diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample.tex | 180 |
1 files changed, 180 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample.tex b/Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample.tex new file mode 100644 index 00000000000..4541405a81d --- /dev/null +++ b/Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample.tex @@ -0,0 +1,180 @@ +\documentclass[11pt,a4paper,onecolumn]{tiet-question-paper} +\date{28 May 2024} +\institute{Alpha} +\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} + +\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[0.4pt] +\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 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[0.4pt] +\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? + \end{enumerate} +\end{enumerate} +\bvrhrule[0.4pt] +\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[0.4pt] +\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[0.4pt] +\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 + $\boldsymbol{\theta}$ wrt. world coordinate system + (WCS); find the location $\mathbf{x}_v$ in VCS, + corresponding to the point $\textbf{x}_w$ 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[0.4pt] +\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[0.4pt] +\end{document} |