[Tex/LaTex] How to draw a shaded sphere

shadingtikz-pgf

Andrew Stacey pointed out that the Rosetta Code entry "Draw a Sphere" doesn't have a TikZ entry yet.

Is there a way to draw a "properly" shaded sphere using TikZ? The ball shading would seem an obvious choice, but it uses a circular highlight, which is not what it would look like in reality. So: is there a way to make a sphere that would resemble a white, matte (i.e. non-shiny) ball that is illuminated by a single white light source?

This would mainly require getting a non-circular, correctly oriented highlight, I believe. Both Yori's and Altermundus' answer already do a great job at using a "softer" highlight, which looks more believable, but Altermundus' highlight is still circular, and while Yoris' is elliptic, it's not oriented correctly, I think.

Compare a circle with the ball shading to the example made with Perl 6:

\documentclass{article}

\usepackage{tikz}

\begin{document}

\begin{minipage}{2.5cm}\centering
\scriptsize That's not a sphere.

\tikz{
    \fill [black] (-1,-1) rectangle (1,1);
    \shade [ball color=white] (0,0) circle [radius=1cm];
}
\end{minipage}%
%
\begin{minipage}{2.5cm}\centering
\scriptsize \emph{That's} a sphere.

\includegraphics[width=2cm]{Sphere-perl6.png}
\end{minipage}
\end{document}

Best Answer

I'm following the earlier post Is there a way to tune ball shading in TikZ ?, particularly Stefan Kottwitz's answer. He showed how to use \pgfdeclareradialshading to change the radial shading. Changing the parameters for the radial and adding some clipping, I can produce this:

Is that sphere enough? Perhaps with some more tweaking it is possible to get an even better result. The code to produce this is:

\documentclass{article}
\usepackage{tikz}

\begin{document}
\makeatletter
\pgfdeclareradialshading[tikz@ball]{ball}{\pgfqpoint{-20bp}{20bp}}{%
 color(0bp)=(tikz@ball!0!white);
 color(17bp)=(tikz@ball!0!white);
 color(21bp)=(tikz@ball!70!black);
 color(25bp)=(black!70);
 color(30bp)=(black!70)}
\makeatother

\begin{tikzpicture}
    \fill [black] (-1,-1) rectangle (1,1);
    \begin{scope}
        \clip (0,0) circle (1);
        \shade [ball color=white] (-0.1,0) ellipse (1.2 and 1);
    \end{scope}
\end{tikzpicture}

\end{document}

Or, with a more ellipsoidal shading, one can get this:

The for this is:

\documentclass{article}

\usepackage{tikz}

\begin{document}

\makeatletter
\pgfdeclareradialshading[tikz@ball]{ball}{\pgfqpoint{0bp}{0bp}}{%
 color(0bp)=(tikz@ball!0!white);
 color(10bp)=(tikz@ball!0!white);
 color(15bp)=(tikz@ball!70!black);
 color(20bp)=(black!70);
 color(30bp)=(black!70)}
\makeatother

\begin{tikzpicture}

    \fill [black] (-1,-1) rectangle (1,1);

    \begin{scope}
        \clip (0,0) circle (1);
        \draw [fill=black!70] (0, 0) circle (1);
        \begin{scope}[transform canvas={rotate=45}]
        \shade [ball color=white] (0,0.5) ellipse (1.8 and 1.6);
        \end{scope}
    \end{scope}

\end{tikzpicture}

\end{document}

It's a matter of experimenting and fiddling around with the parameters to see what looks best according to you (judging from the discussion above, this seems quite subjective matter). Notice that you need to specify transform canvas={rotate=45} in the inner scope, not rotate=45 because the latter does not rotate the fill.

The first diagram:

enter image description here

\documentclass[pstricks,border=20pt]{standalone}
\usepackage{pst-eucl}
\begin{document}
\begin{pspicture}[showgrid=false](6,6)
    % declare the points, specify the labels and the labels' positions.
    \pstGeonode[PosAngle={180,90,0,-30,-90,-135}]
        (0,4){A_1}
        (3,6){A_2}
        (6,4){A_3}
        (5.5,2){A_4}
        (2,0){A_5}
        (0,0.5){A_n}
    % specify the intersection point between line A1A3 and A2A4, name the intersection point I.
    \pstInterLL[PointName=none,PointSymbol=none]{A_1}{A_3}{A_2}{A_4}{I}
    % fill the inner region
    \pspolygon[fillstyle=vlines](A_1)(I)(A_4)
    % construct the remaining inner lines
    \pstLineAB{A_2}{I}% you can also use \psline{A_2}{I} instead.
    \pstLineAB{A_3}{I}% you can also use \psline{A_3}{I} instead.
    % construct the outer lines
    \psline
        ([nodesep=5pt]{A_5}A_n)
        (A_n)
        (A_1)
        (A_2)
        (A_3)
        (A_4)
        (A_5)
        ([nodesep=5pt]{A_n}A_5)
    % construct a dashed line
    \psline[linestyle=dashed]
        ([nodesep=5pt]{A_n}A_5)
        ([nodesep=5pt]{A_5}A_n)
\end{pspicture}
\end{document}

The construction steps are summarized as follows,

enter image description here

The second diagram:

enter image description here

\documentclass[pstricks,border=20pt]{standalone}
\usepackage{pst-eucl}
\begin{document}
\begin{pspicture}[showgrid=false](6,6)
    \pstGeonode[PosAngle={180,90,0,0,-30,-90,-135}]
        (0,4){A_1}
        (3,6){A_2}
        (5,5){A_3}
        (6,3){A_4}
        (4.5,1.5){A_5}
        (2,0){A_6}
        (0,0){A_n}
    % fill the inner regions with even-odd rule.
    \pspolygon[fillstyle=eofill,fillcolor=gray](A_1)(A_4)(A_2)(A_5)(A_3)
    \psline(A_1)(A_5)
    \psline
        ([nodesep=5pt]{A_6}A_n)
        (A_n)
        (A_1)
        (A_2)
        (A_3)
        (A_4)
        (A_5)
        (A_6)
        ([nodesep=5pt]{A_n}A_6)
    \psline[linestyle=dashed]
        ([nodesep=5pt]{A_n}A_6)
        ([nodesep=5pt]{A_6}A_n)
\end{pspicture}
\end{document}

The construction steps are summarized as follows,

enter image description here

The last diagram:

enter image description here

\documentclass[pstricks,border=20pt]{standalone}
\usepackage{pst-eucl}
\usepackage{multido,fp}

\begin{document}
\begin{pspicture}[showgrid=false](-3,-3)(3,3)
    % declare the points, specify the labels and the labels' positions.
    \multido{\n=180+45,\i=1+1}{7}{\pstGeonode[PosAngle=-\n](3;-\n){A_\i}}
    \pstGeonode[PosAngle=-135](3;-135){A_n}
    \pscustom
    {
        \moveto([nodesep=5pt]{A_7}A_n)
        \lineto(A_n)
        \multido{\i=1+1}{7}{\lineto(A_\i)}
        \lineto([nodesep=5pt]{A_n}A_7)
    }
    \psline[linestyle=dashed]([nodesep=5pt]{A_n}A_7)([nodesep=5pt]{A_7}A_n)
    % specify the intersection points.
    \bgroup
        \psset{PointName=none,PointSymbol=none}
        \pstInterLL{A_1}{A_4}{A_2}{A_5}{P}
        \pstInterLL{A_1}{A_4}{A_3}{A_6}{Q}
        \pstInterLL{A_2}{A_5}{A_3}{A_6}{R}
    \egroup
    % fill the shaded region.
    \pspolygon[fillstyle=solid,fillcolor=yellow](P)(Q)(R)
    % construct the remaining lines.
    \multido{\ix=1+1}{4}
    {
        \FPeval\N{round(5-\ix:0)}
        \FPeval\Start{round(\ix+2:0)}
        \multido{\iy=\Start+1}{\N}{\psline(A_\ix)(A_\iy)}
    }
\end{pspicture}
\end{document}

[Tex/LaTex] How to draw a shaded triangle

Just to answer the unanswered.

enter image description here

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}

\definecolor{c1}{RGB}{0,129,188}
\definecolor{c2}{RGB}{252,177,49}
\definecolor{c3}{RGB}{35,34,35}

\begin{tikzpicture}
\begin{axis}[hide axis]
    \addplot[
        patch,
        shader=interp,
        mesh/color input=explicit,
        data cs=cart,
    ]
    coordinates {
        (0,0)   [color=c1]
        (5,2)   [color=c2]
        (10,-3) [color=c3]
    };
\end{axis}
\end{tikzpicture}
\end{document}

One of the easiest ways to do this is using pgfplots. Many other solutions can be found out here on tex.sx with different degrees of complexity and accuracy. But this seems simple with acceptable output.

Here I draw within an axis but hide it. This is essentially a plot with interpolated shading and the vertices colors are given explicitly.

Best Answer

Related Solutions

[Tex/LaTex] How to draw these polygons with shaded regions

The first diagram:

The second diagram:

The last diagram:

[Tex/LaTex] How to draw a shaded triangle

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