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

\documentclass[12pt]{report}
\usepackage{latexsym}
\usepackage{amssymb}
\usepackage{pstricks}

\hyphenpenalty 150 \exhyphenpenalty 150
\tolerance=3000 \relpenalty=4000 \binoppenalty=9999
\spaceskip=3.33333pt plus2.75000pt minus1.11111pt

\def\vecp{{\mathbf p}}
\def\vecq{{\mathbf q}}
\def\vecu{{\mathbf u}}
\def\vecv{{\mathbf v}}
\def\vecw{{\mathbf w}}
\def\vecx{{\mathbf x}}
\def\vecy{{\mathbf y}}
\def\vecz{{\mathbf z}}
\def\veczero{{\mathbf 0}}

\def\Reals{{\mathbb R}}
\def\RR{{\Reals^2}}
\def\lerp{{\hbox{\sc Lerp}}}

\addtolength{\topmargin}{-1.0in}
\addtolength{\textheight}{1.0in}
\addtolength{\textwidth}{0.5in}

\begin{document}

\begin{center}
{\bf Math 155B --- Computer Graphics --- Spring 2017 } \\
{\bf Homework \#1 ---
Due 9:00pm, Friday, April 21 } \\
{\bf Hand in via GradeScope }
\end{center}


\noindent
Please show work and label answers clearly.

\noindent
{\bf 1.} Exercise VII.6, page 165.

\medskip

\noindent
{\bf 2.} Exercise VII.14, page 184.

\medskip

\noindent
{\bf 3.} Exercise VII.19, page 186.

\medskip

\noindent
{\bf 4.} Exercise VII.20, page 186. (This generalizes VII.19, so if you wish you may
work just this problem and not the previous one!)

\medskip

\noindent
{\bf 5.} Exercise VII.24, page 191.

\medskip

\noindent
{\bf 6.} (Linear interpolation in homogeneous coordinates.)
Suppose $w, v > 0$. Let $\langle w\vecx, w \rangle$ and $\langle v\vecy, v \rangle$
be homogeneous representations of two points $\vecx$ and $\vecy$ in~$\Reals^n$. For $0\le u\le 1$,
define $\vecq(u)$ to be the point in $\Reals^n$ represented
in homogeneous coordinates by the $(n{+}1)$-tuple

\[
\lerp(u,\,\langle w\vecx,w \rangle,\,\langle v\vecy, v \rangle ) .
\]
Evaluate the
first derivative~$\vecq^\prime(u)$ of~$\vecq(u)$. What is $\vecq^\prime(0)$ and
$\vecq^\prime(1)$? Does your answer agree with the case of ordinary linear
interpolation where $v=w= 1$?



\end{document}




