Bounding box is larger than expected when drawing a curved path

Question

I have been working on logo for my department and I have the following code. The problem is that whenever I compile the diagram seems to be larger than the actual logo. I do not know what is the problem. I know the numbers I have selected are not the best but any insights into the matter will be highly appreciated.

 \documentclass[letterpaper]{article}
 \usepackage[top=2cm,bottom=2cm,left=2cm,right=2cm]{geometry}
 %\usepackage{amsmath,amssymb,units}
 %\usepackage{enumitem,multicol}
 \usepackage{tikz}
 %\usetikzlibrary{arrows}
 \usepackage{lipsum}

 \begin{document}

 \lipsum[1-2]
 \begin{tikzpicture}[y=0.80pt, x=0.8pt,yscale=-1]
 \path[draw=black,fill=white]
   (258.9527,290.5199) .. controls (173.9885,538.4766) and (568.5860,261.2969) ..
   (306.5098,257.1141) .. controls (44.4337,252.9312) and (429.9845,542.5624) ..
   (352.9767,292.0206) .. controls (275.9689,41.4788) and (119.6549,497.6604) ..
   (334.1376,346.9999) .. controls (548.6203,196.3394) and (66.4622,188.6439) ..
   (276.0276,346.0724) .. controls (485.5930,503.5010) and (343.9169,42.5633) ..
   (258.9527,290.5199) -- cycle;
 \end{tikzpicture}
 \lipsum[1-2]
 \end{document} 

See image below:

Answer 1

Update : before to use a grid it's possible to use pdfcrop to get the dimensions of the "real" picture. You need to use \thispagestyle{empty} and you need to compile only the picture. You get a pdf file then with pdfcrop you get a new pdf file. Inside this pdf, you can read /BBox [0 0 146.908 142.991] (be careful with the units). We don't have the origin but we get the dimensions. pdfcrop can also give a pdf file that you can include with a correct bounding box.

Manually : With a grid

\documentclass[letterpaper]{article}
\usepackage{tikz}

 \begin{document}

 \begin{tikzpicture}[y=0.80pt, x=0.8pt,yscale=-1] 
\draw[help lines,step=8pt] (208,208) grid (400, 400);
 \clip (208,208) rectangle (400, 400);  
\path[draw=black]
   (258.9527,290.5199) .. controls (173.9885,538.4766) and (568.5860,261.2969) ..
   (306.5098,257.1141) .. controls (44.4337,252.9312) and (429.9845,542.5624) ..
   (352.9767,292.0206) .. controls (275.9689,41.4788) and (119.6549,497.6604) ..
   (334.1376,346.9999) .. controls (548.6203,196.3394) and (66.4622,188.6439) ..
   (276.0276,346.0724) .. controls (485.5930,503.5010) and (343.9169,42.5633) ..
   (258.9527,290.5199) -- cycle;
 \end{tikzpicture}
\begin{tikzpicture}[y=0.80pt, x=0.8pt,yscale=-1] 
 \path[draw=black] (213,215) rectangle (398, 395); 
 \clip (213,215) rectangle (398, 395);        
 \path[draw=black]
   (258.9527,290.5199) .. controls (173.9885,538.4766) and (568.5860,261.2969) ..
   (306.5098,257.1141) .. controls (44.4337,252.9312)  and (429.9845,542.5624) ..
   (352.9767,292.0206) .. controls (275.9689,41.4788)  and (119.6549,497.6604) ..
   (334.1376,346.9999) .. controls (548.6203,196.3394) and (66.4622,188.6439) ..
   (276.0276,346.0724) .. controls (485.5930,503.5010) and (343.9169,42.5633) ..
   (258.9527,290.5199) -- cycle;
 \end{tikzpicture}   
 \end{document} 

Answer 2

As seen in the answer by Peter Grill, the size of the bounding box is determined not only by the path points, but also by the control points. In order to reduce the size of the bounding box, we have to specify it explicitly.

The manual states:

PGF is reasonably good at keeping track of the size of your picture and reserving just the right amount of space for it in the main document. However, in some cases you may want to say things like “do not count this for the picture size” or “the picture is actually a little large.” For this you can use the option use as bounding box or the command \useasboundingbox, which is just a shorthand for \path[use as bounding box].

And especially with respect to curved lines:

... Controls points of a curve often lie far “outside” the curve and make the bounding box too large. In this case, you should use the [use as bounding box] option.

As a quick fix, you could add something like the following into your tikzpicture environment before drawing:

 \path[use as bounding box] (220, 200) rectangle (400, 400);

For more precise calculation, find points that will define the convex hull of your logo with sufficient precision and use a polygon as bounding box -- this works equally well.

Here is the result of the quick fix:

Answer 3

This is not an answer, but thought it might be useful to see why this is happening as @user946850 points out. I added the following to the code to see where the control points are:

\foreach \x in {{(173.9885,538.4766)}, {(568.5860,261.2969)}, {(44.4337,252.9312)},
{(429.9845,542.5624)}, {(275.9689,41.4788)}, {(119.6549,497.6604)}, {(548.6203,196.3394)}, {(66.4622,188.6439)}, {(485.5930,503.5010)}, {(343.9169,42.5633)}} {
\node [fill=red,shape=circle] at \x {};
};

Another way to see the bounding box is to apply the following at the end of the picture:

\draw [blue] (current bounding box.south west) rectangle (current bounding box.north east);

Answer 4

I added an experimental library bbox which computes the bounding box for curves. I tested it and it seems to work unless the curve has very steep angles, in which case there might be dimension too large errors. However, in this example and all ``reasonable'' cases it seems to work.

\documentclass[letterpaper]{article}
\usepackage[top=2cm,bottom=2cm,left=2cm,right=2cm]{geometry}
\usepackage{tikz}
\usetikzlibrary{bbox}

\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}[y=0.80pt, x=0.8pt,yscale=-1]
\path[draw=black,fill=white]
  (258.9527,290.5199) .. controls (173.9885,538.4766) and (568.5860,261.2969) ..
  (306.5098,257.1141) .. controls (44.4337,252.9312) and (429.9845,542.5624) ..
  (352.9767,292.0206) .. controls (275.9689,41.4788) and (119.6549,497.6604) ..
  (334.1376,346.9999) .. controls (548.6203,196.3394) and (66.4622,188.6439) ..
  (276.0276,346.0724) .. controls (485.5930,503.5010) and (343.9169,42.5633) ..
  (258.9527,290.5199) -- cycle;
\draw (current bounding box.south west) rectangle  (current bounding box.north
east);
\end{tikzpicture}
\caption{Default.}
\end{figure}
\begin{figure}
\centering
\begin{tikzpicture}[y=0.80pt, x=0.8pt,yscale=-1,bezier bounding box]
\path[draw=black,fill=white]
  (258.9527,290.5199) .. controls (173.9885,538.4766) and (568.5860,261.2969) ..
  (306.5098,257.1141) .. controls (44.4337,252.9312) and (429.9845,542.5624) ..
  (352.9767,292.0206) .. controls (275.9689,41.4788) and (119.6549,497.6604) ..
  (334.1376,346.9999) .. controls (548.6203,196.3394) and (66.4622,188.6439) ..
  (276.0276,346.0724) .. controls (485.5930,503.5010) and (343.9169,42.5633) ..
  (258.9527,290.5199) -- cycle;
\draw (current bounding box.south west) rectangle  (current bounding box.north
east);
\end{tikzpicture}
\caption{With \texttt{bezier bounding box} from the \texttt{bbox} library
switched on.}
\end{figure}
\end{document}

The theory behind this is very simple. The TeX code for the following can be found under this link.

For those who do not want to follow external links: this is the code of the library:

\tikzset{%
  bezier bounding box/.is choice,%
  bezier bounding box/.default=true,%
  bezier bounding box/true/.code=\tikzset{switch on bezier bounding box},%
  bezier bounding box/false/.code=\tikzset{switch off bezier bounding box}}%
\tikzset{switch off bezier bounding box/.code={%
\def\pgf@lt@curveto##1##2##3##4##5##6{%
  \pgf@protocolsizes{##1}{##2}%
  \pgf@protocolsizes{##3}{##4}%
  \pgf@protocolsizes{##5}{##6}%
  \pgfsyssoftpath@curveto{\the##1}{\the##2}{\the##3}{\the##4}{\the##5}{\the##6}%
}%
\let\pgf@nlt@curveto\pgf@lt@curveto}}
%
% it might just be me but according to what I believe to find 
% \pgfmathsetlengthmacro appears to generate spaces
%
\tikzset{switch on bezier bounding box/.code={%
\def\pgf@lt@curveto##1##2##3##4##5##6{%
  % extrema in x
  \pgfmathsetmacro{\pgf@temp@b}{abs(\pgf@path@lastx-##5-3*##1+3*##3)}%
  % ^^^ this is used for the denominator below, cannot become too small
  \pgfmathsetmacro{\pgf@temp@c}{max(1+\pgf@path@lastx,max(##1,max(##3,##5)))}%
  % ^^^ in order to avoid dimension too large errors from squaring lengths in pt
  \pgfmathparse{((##1/\pgf@temp@c)*(##1/\pgf@temp@c)-1*((##1/\pgf@temp@c)*(##3/\pgf@temp@c))+(##3/\pgf@temp@c)*(##3/\pgf@temp@c)-1*((##1/\pgf@temp@c)*(##5/\pgf@temp@c))+(-(##3/\pgf@temp@c)+(##5/\pgf@temp@c))*(\pgf@path@lastx/\pgf@temp@c))}%
  \pgfutil@tempdima=\pgfmathresult pt\relax% 
  % ^^^ discriminant
  \ifdim\pgf@temp@b pt<0.01pt\relax%
   % approximately linear  
   \pgfmathparse{abs(2*(##1)-2*(##3)+(##5))}%
   \pgfutil@tempdimb=\pgfmathresult pt\relax%
   \ifdim\pgfutil@tempdimb<0.1pt\relax%
    % if the denominator is very small, it is *likely* large but could be 0/0
   \else
    \pgfmathsetmacro{\pgf@temp@a}{(2*(##1)-3*(##3)+(##5))/(2*(##1)-2*(##3)+(##5))}%
    \pgfmathparse{\pgf@path@lastx*pow(1-\pgf@temp@a,3)+3*##1*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##3*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##5*pow(\pgf@temp@a,3)}%
    \pgfutil@tempdimb=\pgfmathresult pt\relax%
    \pgf@protocolsizes{\pgfutil@tempdimb}{##6}%
   \fi%
  \else
   \ifdim\pgfutil@tempdima<0pt\relax% negative discriminant -> no turning point
   \else
     \pgfmathsetmacro{\pgf@temp@a}{min(1,max(0,(\pgf@path@lastx-2*##1+##3-\pgf@temp@c*sqrt(\pgfutil@tempdima))/(\pgf@path@lastx-##5-3*##1+3*##3)))}%
     \pgfmathparse{\pgf@path@lastx*pow(1-\pgf@temp@a,3)+3*##1*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##3*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##5*pow(\pgf@temp@a,3)}%
     \pgfutil@tempdimb=\pgfmathresult pt\relax%
     \pgf@protocolsizes{\pgfutil@tempdimb}{##6}%
     \pgfmathsetmacro{\pgf@temp@a}{min(1,max(0,(\pgf@path@lastx-2*##1+##3+\pgf@temp@c*sqrt(\pgfutil@tempdima))/(\pgf@path@lastx-##5-3*##1+3*##3)))}%
     \pgfmathparse{\pgf@path@lastx*pow(1-\pgf@temp@a,3)+3*##1*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##3*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##5*pow(\pgf@temp@a,3)}%
     \pgfutil@tempdimb=\pgfmathresult pt\relax%
     \pgf@protocolsizes{\pgfutil@tempdimb}{##6}%
   \fi% 
  \fi 
  %%%%%%%%%%%%%%%%%%%%%%%%%%%
  % extrema in y (completely analogous to the above)
  \pgfmathsetmacro{\pgf@temp@b}{abs(\pgf@path@lasty-##6-3*##2+3*##4)}%
  \pgfmathsetmacro{\pgf@temp@c}{max(1+\pgf@path@lasty,max(##2,max(##4,##6)))}%
  \pgfmathparse{((##2/\pgf@temp@c)*(##2/\pgf@temp@c)-1*((##2/\pgf@temp@c)*(##4/\pgf@temp@c))+(##4/\pgf@temp@c)*(##4/\pgf@temp@c)-1*((##2/\pgf@temp@c)*(##6/\pgf@temp@c))+(-(##4/\pgf@temp@c)+(##6/\pgf@temp@c))*(\pgf@path@lasty/\pgf@temp@c))}%
  \pgfutil@tempdima=\pgfmathresult pt\relax% 
  % ^^^ discriminant
  \ifdim\pgf@temp@b pt<0.01pt\relax%
   % approximately linear  
   \pgfmathparse{abs(2*(##2)-2*(##4)+(##6))}%
   \pgfutil@tempdimb=\pgfmathresult pt\relax%
   \ifdim\pgfutil@tempdimb<0.1pt\relax%
    % if the denominator is very small, it is *likely* large but could be 0/0
   \else
    \pgfmathsetmacro{\pgf@temp@a}{(2*(##2)-3*(##4)+(##6))/(2*(##2)-2*(##4)+(##6))}%
    \pgfmathparse{\pgf@path@lasty*pow(1-\pgf@temp@a,3)+3*##2*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##4*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##6*pow(\pgf@temp@a,3)}%
    \pgfutil@tempdimb=\pgfmathresult pt\relax%
    \pgf@protocolsizes{##5}{\pgfutil@tempdimb}%
   \fi%
  \else
   \ifdim\pgfutil@tempdima<0pt\relax% negative discriminant -> no turning point
   \else
     \pgfmathsetmacro{\pgf@temp@a}{min(1,max(0,(\pgf@path@lasty-2*##2+##4-\pgf@temp@c*sqrt(\pgfutil@tempdima))/(\pgf@path@lasty-##6-3*##2+3*##4)))}%
     \pgfmathparse{\pgf@path@lasty*pow(1-\pgf@temp@a,3)+3*##2*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##4*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##6*pow(\pgf@temp@a,3)}%
     \pgfutil@tempdimb=\pgfmathresult pt\relax%
     \pgf@protocolsizes{##5}{\pgfutil@tempdimb}%
     \pgfmathsetmacro{\pgf@temp@a}{min(1,max(0,(\pgf@path@lasty-2*##2+##4+\pgf@temp@c*sqrt(\pgfutil@tempdima))/(\pgf@path@lasty-##6-3*##2+3*##4)))}%
     \pgfmathparse{\pgf@path@lasty*pow(1-\pgf@temp@a,3)+3*##2*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##4*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##6*pow(\pgf@temp@a,3)}%
     \pgfutil@tempdimb=\pgfmathresult pt\relax%
     \pgf@protocolsizes{##5}{\pgfutil@tempdimb}%
   \fi% 
  \fi 
  \pgf@protocolsizes{\pgf@path@lastx}{\pgf@path@lasty}%
  \pgf@protocolsizes{##5}{##6}%
  \pgfsyssoftpath@curveto{\the##1}{\the##2}{\the##3}{\the##4}{\the##5}{\the##6}%
}
\let\pgf@nlt@curveto\pgf@lt@curveto}}% fix me: 0/0 cases and occasional
% dimension too large errors (what's the cause?)

If you do not want do load the library, you may just copy the code and sandwich it between \makeatletter and \makeatother.

If you encounter dimension too large errors, you may want to use

\usetikzlibrary{fpu}
\newcommand{\pgfmathsetmacroFPU}[2]{\begingroup%
\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
\pgfmathsetmacro{#1}{#2}%
\pgfmathsmuggle#1\endgroup}
\newcommand{\pgfmathparseFPU}[1]{\begingroup%
\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
\pgfmathparse{#1}%
\pgfmathsmuggle\pgfmathresult\endgroup}
\tikzset{%
  bezier bounding box/.is choice,%
  bezier bounding box/.default=true,%
  bezier bounding box/true/.code=\tikzset{switch on bezier bounding box},%
  bezier bounding box/false/.code=\tikzset{switch off bezier bounding box}}%
\tikzset{switch off bezier bounding box/.code={%
\def\pgf@lt@curveto##1##2##3##4##5##6{%
  \pgf@protocolsizes{##1}{##2}%
  \pgf@protocolsizes{##3}{##4}%
  \pgf@protocolsizes{##5}{##6}%
  \pgfsyssoftpath@curveto{\the##1}{\the##2}{\the##3}{\the##4}{\the##5}{\the##6}%
}%
\let\pgf@nlt@curveto\pgf@lt@curveto}}
%
% it might just be me but according to what I believe to find 
% \pgfmathsetlengthmacro appears to generate spaces
%
\tikzset{switch on bezier bounding box/.code={%
\def\pgf@lt@curveto##1##2##3##4##5##6{%
  % extrema in x
  \pgfmathsetmacroFPU{\pgf@temp@b}{abs(\pgf@path@lastx-##5-3*##1+3*##3)}%
  % ^^^ this is used for the denominator below, cannot become too small
  \pgfmathsetmacroFPU{\pgf@temp@c}{max(1+\pgf@path@lastx,max(##1,max(##3,##5)))}%
  % ^^^ in order to avoid dimension too large errors from squaring lengths in pt
  \pgfmathparseFPU{((##1/\pgf@temp@c)*(##1/\pgf@temp@c)-1*((##1/\pgf@temp@c)*(##3/\pgf@temp@c))+(##3/\pgf@temp@c)*(##3/\pgf@temp@c)-1*((##1/\pgf@temp@c)*(##5/\pgf@temp@c))+(-(##3/\pgf@temp@c)+(##5/\pgf@temp@c))*(\pgf@path@lastx/\pgf@temp@c))}%
  \pgfutil@tempdima=\pgfmathresult pt\relax% 
  % ^^^ discriminant
  \ifdim\pgf@temp@b pt<0.01pt\relax%
   % approximately linear  
   \pgfmathparseFPU{abs(2*(##1)-2*(##3)+(##5))}%
   \pgfutil@tempdimb=\pgfmathresult pt\relax%
   \ifdim\pgfutil@tempdimb<0.1pt\relax%
    % if the denominator is very small, t is *likely* large but could be 0/0
   \else
    \pgfmathsetmacroFPU{\pgf@temp@a}{(2*(##1)-3*(##3)+(##5))/(2*(##1)-2*(##3)+(##5))}%
    \pgfmathparseFPU{\pgf@path@lastx*pow(1-\pgf@temp@a,3)+3*##1*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##3*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##5*pow(\pgf@temp@a,3)}%
    \pgfutil@tempdimb=\pgfmathresult pt\relax%
    \pgf@protocolsizes{\pgfutil@tempdimb}{##6}%
   \fi%
  \else
   \ifdim\pgfutil@tempdima<0pt\relax% negative discriminant -> no turning point
   \else
     \pgfmathsetmacroFPU{\pgf@temp@a}{min(1,max(0,(\pgf@path@lastx-2*##1+##3-\pgf@temp@c*sqrt(\pgfutil@tempdima))/(\pgf@path@lastx-##5-3*##1+3*##3)))}%
     \pgfmathparseFPU{\pgf@path@lastx*pow(1-\pgf@temp@a,3)+3*##1*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##3*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##5*pow(\pgf@temp@a,3)}%
     \pgfutil@tempdimb=\pgfmathresult pt\relax%
     \pgf@protocolsizes{\pgfutil@tempdimb}{##6}%
     \pgfmathsetmacroFPU{\pgf@temp@a}{min(1,max(0,(\pgf@path@lastx-2*##1+##3+\pgf@temp@c*sqrt(\pgfutil@tempdima))/(\pgf@path@lastx-##5-3*##1+3*##3)))}%
     \pgfmathparseFPU{\pgf@path@lastx*pow(1-\pgf@temp@a,3)+3*##1*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##3*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##5*pow(\pgf@temp@a,3)}%
     \pgfutil@tempdimb=\pgfmathresult pt\relax%
     \pgf@protocolsizes{\pgfutil@tempdimb}{##6}%
   \fi% 
  \fi 
  %%%%%%%%%%%%%%%%%%%%%%%%%%%
  % extrema in y (completely analogous to the above)
  \pgfmathsetmacroFPU{\pgf@temp@b}{abs(\pgf@path@lasty-##6-3*##2+3*##4)}%
  \pgfmathsetmacroFPU{\pgf@temp@c}{max(1+\pgf@path@lasty,max(##2,max(##4,##6)))}%
  \pgfmathparseFPU{((##2/\pgf@temp@c)*(##2/\pgf@temp@c)-1*((##2/\pgf@temp@c)*(##4/\pgf@temp@c))+(##4/\pgf@temp@c)*(##4/\pgf@temp@c)-1*((##2/\pgf@temp@c)*(##6/\pgf@temp@c))+(-(##4/\pgf@temp@c)+(##6/\pgf@temp@c))*(\pgf@path@lasty/\pgf@temp@c))}%
  \pgfutil@tempdima=\pgfmathresult pt\relax% 
  % ^^^ discriminant
  \ifdim\pgf@temp@b pt<0.01pt\relax%
   % approximately linear  
   \pgfmathparseFPU{abs(2*(##2)-2*(##4)+(##6))}%
   \pgfutil@tempdimb=\pgfmathresult pt\relax%
   \ifdim\pgfutil@tempdimb<0.1pt\relax%
    % if the denominator is very small, t is *likely* large but could be 0/0
   \else
    \pgfmathsetmacroFPU{\pgf@temp@a}{(2*(##2)-3*(##4)+(##6))/(2*(##2)-2*(##4)+(##6))}%
    \pgfmathparseFPU{\pgf@path@lasty*pow(1-\pgf@temp@a,3)+3*##2*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##4*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##6*pow(\pgf@temp@a,3)}%
    \pgfutil@tempdimb=\pgfmathresult pt\relax%
    \pgf@protocolsizes{##5}{\pgfutil@tempdimb}%
   \fi%
  \else
   \ifdim\pgfutil@tempdima<0pt\relax% negative discriminant -> no turning point
   \else
     \pgfmathsetmacroFPU{\pgf@temp@a}{min(1,max(0,(\pgf@path@lasty-2*##2+##4-\pgf@temp@c*sqrt(\pgfutil@tempdima))/(\pgf@path@lasty-##6-3*##2+3*##4)))}%
     \pgfmathparseFPU{\pgf@path@lasty*pow(1-\pgf@temp@a,3)+3*##2*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##4*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##6*pow(\pgf@temp@a,3)}%
     \pgfutil@tempdimb=\pgfmathresult pt\relax%
     \pgf@protocolsizes{##5}{\pgfutil@tempdimb}%
     \pgfmathsetmacroFPU{\pgf@temp@a}{min(1,max(0,(\pgf@path@lasty-2*##2+##4+\pgf@temp@c*sqrt(\pgfutil@tempdima))/(\pgf@path@lasty-##6-3*##2+3*##4)))}%
     \pgfmathparseFPU{\pgf@path@lasty*pow(1-\pgf@temp@a,3)+3*##2*pow(1-\pgf@temp@a,2)*\pgf@temp@a+3*##4*(1-\pgf@temp@a)*\pgf@temp@a*\pgf@temp@a+##6*pow(\pgf@temp@a,3)}%
     \pgfutil@tempdimb=\pgfmathresult pt\relax%
     \pgf@protocolsizes{##5}{\pgfutil@tempdimb}%
   \fi% 
  \fi 
  \pgf@protocolsizes{\pgf@path@lastx}{\pgf@path@lasty}%
  \pgf@protocolsizes{##5}{##6}%
  \pgfsyssoftpath@curveto{\the##1}{\the##2}{\the##3}{\the##4}{\the##5}{\the##6}%
}
\let\pgf@nlt@curveto\pgf@lt@curveto}}
\endinput

instead. This is even slower than the above but has less problems with the dimension too large errors.

Answer 5

clip the figure before drawing

\documentclass[letterpaper]{article}
 \usepackage[top=2cm,bottom=2cm,left=2cm,right=2cm]{geometry}
 %\usepackage{amsmath,amssymb,units}
 %\usepackage{enumitem,multicol}
 \usepackage{tikz}
 %\usetikzlibrary{arrows}
 \usepackage{lipsum}

 \begin{document}

 \lipsum[1-2]
 \begin{tikzpicture}[y=0.80pt, x=0.8pt,yscale=-1]
    \clip[draw](305,305) circle (100);
 \path[draw=red,fill=white]
   (258.9527,290.5199) .. controls (173.9885,538.4766) and (568.5860,261.2969) ..
   (306.5098,257.1141) .. controls (44.4337,252.9312) and (429.9845,542.5624) ..
   (352.9767,292.0206) .. controls (275.9689,41.4788) and (119.6549,497.6604) ..
   (334.1376,346.9999) .. controls (548.6203,196.3394) and (66.4622,188.6439) ..
   (276.0276,346.0724) .. controls (485.5930,503.5010) and (343.9169,42.5633) ..
   (258.9527,290.5199) -- cycle;
 \end{tikzpicture}
 \lipsum[1-2]
 \end{document}

Answer 6

There is/was a library taking care of this. The first version of the library was incorporated in pgf without my approval, and had bugs. Some bugs were pointed out on the GitHub site, and fixed. In particular this issue was a very nice issue report which pointed out some nontrivial problems. I hadn't appreciated that arrow heads deform a path after it got reported to the bounding box protocol (unless one loads bending). Henri Menke has decided to take the library out of pgf.¹ Because of the use of strong language and inappropriate mocking in a chat room I have decided to leave the chat and to delete my GitHub account, the more so since I never really got used to that repository.

However, the good news is that you can still use the library. Save the following under pgflibrarybbox.code.tex:

% Copyright 2020 by an anonymous contributor
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU General Public License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.


\usepgflibrary{fpu}
\global\let\pgf@bbox@lt@curveto@normal\pgf@lt@curveto
\global\let\pgf@bbox@nlt@curveto@normal\pgf@nlt@curveto

\pgfqkeys{/pgf}{bezier bounding box/.is if=pgf@bbox@switch@}


\pgfqkeys{/pgf}{use fpu reciprocal/.code={%
\def\pgfmathreciprocal@##1{%
    \begingroup
    \pgfkeys{/pgf/fpu=true,/pgf/fpu/output format=fixed}%
    \pgfmathparse{1/##1}%
    \pgfmath@smuggleone\pgfmathresult
    \endgroup
}}}%


\def\pgf@bbox@switch@false{%
  \let\pgf@lt@curveto \pgf@bbox@lt@curveto@normal
  \let\pgf@nlt@curveto\pgf@bbox@nlt@curveto@normal
}

\def\pgf@bbox@switch@true{%
  \let\pgf@lt@curveto \pgf@bbox@curveto
  \let\pgf@nlt@curveto\pgf@bbox@curveto
}
\def\pgf@bbox@curveto#1#2#3#4#5#6{%
\begingroup
\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
  % extrema in x
  % first discriminant d1, must be \ne 0
  \pgfmathsetmacro{\pgf@temp@a}{(\pgf@path@lastx)-(#5)-3*(#1)+3*(#3)}%
  \pgfmathtruncatemacro{\pgf@temp@c}{(abs(\pgf@temp@a)>0.1?1:0)}%
  \ifnum\pgf@temp@c=1\relax
    % second discriminant d2, must be \ge 0
    \pgfmathsetmacro{\pgf@temp@b}{(\pgf@path@lastx)*(#5)-(#5)*(#1)+(#1)*(#1)-(\pgf@path@lastx)*(#3)-(#1)*(#3)+(#3)*(#3)}%
    \pgfmathtruncatemacro{\pgf@temp@c}{sign(\pgf@temp@b)}%
    \ifnum\pgf@temp@c<0
    \else
      \pgfmathsetmacro{\pgf@temp@b}{sqrt(abs(\pgf@temp@b))}%
      \pgfmathsetmacro{\pgf@temp@c}{max(0,min(1,((\pgf@path@lastx)-2*(#1)+(#3)-\pgf@temp@b)/\pgf@temp@a))}%  
      \pgfmathparse{(\pgf@path@lastx)*pow((1-\pgf@temp@c),3)+3*(#1)*pow((1-\pgf@temp@c),2)*\pgf@temp@c+3*(#3)*(1-\pgf@temp@c)*\pgf@temp@c*\pgf@temp@c+(#5)*\pgf@temp@c*\pgf@temp@c*\pgf@temp@c}%
      \pgfutil@tempdimb=\pgfmathresult pt\relax%
      \pgf@protocolsizes{\pgfutil@tempdimb}{\pgf@path@lasty}%
      \pgfmathsetmacro{\pgf@temp@c}{max(0,min(1,((\pgf@path@lastx)-2*(#1)+(#3)+\pgf@temp@b)/\pgf@temp@a))}%  
      \pgfmathparse{(\pgf@path@lastx)*pow((1-\pgf@temp@c),3)+3*(#1)*pow((1-\pgf@temp@c),2)*\pgf@temp@c+3*(#3)*(1-\pgf@temp@c)*\pgf@temp@c*\pgf@temp@c+(#5)*\pgf@temp@c*\pgf@temp@c*\pgf@temp@c}%
      \pgfutil@tempdimb=\pgfmathresult pt\relax%
      \pgf@protocolsizes{\pgfutil@tempdimb}{\pgf@path@lasty}%
    \fi
  \else
    % third discriminant d3, must be \ne 0
    \pgfmathsetmacro{\pgf@temp@b}{abs((#5)+(#1)-2*(#3))}%
    \pgfmathtruncatemacro{\pgf@temp@c}{(abs(\pgf@temp@b)>0.1?1:0)}%
    \ifnum\pgf@temp@c=1\relax
      \pgfmathsetmacro{\pgf@temp@c}{((#5)+2*(#1)-3*(#3))/((#5)+(#1)-2*(#3))}%
      \pgfmathparse{(\pgf@path@lastx)*pow((1-\pgf@temp@c),3)+3*(#1)*pow((1-\pgf@temp@c),2)*\pgf@temp@c+3*(#3)*(1-\pgf@temp@c)*\pgf@temp@c*\pgf@temp@c+(#5)*\pgf@temp@c*\pgf@temp@c*\pgf@temp@c}%
      \pgfutil@tempdimb=\pgfmathresult pt\relax%
      \pgf@protocolsizes{\pgfutil@tempdimb}{\pgf@path@lasty}%
    \fi
  \fi
  % 0/0
  \pgfmathsetmacro{\pgf@temp@a}{(#5)+(#1)-2*(#3)}%
  \pgfmathtruncatemacro{\pgf@temp@b}{(abs(\pgf@temp@a)>0.1?1:0)}%
  \ifnum\pgf@temp@b=1\relax
    \pgfmathsetmacro{\pgf@temp@c}{max(0,min(1,((#5)+2*(#1)-3*(#3))/(2*\pgf@temp@a)))}%
  \else 
    \pgfmathsetmacro{\pgf@temp@c}{0.5}%
  \fi   
  \pgfmathparse{(\pgf@path@lastx)*pow((1-\pgf@temp@c),3)+3*(#1)*pow((1-\pgf@temp@c),2)*\pgf@temp@c+3*(#3)*(1-\pgf@temp@c)*\pgf@temp@c*\pgf@temp@c+(#5)*\pgf@temp@c*\pgf@temp@c*\pgf@temp@c}%
  \pgfutil@tempdimb=\pgfmathresult pt\relax%
  \pgf@protocolsizes{\pgfutil@tempdimb}{\pgf@path@lasty}%
%  
% y code
  % first discriminant d1, must be \ne 0
  \pgfmathsetmacro{\pgf@temp@a}{(\pgf@path@lasty)-(#6)-3*(#2)+3*(#4)}%
  \pgfmathtruncatemacro{\pgf@temp@c}{(abs(\pgf@temp@a)>0.1?1:0)}%
  \ifnum\pgf@temp@c=1\relax
    % second discriminant d2, must be \ge 0
    \pgfmathsetmacro{\pgf@temp@b}{(\pgf@path@lasty)*(#6)-(#6)*(#2)+(#2)*(#2)-(\pgf@path@lasty)*(#4)-(#2)*(#4)+(#4)*(#4)}%
    \pgfmathtruncatemacro{\pgf@temp@c}{sign(\pgf@temp@b)}%
    \ifnum\pgf@temp@c<0
    \else
      \pgfmathsetmacro{\pgf@temp@b}{sqrt(abs(\pgf@temp@b))}%
      \pgfmathsetmacro{\pgf@temp@c}{max(0,min(1,((\pgf@path@lasty)-2*(#2)+(#4)-\pgf@temp@b)/\pgf@temp@a))}%  
      \pgfmathparse{(\pgf@path@lasty)*pow((1-\pgf@temp@c),3)+3*(#2)*pow((1-\pgf@temp@c),2)*\pgf@temp@c+3*(#4)*(1-\pgf@temp@c)*\pgf@temp@c*\pgf@temp@c+(#6)*\pgf@temp@c*\pgf@temp@c*\pgf@temp@c}%
      \pgfutil@tempdimb=\pgfmathresult pt\relax%
      \pgf@protocolsizes{\pgf@path@lastx}{\pgfutil@tempdimb}%
      \pgfmathsetmacro{\pgf@temp@c}{max(0,min(1,((\pgf@path@lasty)-2*(#2)+(#4)+\pgf@temp@b)/\pgf@temp@a))}%  
      \pgfmathparse{(\pgf@path@lasty)*pow((1-\pgf@temp@c),3)+3*(#2)*pow((1-\pgf@temp@c),2)*\pgf@temp@c+3*(#4)*(1-\pgf@temp@c)*\pgf@temp@c*\pgf@temp@c+(#6)*\pgf@temp@c*\pgf@temp@c*\pgf@temp@c}%
      \pgfutil@tempdimb=\pgfmathresult pt\relax%
      \pgf@protocolsizes{\pgf@path@lastx}{\pgfutil@tempdimb}%
    \fi
  \else
    % third discriminant d3, must be \ne 0
    \pgfmathsetmacro{\pgf@temp@b}{abs((#6)+(#2)-2*(#4))}%
    \pgfmathtruncatemacro{\pgf@temp@c}{(abs(\pgf@temp@b)>0.1?1:0)}%
    \ifnum\pgf@temp@c=1\relax
      \pgfmathsetmacro{\pgf@temp@c}{((#6)+2*(#2)-3*(#4))/((#6)+(#2)-2*(#4))}%
      \pgfmathparse{(\pgf@path@lasty)*pow((1-\pgf@temp@c),3)+3*(#2)*pow((1-\pgf@temp@c),2)*\pgf@temp@c+3*(#4)*(1-\pgf@temp@c)*\pgf@temp@c*\pgf@temp@c+(#6)*\pgf@temp@c*\pgf@temp@c*\pgf@temp@c}%
      \pgfutil@tempdimb=\pgfmathresult pt\relax%
      \pgf@protocolsizes{\pgf@path@lastx}{\pgfutil@tempdimb}%
    \fi
  \fi
  % 0/0
  \pgfmathsetmacro{\pgf@temp@a}{(#6)+(#2)-2*(#4)}%
  \pgfmathtruncatemacro{\pgf@temp@b}{(abs(\pgf@temp@a)>0.1?1:0)}%
  \ifnum\pgf@temp@b=1\relax
    \pgfmathsetmacro{\pgf@temp@c}{max(0,min(1,((#6)+2*(#2)-3*(#4))/(2*\pgf@temp@a)))}%
  \else 
    \pgfmathsetmacro{\pgf@temp@c}{0.5}%
  \fi   
  \pgfmathparse{(\pgf@path@lasty)*pow((1-\pgf@temp@c),3)+3*(#2)*pow((1-\pgf@temp@c),2)*\pgf@temp@c+3*(#4)*(1-\pgf@temp@c)*\pgf@temp@c*\pgf@temp@c+(#6)*\pgf@temp@c*\pgf@temp@c*\pgf@temp@c}%
  \pgfutil@tempdimb=\pgfmathresult pt\relax%
  \pgf@protocolsizes{\pgf@path@lastx}{\pgfutil@tempdimb}%
%  
  \pgf@protocolsizes{\pgf@path@lastx}{\pgf@path@lasty}%
  \pgf@protocolsizes{#5}{#6}%
  \endgroup
  \pgfsyssoftpath@curveto{\the#1}{\the#2}{\the#3}{\the#4}{\the#5}{\the#6}%
}
\endinput

This is a sample document.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{bbox}
\usetikzlibrary{positioning,calc,bending}
\begin{document}
\message{For one hundred curves the compilation takes a few seconds.}

\subsection*{Code example from issue \#856}


\begin{tikzpicture}[bezier bounding box=true,
    atomicNode/.style={rectangle,draw,minimum width=4em,minimum height=4em}]
    \node[atomicNode] (upper) {};
    \node[atomicNode,below=of upper] (lower) {};
    \coordinate (zUpper) at ($(upper.north west)!.75!(upper.south west)$);
    \coordinate (yUpper) at (upper.east);
    \coordinate (zLower) at ($(lower.north east)!.25!(lower.south east)$);
    \coordinate (yLower) at (lower.west);
    \draw[-latex] (yUpper) .. controls ($(yUpper)+(13em,0)$) and ($(yLower)-(13em,0)$) .. (yLower);
    \draw[-latex] (zLower) .. controls ($(zLower)+(13em,0)$) and ($(zUpper)-(13em,0)$) .. (zUpper);
    \draw  (current bounding box.north west) rectangle (current bounding box.south east);
\end{tikzpicture}

\subsection*{Code example from issue \#838}

\begin{tikzpicture}[bezier bounding box=true]
  \draw (1,0) .. controls (5,1) and (5,2) .. (1,1);
  \draw (current bounding box.south west) rectangle
    (current bounding box.north east);
\end{tikzpicture}

  
\subsection*{Cubic B\'ezier curves}

\foreach \X in {1,...,100}
{\begin{tikzpicture}
\pgfmathsetseed{\X}
\pgfmathsetmacro{\rnda}{360*rnd}
\pgfmathsetmacro{\rndb}{360*rnd}
\pgfmathsetmacro{\rndc}{360*rnd}
\pgfmathsetmacro{\rndd}{3*rnd}
\pgfmathsetmacro{\rnde}{3*rnd}
\pgfmathsetmacro{\rndf}{3*rnd}
 \begin{scope}[local bounding box=without,red]
  \draw (0,0)  .. controls (\rnda:\rndd) and (\rndb:\rnde) .. (\rndc:\rndf);
  \draw[overlay] (0,0) circle[radius=1pt] (\rnda:\rndd) circle[radius=1pt]
   (\rndb:\rnde) circle[radius=1pt] 
   (\rndc:\rndf) circle[radius=1pt];
 \end{scope}
 \draw[red] (without.south west) rectangle (without.north east);
 %
 \begin{scope}[xshift=3.5cm]
  \begin{scope}[local bounding box=with,use fpu reciprocal,bezier bounding box=true]
   \draw (0,0)  .. controls (\rnda:\rndd) and (\rndb:\rnde) .. (\rndc:\rndf);
  \end{scope} 
  \draw[overlay] (0,0) circle[radius=1pt] (\rnda:\rndd) circle[radius=1pt]
   (\rndb:\rnde) circle[radius=1pt] 
   (\rndc:\rndf) circle[radius=1pt];
 \end{scope}
 \draw (with.south west) rectangle (with.north east);
\end{tikzpicture}\par}
\clearpage

\subsection*{Quadratic B\'ezier curves}

\foreach \X in {1,...,100}
{\begin{tikzpicture}
\pgfmathsetseed{\X}
\pgfmathsetmacro{\rnda}{360*rnd}
\pgfmathsetmacro{\rndc}{360*rnd}
\pgfmathsetmacro{\rndd}{3*rnd}
\pgfmathsetmacro{\rnde}{3*rnd}
\pgfmathsetmacro{\rndf}{3*rnd}
 \begin{scope}[local bounding box=without,red]
  \draw (0,0)  .. controls (\rnda:\rndd) .. (\rndc:\rndf);
  \draw[overlay] (0,0) circle[radius=1pt] (\rnda:\rndd) circle[radius=1pt]
   (\rndc:\rndf) circle[radius=1pt];
 \end{scope}
 \draw[red] (without.south west) rectangle (without.north east);
 %
 \begin{scope}[xshift=3.5cm]
  \begin{scope}[local bounding box=with,bezier bounding box=true]
   \draw (0,0)  .. controls (\rnda:\rndd) .. (\rndc:\rndf);
  \end{scope} 
   \draw[overlay] (0,0) circle[radius=1pt] (\rnda:\rndd) circle[radius=1pt]
    (\rndc:\rndf) circle[radius=1pt];
 \end{scope}
 \draw (with.south west) rectangle (with.north east);
\end{tikzpicture}\par}
\end{document}

I have also written a manual for that, but there is no space to upload it.² The pgf maintainers have a copy. Let me mention two potentially important points:

1. Adding arrow heads deforms a path after it has been reported to the bounding box. Loading the bending library, which switches on the key /pgf/arrow keys/flex, is sufficient to avoid the deformation, and thus to obtain the correct bounding box.
2. Another potentially important point concerns Dimension too large errors. Empirically I find that they occur very rarely, if at all. The culprit is the reciprocal, see this post and this issue. Installing an fpu reciprocal solved the problem in all cases I have encountered. Apart from that, installing an fpu reciprocal fixes a large subset of the Dimension too large errors that occur in decorations, but not all of them.³

_{¹The reason is not that the library would not work, it does work, in particular after the upgrade. The dispute was on how one writes Bézier, apparently using B\'ezier in the source code is a crime, and reason for others to step on me. I do not support this view, nor behavior, and quit.}

_{²I'd like to thank Stefan Pinnow for improvements.}

_{³The use fpu reciprocal key will probably appear under the name /pgf/fpu/install only={reciprocal} in pgf. Of course, I got first shouted at for suggesting to add such a key/functionality to pgf. After it turned out useful, it got renamed, and the credit goes to others. Anyway, the upshot is that you may use use /pgf/fpu/install only={reciprocal} instead of use fpu reciprocal. Apart from explaining why the library will disappear from the distributions, these discussions are irrelevant. This post is an attempt to pass some useful information on, hoping it will be useful for others. To reiterate, to the best of my knowledge the library does work, and this version is strictly better than the one that is/was part of pgf v3.1.5.}