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% Document Info
\author{Ozzypig (Ozzypig)}
\pdfinfo{
  /Title (roblox-cframes.pdf)
  /Creator (Cheatography)
  /Author (Ozzypig (Ozzypig))
  /Subject (Roblox: CFrames Cheat Sheet)
}

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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Roblox: CFrames Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Ozzypig (Ozzypig)} via \textcolor{DarkBackground}{\uline{cheatography.com/25526/cs/10637/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Ozzypig (Ozzypig) \\
  \uline{cheatography.com/ozzypig} \\
        \uline{\seqsplit{ozzypig}.com}
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 24th January, 2017.\\
   Updated 24th January, 2017.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{What is a CFrame?}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{A {\bf{CFrame}} is a mix of a position and rotation. CFrames are used to define the position/orientation of bricks, cameras, and many other objects in Roblox places. Think of them as paper airplanes that are frozen in time. They are different from \{\{link="http://wiki.roblox.com/index.php?title=Vector3"\}\}Vector3s\{\{/link\}\} and \{\{link="http://wiki.roblox.com/index.php?title=Ray"\}\}Rays\{\{/link\}\}.% Row Count 8 (+ 8)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Math involving CFrames isn't as difficult as you might think, but you must understand what's going on behind the code!}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Constructors}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`CFrame.new()`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Identity CFrame at (0, 0, 0) facing forward.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`CFrame.new({\bf{Vector3}} v3)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}CFrame at Vector3 facing forward.} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`CFrame.new({\bf{Vector3}} pos, {\bf{Vector3}} target)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}CFrame at Vector3 \{\{nobreak\}\}`pos` facing Vector3 \{\{nobreak\}\}`target`.} \tn 
% Row Count 8 (+ 4)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`CFrame.new(x, y, z)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}CFrame at (x, y, z) facing forward.} \tn 
% Row Count 10 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`CFrame.new(x, y, z, qX, qY, qZ, qW)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}CFrame at (x, y, z) with quaternion (qX, qY, qZ, qW).} \tn 
% Row Count 13 (+ 3)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`CFrame.new(x, y, z, r00, r01, r02, r10, r11, r12, r20, r21, r22)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}CFrame at (x, y, z) with given rotation matrix.} \tn 
% Row Count 16 (+ 3)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`CFrame.Angles(rX, rY, rZ)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}CFrame at (0, 0, 0) rotated with \{\{link="http://wiki.roblox.com/index.php?title=Euler\_angles"\}\}Euler angles\{\{/link\}\} (rX, rY, rZ) in {\bf{radians}}.} \tn 
% Row Count 21 (+ 5)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`CFrame.fromAxisAngles({\bf{Vector3}} unit, {\bf{number}} rotation)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Rotated CFrame from unit Vector3 and a rotation in {\bf{radians}}.} \tn 
% Row Count 25 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{All of these return a new {\bf{CFrame}} value. Unless otherwise specified, parameters are {\bf{numbers}}.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Operators}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`{\bf{CFrame}} * {\bf{CFrame}}`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Return the composition of two CFrames.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`{\bf{CFrame}} * {\bf{Vector3}}`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns Vector3 transformed from Object to World coordinates.} \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`{\bf{CFrame}} + {\bf{Vector3}}`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Return CFrame translated in world space by Vector3.} \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}`{\bf{CFrame}} - {\bf{Vector3}}`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Return CFrame translated in world space by negative Vector3.} \tn 
% Row Count 11 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Remember that {\bf{order matters}}! This means that if you flip the values you will get a different value. These expressions give two different results:\{\{nobreak\}\}\{\{nl\}\}`cf * cf2\{\{nl\}\}cf2 * cf`}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Object space versus World space?}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{When working with CFrames, we often talk about {\bf{object}} versus {\bf{world}} space. What we're really talking about is {\bf{relativity}}. Everything has a position that is relative to everything else. Object space is a way of saying "relative to {\emph{this}} CFrame". World space is a way of saying "relative to the origin", or (0, 0, 0).% Row Count 7 (+ 7)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{This terminology is most often used in method documentation. Use it when trying to code up solutions to CFrame math problems. For example, might you want to transform a Vector3 that you know to be relative to something else (object space) into world space. In that case, you would use \{\{nobreak\}\}`brick.CFrame:toWorldSpace(v3)`.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Properties}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Property}} & {\bf{Description}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\{\{nobreak\}\}{\bf{Vector3}}~`p` & The 3D position of the CFrame. \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\{\{nobreak\}\}{\bf{number}}~`x` & The x-component of the Vector3 position. \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
\{\{nobreak\}\}{\bf{number}}~`y` & The y-component of the Vector3 position. \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\{\{nobreak\}\}{\bf{number}}~`z` & The z-component of the Vector3 position. \tn 
% Row Count 9 (+ 2)
% Row 5
\SetRowColor{white}
\{\{nobreak\}\}{\bf{Vector3}}~`lookVector` & The forward-direction component of the CFrame's orientation. \tn 
% Row Count 12 (+ 3)
% Row 6
\SetRowColor{LightBackground}
\{\{nobreak\}\}{\bf{Vector3}}~`rightVector` & The right-direction component of the CFrame's orientation. \tn 
% Row Count 15 (+ 3)
% Row 7
\SetRowColor{white}
\{\{nobreak\}\}{\bf{Vector3}}~`upVector` & The up-direction component of the CFrame's orientation. \tn 
% Row Count 18 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{These properties are all {\bf{read-only}}, meaning they can be read from, but not changed. This is called {\bf{immutability}}.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Methods}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{CFrame}}~`cf:inverse()`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns the inverse of this CFrame.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{CFrame}}~`cf:lerp({\bf{CFrame}} goal, {\bf{number}} alpha)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns a CFrame interpolated between this CFrame, and the goal CFrame by the fraction alpha.} \tn 
% Row Count 6 (+ 4)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{CFrame}}~`cf:toWorldSpace({\bf{CFrame}} cf2)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns a CFrame transformed from Object to World coordinates. Equivalent to \{\{nobreak\}\}`cf * cf2`} \tn 
% Row Count 11 (+ 5)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{CFrame}}~`cf:toObjectSpace({\bf{CFrame}} cf2)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns a CFrame transformed from World to Object coordinates. Equivalent to \{\{nobreak\}\}`cf:inverse() * cf2`} \tn 
% Row Count 16 (+ 5)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{Vector3}}~`cf:pointToWorldSpace({\bf{Vector3}} v3)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns a Vector3 transformed from Object to World coordinates. Equivalent to \{\{nobreak\}\}`cf * v3`} \tn 
% Row Count 21 (+ 5)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{Vector3}}~`cf:pointToObjectSpace({\bf{Vector3}} v3)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns a Vector3 transformed from World to Object coordinates. Equivalent to \{\{nobreak\}\}`cf:inverse() * v3`} \tn 
% Row Count 26 (+ 5)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{Vector3}}~`cf:vectorToWorldSpace({\bf{Vector3}} v3)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns a Vector3 rotated from Object to World coordinates. Equivalent to \{\{nobreak\}\}`(cf - cf.p) * v3`} \tn 
% Row Count 31 (+ 5)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Methods (cont)}}  \tn
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{Vector3}}~`cf:vectorToObjectSpace({\bf{Vector3}} v3)`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns a Vector3 rotated from World to Object coordinates. Equivalent to \{\{nobreak\}\}`(cf - cf.p):inverse() * v3`} \tn 
% Row Count 5 (+ 5)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{numbers}}~`cf:components()`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns the components of the CFrame in this order: x, y, z, R00, R01, R02, R10, R11, R12, R20, R21, R22.} \tn 
% Row Count 9 (+ 4)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\{\{nobreak\}\}{\bf{numbers}}~`cf:toEulerAnglesXYZ()`} \tn 
\mymulticolumn{1}{x{8.4cm}}{\hspace*{6 px}\rule{2px}{6px}\hspace*{6 px}Returns the {\emph{best guess}} angles that could be used to generatea CFrame using \{\{nobreak\}\}`CFrame.Angles`. See \{\{link="http://wiki.roblox.com/index.php?title=Euler\_angles"\}\}Euler angles\{\{/link\}\}.} \tn 
% Row Count 16 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}