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+\usepackage{mdwlist} %less space for lists +\usepackage{tikz} +% Turn off header and footer +\pagestyle{empty} +% Don't print section numbers +\setcounter{secnumdepth}{0} + +\newlist{todolist}{itemize}{2} +\setlist[todolist]{label=$\square$} + +\pdfinfo{ + /Title (Computergrafik - Übungsklausur) + /Creator (TeX) + /Producer (pdfTeX 1.40.0) + /Subject () +} +\title{Computergrafik - Übungsklausur} +\date{} +\begin{document} +\maketitle +\textbf{Für die Klausur sind keinerlei Hilfsmittel wie Skript, Bücher oder Taschenrechner zulässig. \newline Bei Berechnungen reicht die Angabe der Herleitung aus, z.B. reicht $8^3$ für $512$.} + +\section{Objekt- und Ansichtstransformationen} +\subsection{Aufgabe 1\newline Der Punkt P mit den Koordinaten $(x,y)$ soll erst um den Vektor $(\delta x,\delta y)$ verschoben und anschließend um den Winkel $\alpha$ um den Ursprung rotiert werden.} +\subsubsection{a) Geben Sie die beteiligten Transformationsmatrizen in allgemeiner Form an.} +\begin{center} + \framebox(450,100){} +\end{center} + +\subsubsection{b) Leiten Sie die beiden Gleichungen für die Koordinaten $(x',y')$ des transformierten Punktes $P'$ her, wenn zuerst verschoben und danach rotiert wird.} +\begin{center} + \framebox(450,100){} +\end{center} + +\subsection{Aufgabe 2\newline Die nachstehende Skizze veranschaulicht einen Abbildungsprozess, bei dem ein Punkt P auf die Projektionsebene E projiziert wird. E befindet sich im Abstand e vom Ursprung entfernt und ist parallel zur xy-Ebene.} +\begin{figure}[h] + \centering + \begin{tikzpicture} + \draw[thick,->] (0,0) -- (0,4) node[anchor=north west] {X}; + \draw[thick,->] (0,0) -- (6,0) node[anchor=south east] {Z}; + \draw (0,0) node[anchor=south east] {Y}; + + \draw[thick,-] (0,0) -- (5,3) node[anchor=north west] {P}; + \draw[thick,-] (0,0) -- (3,1.8) node[anchor=north west] {P'}; + \draw[thin,-] (5,3)--(0,3) node[anchor=east] {$x_{P}$}; + \draw[thin,-] (3,1.8)--(0,1.8) node[anchor=east] {$x_{P'}$}; + \draw[thin,-] (5,3)--(5,0) node[anchor=north] {$z_P$}; + \draw[thick,-] (3,3)--(3,0) node[anchor=north] {$e$}; + \end{tikzpicture} +\end{figure} +\subsubsection{a) Um welche Projektionsart handelt es sich?} +\begin{center} + \framebox(450,100){} +\end{center} +\subsubsection{b) Geben Sie eine Formel an, mit der $x'_P$ berechnet werden kann.} +\begin{center} + \framebox(450,100){} +\end{center} +\subsubsection{c) Geben Sie eine entsprechende Formel an, mit der $y'_P$ berechnet werden kann.} +\begin{center} + \framebox(450,100){} +\end{center} + + +\section{Farbmodelle und Farbwahrnehmung} +\subsection{Aufgabe 3\newline Welche Farbe nehmen Sie wahr, wenn... \newline Begründen Sie jeweils Ihre Antwort.} +\subsubsection{a) grünes Licht auf eine gelbe Oberfläche fällt?} +\begin{center} + \framebox(450,100){} +\end{center} +\subsubsection{b) magentafarbenes Licht auf eine gelbe Oberfläche fällt?} +\begin{center} + \framebox(450,100){} +\end{center} +\subsubsection{c) weißes Licht auf eine gelbe Oberfläche fällt?} +\begin{center} + \framebox(450,100){} +\end{center} + + +\subsection{Aufgabe 4\newline Kreuzen Sie jeweils ja oder nein an. Jede richtige Antwort gibt $0.5$ Punkte, jede falsche Antwort gibt $-0.5$ Punkte. Wenn Sie sich nicht sicher sind, lassen Sie das Feld frei oder erläutern Sie Ihre Entscheidung ausführlich. Es werden zwischen 0 und 15 Punkte vergeben.} +\subsubsection{a) Welche Räume stellen geräteabhängige Farbräume dar?} +\begin{multicols}{3} + \begin{todolist} + \item $CIE_{LAB}$ + \item CMYK + \item HSI + \item RGB + \item XYZ + \end{todolist} +\end{multicols} + +\subsubsection{b) Welchen Farbumfang des sichtbaren Lichtes kann ein typischer Monitor darstellen?} +\begin{multicols}{3} + \begin{todolist} + \item $<5\%$ + \item ca. 1/6 + \item ca. 1/3 + \item ca. 80-90\% + \item $>99\%$ + \end{todolist} +\end{multicols} + +\subsubsection{c) Welches Verfahren wird angewendet, um Farbkörperunterschiede von Geräten auszugleichen?} +\begin{multicols}{3} + \begin{todolist} + \item Anti-Aliasing + \item Automatischer Weißabgleich + \item Double Buffering + \item Ersatzfarbenbildung + \item Gamnt Mapping + \end{todolist} +\end{multicols} + +\subsubsection{d) Das Lambert-Beersche Gesetz beschreibt den Grad der Abschwächung beim Durchgang von Strahlung durch eine lichtabsorbierende Substanz. Als Parameter geht in das Gesetz ein:} +\begin{multicols}{3} + \begin{todolist} + \item Einfallswinkel + \item Konzentration + \item Lichtgeschwindigkeit + \item Raumtemperatur + \item Schichtdicke + \end{todolist} +\end{multicols} + +\subsubsection{e) In welchen Fällen leigt stets maximale Sättigung (gesättigte Farbvalenz) vor? Die skalaren Werte in $F=(R,G,B)$ seien auf $[0,1]$ normiert.} +\begin{multicols}{3} + \begin{todolist} + \item $|F|>0$, aber mindestens ein Farbwert $=0$ + \item $R=G=B=1/3$ + \item $R=0$, $G=0.7$ und $B=0.5$ + \item Für Intensitäten $>0.5$ + \item Für Intensitäten $=1$ + \end{todolist} +\end{multicols} + +\subsubsection{f) Bewerten Sie die folgenden bezüglich des CMY-Farbmodells getroffenen Aussagen.} +\begin{multicols}{3} + \begin{todolist} + \item Modifikation eines Parameters genügt, um einen Rotstich zu beseitigen + \item Modifikation eines Parameters genügt, um die Farben aufzuhellen + \item Schwarz liegt im Koordinatenursprung + \item Die Koordinaten $(0,1,0)$ charakterisieren weiß + \item Der Farbraum wird aus genau drei linear unabhängigen Größen gebildet + \end{todolist} +\end{multicols} + +\section{2D Rastergrafik} +\subsection{Aufgabe 5} +\subsubsection{a) Geben Sie ein Beispiel (Menge von Polygonen bzw. im einfachsten Fall Dreiecken), das vom painteralgorithmus fehlerhaft gerendert wird und erläutern Sie, warum das Problem in diesem Beispiel auftritt.} +\begin{center} + \framebox(450,100){} +\end{center} +\subsubsection{b) Erläutern Sie die Z-Buffer-Methode. Gehen Sie dabei auch darauf ein, wie das von Ihnen unter a) gebrachte Beispiel gerendert wird.} +\begin{center} + \framebox(450,100){} +\end{center} +\subsubsection{Zusatzaufgabe: Wie eignen sich die Painters-Algorithmus und Z-Buffer-Methode zum Rendern transparenter Polygone? Welche Probleme treten jeweils auf, und wie lassen sie sich beheben?} +\begin{center} + \framebox(450,100){} +\end{center} + +\section{3D Rendering} +\subsection{Aufgabe 6\newline erläutern Sie das Gourad-Shading-Verfahren zum Schattieren von Dreiecken.} +\subsubsection{a) Wie werden die Intensitäten der einzelnen Pixel bestimmt?} +\begin{center} + \framebox(450,100){} +\end{center} +\subsubsection{b) Welche Möglichkeiten bestehen, um den Machband-Effekt abzuschwächen bzw. ganz zu vermeiden?} +\begin{center} + \framebox(450,100){} +\end{center} +\subsubsection{c) In welchen Fällen werden beim Gourad-Shading Glanzlichter nicht korrekt wiedergegeben (Skizze und Erläuterung)?} +\begin{center} + \framebox(450,100){} +\end{center} + +\section{Effiziente Datenstrukturen} +\subsection{Aufgabe 7\newline Acht Punkte A bis H sollen in einem zweidimensionalen kd-Tree gespeichert werden. Jede Raumzelle enthalte maximal einen Punkt. Für zwei verschiedene Einfügestrategien sind sowohl die Raumzerlegung zu skizzieren als auch der zugehörige kd-Tree zu zeichnen.} +\subsubsection{a) Zeichnen Sie kd-Baum und Raumzerlegung bei Median-Teilung. Die erste Teilung erfolge parallel zur x-Achse. Die Teilungsachse verlaufe entlang der Koordinate des jeweiligen Punktes bzw. entlang des Mittelwerts zwischen zwei Punkten.} +\subsubsection{b) Zeichnen Sie kd-Baum und Raumzerlegung bei Einfügung der Punkte in der Reihenfolge $A,B,...,H$. Die erste Teilung erfolge parallel zur x-Achse. Die Teilungsachse verlaufe entlang der Koordinate des jeweiligen Punktes.} + +\begin{tikzpicture}[ + dot/.style = { + draw, + fill = white, + circle, + inner sep = 0pt, + minimum size = 4pt + } + ] + \draw[thick,->] (0,0) -- (10,0) node[anchor=south west] {Y}; + \draw[thick,->] (0,0) -- (0,10) node[anchor=south west] {X}; + \foreach \x in {0,1,2,3,4,5,6,7,8,9,10} + \draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$}; + \foreach \y in {0,1,2,3,4,5,6,7,8,9,10} + \draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$}; + \draw[thin,-] (10,0) -- (10,10); + \draw[thin,-] (0,10) -- (10,10); + + \draw (6,9) node[dot, label={above:$A$}]{}; + \draw (9,2) node[dot, label={above:$B$}]{}; + \draw (8,8) node[dot, label={above:$C$}]{}; + \draw (7,6) node[dot, label={above:$D$}]{}; + \draw (3,7) node[dot, label={above:$E$}]{}; + \draw (2,1) node[dot, label={above:$F$}]{}; + \draw (4,4) node[dot, label={above:$G$}]{}; + \draw (1,3) node[dot, label={above:$H$}]{}; +\end{tikzpicture} + +\end{document} \ No newline at end of file