__sup}-\thisrow{y_f__inf}]   {\table} \closedcycle;

    % the line plots (y_h and y_f)    
    \addplot [stack plots=false, very thick,smooth,blue]  table [x=temps, y=y_h]   {\table};
    \addplot [stack plots=false, very thick,smooth,blue]  table [x=temps, y=y_f]   {\table};
    \end{axis}

\end{tikzpicture}
\end{document}

[Tex/LaTex] TikZ: two ellipses in different planes

One possibility would be to use xslant, yslant; the effect is better is one draws some containing planes:

\documentclass[convert = false, border = 1cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
  \pgfmathsetmacro{\as}{2};
  \pgfmathsetmacro{\bs}{1.95};
  \pgfmathsetmacro{\cs}{sqrt(\as^2 - \bs^2)}
  \pgfmathsetmacro{\al}{3};
  \pgfmathsetmacro{\bl}{2.25};
  \pgfmathsetmacro{\cl}{sqrt(\al^2 - \bl^2)}
  \pgfmathsetmacro{\xs}{abs(\cs - \cl)}

\begin{scope}[xslant=1,yslant=-1.2]
  \draw (0, 0) ellipse [x radius = \as cm, y radius = \bs cm];
  \draw[blue] (-2.5,-2.5) rectangle (3,2.5);
\end{scope}
\begin{scope}[xslant=0.2,yslant=-1.2]
  \draw[red] (\xs, 0) ellipse [x radius = \al cm, y radius = \bl cm];
  \draw[green] (-3,-2.5) rectangle (5.5,2.5);
\end{scope}
  \filldraw[black] (-\cs, 0) circle [radius = .1cm];

  \filldraw[black] (-\cl + \xs, 0) circle [radius = .1cm];
\end{tikzpicture}
\end{document}

enter image description here

A brief description of xslant and yslant:

\documentclass{article}
\usepackage[margin=3cm]{geometry}
\usepackage{amsmath}

\begin{document}

\verb|xslant| is the high-level version of \verb|\pgftransformxslant|. In \verb|pgfcoretransformations.code.tex| one finds
\begin{verbatim}
\def\pgftransformxslant#1{\pgftransformcm{1.0}{0}{#1}{1.0}{\pgfpointorigin}}
\end{verbatim}
where \verb|\pgftransformcm{<a>}{<b>}{<c>}{<d>}{<coordinate>}| is the low-level equivalent to
\begin{verbatim}
cm={<a>,<b>,<c>,<d>,<coordinate>}
\end{verbatim}
which has the following effect: if \verb|<coordinate>| specifies the point $(t_x,t_y)$, a given point $(x,y)$ will be transformed in $(x',y')$, where
\[
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
a & c \\
b & d
\end{bmatrix}
\begin{bmatrix}
x \\ y
\end{bmatrix}
+
\begin{bmatrix}
t_x \\ t_y
\end{bmatrix}.
\]
In particular, for \verb|xslant=k|, we have
\[
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
1 & k \\
0 & 1
\end{bmatrix}
\begin{bmatrix}
x \\ y
\end{bmatrix}
+
\begin{bmatrix}
t_x \\ t_y
\end{bmatrix}
\]
and from here,
\begin{align*}
x' &= x + ky + t_x, \\
y' &= y + t_y.
\end{align*}

Analogously, one can ontain the transformation associated to \verb|yslant|, taking into account the following definition:
\begin{verbatim}
\def\pgftransformyslant#1{\pgftransformcm{1.0}{#1}{0}{1.0}{\pgfpointorigin}}
\end{verbatim}

\end{document}

enter image description here

Best Answer

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[Tex/LaTex] plotting two time series with bounds

[Tex/LaTex] TikZ: two ellipses in different planes

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