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diff --git a/Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample-org.tex b/Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample-org.tex new file mode 100644 index 00000000000..54c7290a679 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample-org.tex @@ -0,0 +1,204 @@ +% Created 2024-06-22 Sat 22:57 +% Intended LaTeX compiler: pdflatex +\documentclass[11pt]{tiet-question-paper} +\usepackage{amsmath} +\usepackage{graphicx} +\usepackage{wrapfig} +\usepackage{amssymb} +\usepackage[unicode]{hyperref} + + +\hypersetup{% +colorlinks,% +breaklinks,% +urlcolor=[rgb]{0,0.35,0.65},% +linkcolor=[rgb]{0,0.35,0.65}% +} +\usepackage{libertinus} +\instlogo{images/tiet-logo.pdf} +\schoolordepartment{% +Computer Science \& Engineering Department} +\examname{End Semester Examination} +\coursecode{UCS505} +\coursename{Computer Graphics} +\timeduration{3 hours} +\maxmarks{45} +\faculty{ANG,AMK,HPS,YDS,RGB} +\date{\today} +\title{} +\hypersetup{ + pdfauthor={B.V. Raghav}, + pdftitle={}, + pdfkeywords={}, + pdfsubject={}, + pdfcreator={Emacs 29.3 (Org mode 9.6.15)}, + pdflang={English}} +\begin{document} + +\maketitle + +\textbf{Instructions:} +\begin{enumerate} +\item Attempt any 5 questions; +\item Attempt all the subparts of a question at one place. +\end{enumerate} + +\bvrhrule\bvrskipline + +\begin{enumerate} +\item \begin{enumerate} +\item Given the control polygon \(\textbf{b}_0, + \textbf{b}_1, \textbf{b}_2, \textbf{b}_3\) of a +Cubic Bezier curve; determine the vertex +coordinates for parameter values \(\forall t\in + T\). \hfill [7 marks] +\begin{align*} + T \equiv + & \{0, 0.15, 0.35, 0.5, 0.65, 0.85, 1\} \\ + \begin{bmatrix} + \textbf{b}_0 &\textbf{b}_1& \textbf{b}_2& \textbf{b}_3 + \end{bmatrix} \equiv& \begin{bmatrix} + 1&2&4&3\\ 1&3&3&1 + \end{bmatrix} +\end{align*} + +\item Explain the role of convex hull in curves. +\hfill[2 marks] +\end{enumerate} +\end{enumerate} + +\bvrhrule + +\begin{enumerate}[resume] +\item \begin{enumerate} +\item Describe the continuity conditions for +curvilinear geometry. \hfill[5 marks] +\item Define formally, a B-Spline curve. \hfill [2 +marks] +\item How is a Bezier curve different from a B-Spline +curve? \hfill [2 marks] +\end{enumerate} +\end{enumerate} + +\bvrhrule + +\begin{enumerate}[resume] +\item \begin{enumerate} +\item Given a triangle, with vertices defined by column +vectors of \(P\); find its vertices after +reflection across XZ plane. \hfill [3 marks] +\begin{align*} + P\equiv + &\begin{bmatrix} + 3&6&5 \\ 4&4&6 \\ 1&2&3 + \end{bmatrix} +\end{align*} +\item Given a pyramid with vertices defined by the +column vectors of \(P\), and an axis of rotation +\(A\) with direction \(\textbf{v}\) and passing +through \(\textbf{p}\). Find the coordinates of +the vertices after rotation about \(A\) by an angle +of \(\theta=\pi/4\).\hfill [6 marks] +\begin{align*} + P\equiv + &\begin{bmatrix} + 0&1&0&0 \\ 0&0&1&0 \\0&0&0&1 + \end{bmatrix} \\ + \begin{bmatrix} + \mathbf{v} & \mathbf{p} + \end{bmatrix}\equiv + &\begin{bmatrix} + 0&0 \\1&1\\1&0 + \end{bmatrix} +\end{align*} +\end{enumerate} +\end{enumerate} +\bvrhrule + +\begin{enumerate}[resume] +\item \begin{enumerate} +\item Explain the two winding number rules for inside +outside tests. \hfill [4 marks] +\item Explain the working principle of a CRT. \hfill [5 +marks] +\end{enumerate} +\end{enumerate} + +\bvrhrule + +\begin{enumerate}[resume] +\item \begin{enumerate} +\item Given a projection plane \(P\) defined by normal +\(\textbf{n}\) and a reference point \(\textbf{a}\); +and the centre of projection as \(\mathbf{p}_0\); +find the perspective projection of the point +\(\textbf{x}\) on \(P\). \hfill [5 marks] +\begin{align*} + \begin{bmatrix} + \mathbf{a}&\mathbf{n}&\mathbf{p}_0&\mathbf{x} + \end{bmatrix}\equiv + & + \begin{bmatrix} + 3&-1&1&8\\4&2&1&10\\5&-1&3&6 + \end{bmatrix} +\end{align*} +\item Given a geometry \(G\), which is a standard unit +cube scaled uniformly by half and viewed through +a Cavelier projection bearing \(\theta=\pi/4\) +wrt. \(X\) axis. \hfill [2 marks] +\item Given a view coordinate system (VCS) with origin +at \(\textbf{p}_v\) and euler angles ZYX as +\(\boldsymbol{\theta}\) wrt. the world coordinate +system (WCS); find the location \(\mathbf{x}_v\) in +VCS, corresponding to \(\textbf{x}_w\) in +WCS. \hfill [2 marks] +\begin{align*} + \begin{bmatrix} + \mathbf{p}_v & \boldsymbol{\theta} & \mathbf{x}_w + \end{bmatrix}\equiv + &\begin{bmatrix} + 5&\pi/3&10\\5&0&10\\0&0&0 + \end{bmatrix} +\end{align*} +\end{enumerate} +\end{enumerate} + +\bvrhrule + +\begin{enumerate}[resume] +\item \begin{enumerate} +\item Describe the visible surface detection problem in +about 25 words. \hfill [1 mark] +\item To render a scene with \(N\) polygons into a +display with height \(H\); what are the space and +time complexities respectively of a typical +image-space method. \hfill [2 marks] +\item Given a 3D space bounded within \([0\quad0\quad0]\) +and \([7\quad7\quad-7]\), containing two infinite +planes each defined by 3 incident points +\(\mathbf{a}_0, \mathbf{a}_1, \mathbf{a}_2\) and +\(\mathbf{b}_0, \mathbf{b}_1, \mathbf{b}_2\) +respectively bearing colours (RGB) as +\(\mathbf{c}_a\) and \(\textbf{c}_b\) respectively. +\begin{align*} + \begin{bmatrix} + \mathbf{a}_0&\mathbf{a}_1&\mathbf{a}_2 + &\mathbf{b}_0&\mathbf{b}_1&\mathbf{b}_2 + &\mathbf{c}_a&\mathbf{c}_b + \end{bmatrix}\equiv + &\begin{bmatrix} + 1&6&1&6&1&6&1&0 \\ + 1&3&6&6&3&1&0&0 \\ + -1&-6&-1&-1&-6&-1&0&1 + \end{bmatrix} +\end{align*} +Compute and/ or determine using the depth-buffer +method, the colour at pixel \(\mathbf{x}=(2,4)\) on +a display resolved into \(7\times7\) pixels. The +projection plane is at \(Z=0\), looking at +\(-Z\). \hfill [6 marks] +\end{enumerate} +\end{enumerate} + +\bvrhrule +\end{document} |