\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{racheleva}
\pdfinfo{
  /Title (computer-graphics-3.pdf)
  /Creator (Cheatography)
  /Author (racheleva)
  /Subject (Computer Graphics 3 Cheat Sheet)
}

% Lengths and widths
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\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{4897A3}
\definecolor{LightBackground}{HTML}{F3F8F9}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\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{Computer Graphics 3 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{racheleva} via \textcolor{DarkBackground}{\uline{cheatography.com/217931/cs/48017/}}}
\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}racheleva \\
  \uline{cheatography.com/racheleva} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 27th April, 2026.\\
   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}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.18988 cm} x{2.78712 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{UNIT 3}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{PART A} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
three primary geometric elements & Vertex (Point), Edge (Line), Polygon (Face) \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{Quadric Surface}} & defined by second-degree equations \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
{\bf{polygon table}} & data structure storing lists of geometric and attribute data (to store connectivity information) \tn 
% Row Count 10 (+ 5)
% Row 4
\SetRowColor{LightBackground}
{\bf{Plane equation}} & Ax+By+Cz+D=0; x,y,z → components of normal vector \{\{nl\}\}\textless{}0 inside; \textgreater{}0 outside \tn 
% Row Count 14 (+ 4)
% Row 5
\SetRowColor{white}
{\bf{polygon meshes}} & Triangle and Quadrilateral Meshes \tn 
% Row Count 16 (+ 2)
% Row 6
\SetRowColor{LightBackground}
{\bf{spline}} & defined by a set of polynomial functions \tn 
% Row Count 18 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.33919 cm} x{2.63781 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Plane Equations in Rendering Pipeline}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Back-Face Culling:}} & substitute viewport into plane equation (sign determines direction of plan for clipping) \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
{\bf{Inside-Outside Testing \& Depth:}} & if a point is inside a polygon; calculate depth of any point \tn 
% Row Count 8 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Meshes}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Polygon Meshes}} & {\bf{Quadratic (or Parametric) Surfaces}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
made of triangles/quads & equations/control points \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Modelling Accuracy}}} \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
Approximate, depends on number of polygons & High precision, smooth surfaces \tn 
% Row Count 8 (+ 3)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Resource Requirements}}} \tn 
% Row Count 9 (+ 1)
% Row 5
\SetRowColor{white}
Needs more memory for high detail & Compact representation, fewer parameters \tn 
% Row Count 11 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Rendering Efficiency}}} \tn 
% Row Count 12 (+ 1)
% Row 7
\SetRowColor{white}
Very efficient, directly supported by GPUs & Not directly renderable, must be converted to meshes \tn 
% Row Count 15 (+ 3)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Ray surface intersection} \tn 
% Row Count 16 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Advantages}}} \tn 
% Row Count 17 (+ 1)
% Row 10
\SetRowColor{LightBackground}
fast; basic algebraic math; computation time predictable; universal for any shape & exact representation; compact storage; analytical precision \tn 
% Row Count 22 (+ 5)
% Row 11
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Disadvantages}}} \tn 
% Row Count 23 (+ 1)
% Row 12
\SetRowColor{LightBackground}
approximation error; memory performance trade-off & computational cost; specialization required \tn 
% Row Count 26 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Polygon meshes }}= standard for real-time rendering (fast, GPU-friendly) \newline {\bf{Quadratic surfaces }}= better for design accuracy, but used as pre-processing before conversion to polygons}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.63781 cm} x{2.33919 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{B-Spline and Bézier}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{B-Spline}} & {\bf{Bézier}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
local control & global control \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
single compact representation & needs many separate curves \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{B-Splines are flexible, efficient (faster updates, less recomputation) and manageable.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.04057 cm} x{2.93643 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Polygon tables}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Geometric (Vertex) Table}} & Avoids duplication \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Attribute Table}} & Stores properties (color, texture, reflectivity) \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
{\bf{Surface (Polygon) Table}} & Stores faces using vertex indices (geometry + attributes) \tn 
% Row Count 8 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.04057 cm} x{2.93643 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Polygon tables}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Geometric (Vertex) Table}} & Avoids duplication \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Attribute Table}} & Stores properties (color, texture, reflectivity) \tn 
% Row Count 5 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}