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diff --git a/Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample-org.org b/Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample-org.org new file mode 100644 index 00000000000..50b55b4275a --- /dev/null +++ b/Master/texmf-dist/doc/latex/tiet-question-paper/tiet-question-paper-sample-org.org @@ -0,0 +1,182 @@ +#+date: \today + +#+latex_class: tiet-question-paper +#+latex_class_options: [11pt] +#+options: num:nil toc:nil author:nil email:nil + +#+latex_header_extra: \hypersetup{% +#+latex_header_extra: colorlinks,% +#+latex_header_extra: breaklinks,% +#+latex_header_extra: urlcolor=[rgb]{0,0.35,0.65},% +#+latex_header_extra: linkcolor=[rgb]{0,0.35,0.65}% +#+latex_header_extra: } + +#+latex_header_extra: \usepackage{libertinus} + +#+latex_header_extra: \instlogo{images/tiet-logo.pdf} +#+latex_header_extra: \schoolordepartment{% +#+latex_header_extra: Computer Science \& Engineering Department} +#+latex_header_extra: \examname{End Semester Examination} +#+latex_header_extra: \coursecode{UCS505} +#+latex_header_extra: \coursename{Computer Graphics} +#+latex_header_extra: \timeduration{3 hours} +#+latex_header_extra: \maxmarks{45} +#+latex_header_extra: \faculty{ANG,AMK,HPS,YDS,RGB} + +#+latex: \maketitle + +*Instructions:* +1. Attempt any 5 questions; +2. Attempt all the subparts of a question at one place. + +#+latex: \bvrhrule\bvrskipline + +1. + 1. 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*} + + 2. Explain the role of convex hull in curves. + \hfill[2 marks] + +#+latex: \bvrhrule + +#+ATTR_LATEX: :options [resume] +1. + 1. Describe the continuity conditions for + curvilinear geometry. \hfill[5 marks] + 2. Define formally, a B-Spline curve. \hfill [2 + marks] + 3. How is a Bezier curve different from a B-Spline + curve? \hfill [2 marks] + +#+latex: \bvrhrule + +#+ATTR_LATEX: :options [resume] +1. + 1. 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*} + 2. 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*} +#+latex: \bvrhrule + +#+ATTR_LATEX: :options [resume] +1. + 1. Explain the two winding number rules for inside + outside tests. \hfill [4 marks] + 2. Explain the working principle of a CRT. \hfill [5 + marks] + +#+latex: \bvrhrule + +#+ATTR_LATEX: :options [resume] +1. + 1. 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*} + 2. 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] + 3. 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*} + +#+latex: \bvrhrule + +#+ATTR_LATEX: :options [resume] +1. + 1. Describe the visible surface detection problem in + about 25 words. \hfill [1 mark] + 2. 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] + 3. 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] + +#+latex: \bvrhrule + + +# Local Variables: +# org-latex-default-packages-alist: nil +# org-latex-packages-alist: nil +# End: |