diff options
Diffstat (limited to 'Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-base-points.tex')
| -rw-r--r-- | Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-base-points.tex | 146 |
1 files changed, 118 insertions, 28 deletions
diff --git a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-base-points.tex b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-base-points.tex index ae7e3e142b2..931a6a7bcf9 100644 --- a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-base-points.tex +++ b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-base-points.tex @@ -38,7 +38,7 @@ coordinate. \pgfpathcircle{\pgfpoint{2cm}{5pt}} {2pt} \pgfpathcircle{\pgfpoint{0pt}{.5in}}{2pt} \pgfusepath{fill} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} @@ -69,7 +69,7 @@ coordinate. \foreach \angle in {0,10,...,90} {\pgfpathcircle{\pgfpointpolar{\angle}{1cm/2cm}}{2pt}} \pgfusepath{fill} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} @@ -94,19 +94,19 @@ $y$-vector do not necessarily point ``horizontally'' and \pgfpathmoveto{\pgfpointxy{1}{0}} \pgfpathlineto{\pgfpointxy{2}{2}} \pgfusepath{stroke} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} \begin{command}{\pgfsetxvec\marg{point}} Sets that current $x$-vector for usage in the $xyz$-coordinate - system. + system. \example \begin{codeexample}[] \begin{tikzpicture} \draw[help lines] (0,0) grid (3,2); - + \pgfpathmoveto{\pgfpointxy{1}{0}} \pgfpathlineto{\pgfpointxy{2}{2}} \pgfusepath{stroke} @@ -116,7 +116,7 @@ $y$-vector do not necessarily point ``horizontally'' and \pgfpathmoveto{\pgfpointxy{1}{0}} \pgfpathlineto{\pgfpointxy{2}{2}} \pgfusepath{stroke} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} @@ -131,7 +131,7 @@ $y$-vector do not necessarily point ``horizontally'' and \meta{radius} is now a factor to be interpreted in the $xy$-coordinate system. This means that a degree of |0| is the same as the $x$-vector of the $xy$-coordinate system times \meta{radius} - and a degree of |90| is the $y$-vecotr times \meta{radius}. As for + and a degree of |90| is the $y$-vector times \meta{radius}. As for |\pgfpointpolar|, a \meta{radius} can also be a pair separated by a slash. In this case, the $x$- and $y$-vectors are multiplied by different factors. @@ -163,7 +163,7 @@ three dimensional graphics. \begin{codeexample}[] \begin{pgfpicture} \pgfsetarrowsend{to} - + \pgfpathmoveto{\pgfpointorigin} \pgfpathlineto{\pgfpointxyz{0}{0}{1}} \pgfusepath{stroke} @@ -214,7 +214,7 @@ using spherical and cylindrical coordinates. \pgfsetfillcolor{lightgray} \foreach \latitude in {-90,-75,...,30} - { + { \foreach \longitude in {0,20,...,360} { \pgfpathmoveto{\pgfpointspherical{\longitude}{\latitude}{1}} @@ -245,7 +245,7 @@ coordinates. \begin{tikzpicture} \draw[help lines] (0,0) grid (3,2); \pgfpathcircle{\pgfpointadd{\pgfpoint{1cm}{0cm}}{\pgfpoint{1cm}{1cm}}}{2pt} - \pgfusepath{fill} + \pgfusepath{fill} \end{tikzpicture} \end{codeexample} \end{command} @@ -256,7 +256,7 @@ coordinates. \begin{tikzpicture} \draw[help lines] (0,0) grid (3,2); \pgfpathcircle{\pgfpointscale{1.5}{\pgfpoint{1cm}{0cm}}}{2pt} - \pgfusepath{fill} + \pgfusepath{fill} \end{tikzpicture} \end{codeexample} \end{command} @@ -267,7 +267,7 @@ coordinates. \begin{tikzpicture} \draw[help lines] (0,0) grid (3,2); \pgfpathcircle{\pgfpointdiff{\pgfpoint{1cm}{0cm}}{\pgfpoint{1cm}{1cm}}}{2pt} - \pgfusepath{fill} + \pgfusepath{fill} \end{tikzpicture} \end{codeexample} \end{command} @@ -293,9 +293,9 @@ coordinates. \pgfpathcircle{\pgfpoint{2cm}{1cm}}{2pt} \pgfpathcircle{\pgfpointscale{20} {\pgfpointnormalised{\pgfpoint{2cm}{1cm}}}}{2pt} - \pgfusepath{fill} + \pgfusepath{fill} \end{tikzpicture} -\end{codeexample} +\end{codeexample} \end{command} @@ -331,7 +331,7 @@ on Bézier curves. \foreach \t in {0,0.25,...,1.25} {\pgftext[at= \pgfpointlineattime{\t}{\pgfpointorigin}{\pgfpoint{2cm}{2cm}}]{\t}} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} @@ -350,12 +350,12 @@ on Bézier curves. \foreach \d in {0pt,20pt,40pt,70pt} {\pgftext[at= \pgfpointlineatdistance{\d}{\pgfpointorigin}{\pgfpoint{3cm}{2cm}}]{\d}} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} \begin{command}{\pgfpointcurveattime\marg{time $t$}\marg{point - $p$}\marg{point $s_1$}\marg{point $s_2$}\marg{point $q$}} + $p$}\marg{point $s_1$}\marg{point $s_2$}\marg{point $q$}} Yields a point that is on the Bézier curve from $p$ to $q$ with the support points $s_1$ and $s_2$. The time $t$ is used to determine the location, where $t=0$ yields $p$ and $t=1$ yields $q$. @@ -372,7 +372,7 @@ on Bézier curves. {\pgfpoint{0cm}{2cm}} {\pgfpoint{0cm}{2cm}} {\pgfpoint{3cm}{2cm}}]{\t}} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} @@ -407,7 +407,7 @@ mechanism to determine border points of shapes. \pgfpathcircle{\pgfpointborderrectangle {\pgfpoint{-10pt}{5pt}}{\pgfpoint{1cm}{1.25cm}}}{2pt} \pgfusepath{fill} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} @@ -432,7 +432,7 @@ mechanism to determine border points of shapes. \pgfpathcircle{\pgfpointborderellipse {\pgfpoint{-10pt}{5pt}}{\pgfpoint{1cm}{1.25cm}}}{2pt} \pgfusepath{fill} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} @@ -456,7 +456,7 @@ mechanism to determine border points of shapes. {\pgfpointxy{1}{2}}{\pgfpointxy{2}{0}}} {2pt} \pgfusepath{stroke} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} @@ -481,15 +481,92 @@ mechanism to determine border points of shapes. {1cm}{0.8cm}{1}} {2pt} \pgfusepath{stroke} -\end{tikzpicture} +\end{tikzpicture} \end{codeexample} \end{command} +\subsubsection{Points on the Intersection of Two Paths} + + +\begin{pgflibrary}{intersections} + This library defines the below command and allows you to calculate + the intersections of two arbitrary paths. However, due to the low accuracy of + \TeX, the paths should not be ``too complicated''. + In particular, you should not try to intersect paths consisting + lots of very small segments such as plots or decorated paths. +\end{pgflibrary} + +\begin{command}{\pgfintersectionofpaths\marg{path 1}\marg{path 2}} + This command finds the intersection points on the paths + \meta{path 1} and \meta{path 2}. The number of intersection points + (``solutions'') that are found will be stored, and each point + can be accessed afterward. The code for \meta{path 1} and + \meta{path 2} is executed within a \TeX{} group and so can contain + transformations (which will be in addition to any existing + transformations). The code should not use the path in any way, + unless the path is saved first and restored afterward. + \pgfname{} will regard solutions as ``a bit + special'', in that the points returned will be ``absolute'' and + unaffected by any further transformations. + +\begin{codeexample}[] +\begin{pgfpicture} +\pgfintersectionofpaths +{ + \pgfpathellipse{\pgfpointxy{0}{0}}{\pgfpointxy{1}{0}}{\pgfpointxy{0}{2}} + \pgfgetpath\temppath + \pgfusepath{stroke} + \pgfsetpath\temppath +} +{ + \pgftransformrotate{-30} + \pgfpathrectangle{\pgfpointorigin}{\pgfpointxy{2}{2}} + \pgfgetpath\temppath + \pgfusepath{stroke} + \pgfsetpath\temppath +} +\foreach \s in {1,...,\pgfintersectionsolutions} + {\pgfpathcircle{\pgfpointintersectionsolution{\s}}{2pt}} +\pgfusepath{stroke} +\end{pgfpicture} +\end{codeexample} + + \begin{command}{\pgfintersectionsolutions} + After using the |\pgfintersectionofpaths| command, this \TeX-macro + will indicate the number of solutions found. + \end{command} + + \begin{command}{\pgfpointintersectionsolution\marg{number}} + After using the |\pgfintersectionofpaths| command, this command + will return the point for solution \meta{number} or the origin + if this solution was not found. + By default, the intersections are simply returned in the order that + the intersection algorithm finds them. Unfortunately, this is not + necessarily a ``helpful'' ordering. However the following two + commands can be used to order the solutions more helpfully. + \end{command} + +\let\ifpgfintersectionsortbyfirstpath=\relax + \begin{command}{\pgfintersectionsortbyfirstpath} + Using this command will mean the solutions will be sorted along + \meta{path 1}. + \end{command} + +\let\ifpgfintersectionsortbysecondpath=\relax + \begin{command}{\pgfintersectionsortbysecondpath} + Using this command will mean the solutions will be sorted along + \meta{path 2}. + \end{command} + +\end{command} + + + \subsection{Extracting Coordinates} There are two commands that can be used to ``extract'' the $x$- or -$y$-coordinate of a coordinate. +$y$-coordinate of a coordinate. \begin{command}{\pgfextractx\marg{dimension}\marg{point}} Sets the \TeX-\meta{dimension} to the $x$-coordinate of the point. @@ -505,18 +582,31 @@ $y$-coordinate of a coordinate. Like |\pgfextractx|, except for the $y$-coordinate. \end{command} +\begin{command}{\pgfgetlastxy\marg{macro for $x$}\marg{macro for $y$}} + Stores the most recently used $(x,y)$ coordinates into two macros. +\begin{codeexample}[] +\pgfpoint{2cm}{4cm} +\pgfgetlastxy{\macrox}{\macroy} +Macro $x$ is `\macrox' and macro $y$ is `\macroy'. +\end{codeexample} + Since $(x,y)$ coordinates are usually assigned globally, it is safe to use this command after path operations. +\end{command} \subsection{Internals of How Point Commands Work} +\label{section-internal-pointcmds} + As a normal user of \pgfname\ you do not need to read this section. It is relevant only if you need to understand how the point commands work -internally. +internally. When a command like |\pgfpoint{1cm}{2pt}| is called, all that happens is that the two \TeX-dimension variables |\pgf@x| and |\pgf@y| are set -to |1cm| and |2pt|, respectively. A command like |\pgfpathmoveto| that +to |1cm| and |2pt|, respectively. These variables belong to the set of +internal \pgfname\ registers, see section~\ref{section-internal-registers} +for details. A command like |\pgfpathmoveto| that takes a coordinate as parameter will just execute this parameter and then use the values of |\pgf@x| and |\pgf@y| as the coordinates to which it will move the pen on the current path. @@ -534,7 +624,7 @@ command like |\pgfpoint| in a \TeX-scope and then make the changes of \global\pgf@y=\pgf@y % make the change of \pgf@y persist past the scope } % \pgf@x and \pgf@y are now set correctly, all other variables are -% unchanged +% unchanged \end{codeexample} \makeatletter @@ -564,7 +654,7 @@ the code of the command |\pgfpointadd|: -%%% Local Variables: +%%% Local Variables: %%% mode: latex %%% TeX-master: "pgfmanual" -%%% End: +%%% End: |