TIET-Question-Paper-Template
作者:
Raghav B. Venkataramaiyer
最近上传:
6 个月前
许可:
Other (as stated in the work)
摘要:
A LATEX question paper class for the TIET
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\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}