
\hyphenation{Bool-ean com-plete other-wise manu-script}

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\def\veci{{\mathbf i}}
\def\vecj{{\mathbf j}}
\def\veck{{\mathbf k}}
\def\vecp{{\mathbf p}}
\def\vecq{{\mathbf q}}
\def\vecu{{\mathbf u}}
\def\vecv{{\mathbf v}}
\def\vecw{{\mathbf w}}
\def\vecx{{\mathbf x}}
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\begin{document}

\begin{center}
{\bf Math 155B --- Computer Graphics --- Spring 2017 } \\
{\bf Homework \#3 ---
Due 9:00pm, Monday, May 15 } \\
{\bf Hand in via GradeScope }
\end{center}


\noindent
Please show work and label answers clearly.

\noindent{\bf 1.}  Consider the rotation matrix
$\left(\begin{array}{ccc}
0 & 0 & 1 \\
1 & 0 & 0 \\
0 & 1 & 0 
\end{array}\right)$.
Express this in terms of yaw, pitch and roll.

\medskip

\noindent{\bf 2.}
Express the following rotations (expressed as compositions)
with yaw (y), pitch (p) and roll (r):
\begin{enumerate}
\item[a.] $R_{90^\circ,\vecj} \circ R_{90^\circ,\veci} \circ R_{90^\circ,\veck}$.
\item[b.] $R_{90^\circ,\veci} \circ R_{90^\circ,\vecj} \circ R_{90^\circ,\veck}$.
\item[c.] $R_{90^\circ,\vecj} \circ R_{90^\circ,\veck} \circ R_{90^\circ,\veci}$.
\item[d.] $R_{90^\circ,\veck} \circ R_{90^\circ,\veci} \circ R_{90^\circ,\vecj}$.
\item[e.] $R_{90^\circ,\veci} \circ R_{90^\circ,\veck} \circ R_{90^\circ,\vecj}$.
\item[f.] $R_{90^\circ,\veck} \circ R_{90^\circ,\vecj} \circ R_{90^\circ,\veci}$.
\end{enumerate}

\medskip


\noindent
{\bf 3.} Exercise XII.2, page 296.

\medskip

\noindent
{\bf 4.} Exercise XII.3, page 298.  Please be sure to use the correct equations XII.3
on page 297. Hints: (a)~Use the previous exercise. 
(b)~Which of the values $s_y$, $c_y$, etc., change sign when 
replacing $\theta_y,\theta_p,\theta_r$ with
$\theta^\prime_y,\theta^\prime_p,\theta^\prime_r$?


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