From a9366259962a322b5d8828470a83996b41c129e5 Mon Sep 17 00:00:00 2001 From: fruitstaa Date: Sat, 5 Jan 2019 14:19:37 +0100 Subject: [PATCH] Theorie added --- exercise2/Theorie.pdf | Bin 71801 -> 71786 bytes exercise2/Theorie.tex | 2 +- exercise3/Theorie.pdf | Bin 0 -> 74364 bytes exercise3/Theorie.tex | 52 ++++++++++++++++++++++++++++++++++++++++++ 4 files changed, 53 insertions(+), 1 deletion(-) create mode 100644 exercise3/Theorie.pdf create mode 100644 exercise3/Theorie.tex diff --git a/exercise2/Theorie.pdf b/exercise2/Theorie.pdf index af114ed0120443835b47cd626edaa00cb6b00509..0a0d52a41645d52eec340e2aad181a303a480796 100644 GIT binary patch delta 1204 zcmV;l1WWt*umtL`1h5VX12{Q1lMx9je^^a#6G05U=U2=z5n5w=#`A&1p_M?QHz4BD z_SCcpsUMKg^7rv>c9WfC@}&eMxHPM*`^MwM{AxlU39s)Wd@ZeBosDnV+mz}SaugJRDC^Ezpxu`NlwVUx+$ zs$It6+$a(Nqc@fID(8If)oQ+?u5^Btk$x&lh(4^RlB>l*P;*lP?`R3cRh4G1D{u{~XINF-rqT)Lg!2!WWJqsl2!E=x# z%8FpX3)N6t2sJM^> zt~5)1mx-dXzM~=cr8-Rq*<~yi&x-lu$(-blaMHS9)2Rgek7%u;AR9Eo9$d0nQ&d89 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top=25mm, left=18mm, right=15mm, bottom=30mm, +headsep=10mm, footskip=12mm} + + +\begin{document} + +\section*{Computer Graphics - Excercise 2} +\subsection*{3.1.1} +\subsection*{(a)} +The more obtuse the triangle, the more acute the angle of the corner of the voronoi area gets. Because the both sides of this corner has to be in a 90° angle to the sides of the traingle. +\subsection*{(b)} +The formula of triangle is: $\frac{1}{2}*h*b$ +As for the red triangle: $\frac{1}{2}*h*b$ +with: $h=\frac{||p_i - p_j||}{2}$ and $b=$ + +\subsection*{(c)} + +\subsection*{3.1.2} +\subsection*{(a)} +We know every vertex($v$) has three edges($e$) and 2 faces($f$). In addition every edge($e$) can separated into two half edges ($e_h$), this means $e_h = 2*e = 6*v$.\\ +If we add the memory for every part it results in a formula:\\ +\begin{center} +memory $= v*16\text{bytes} + e*4\text{bytes} + e_h*16\text{bytes} + f*4\text{bytes}$\\ +$\rightarrow \text{through assumptions:}$\\ +memory $= v*(16+3*4+6*16+2*4)\text{bytes}=v*132\text{bytes}$ +\end{center} +\subsection*{(b)} +Because in a quad mash two triangles are combined into one quad, the resulting faces will be reduced by a half. The resulting ratio will be 1:3:1 (for v : e : f) +\subsection*{(c)} +We know every vertex($v$) has three edges($e$) and one face($f$). In addition every edge($e$) can separated into two half edges ($e_h$), this means $e_h = 2*e = 6*v$.\\ +If we add the memory for every part it results in a formula:\\ +\begin{center} +memory $= v*16\text{bytes} + e*4\text{bytes} + e_h*16\text{bytes} + f*4\text{bytes}$\\ +$\rightarrow \text{through assumptions:}$\\ +memory $= v*(16+3*4+6*16+1*4)\text{bytes}=v*132\text{bytes}$ +\end{center} +\end{document} +