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{\bf  Computer Graphics Intro}\hfill \today \hrule {\bf G. Farin }
\hfill \fbox{ \bf Name:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}\\

\hfill \fbox{ \bf ASU ID:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}


\vskip 1 cm
\begin {center} {\bf  Final }\\
\end {center}


\vskip 2 cm




{\bf 1.} Sketch the geometry (vectors from a vertex) of the Phong
lighting model. \vspace{4cm}

{\bf 2.} Which are the three types of light sources in the Phong
ligthing model? Which are viewer dependent?

\vspace{2cm}

{\bf 3.} State Lambert's law.

{\vspace{2cm}


{\bf 4.} Fig. \ref{fig:bilin} shows four 3D points. Using bilinear
interpolation, sketch where the domain point corresponding to
$(u,v)=(0.33,0.66)$ is mapped to.

\vfill \eject

\begin{figure}
    \epsfig{file=bilin.ps,height=2in}
    \caption{Bilinear interpolation.}
     \label{fig:bilin}
\end{figure}


{\bf 5.} Let the input polygon to Chaikin's algorithm be a
triangle. After four iterations (the initial triangle counting as
the $0^{\rm th}$ iteration), you will have a refined polygon. How
many vertices does it have?


{\bf 6.} Figure \ref{fig:triang} shows a triangulation. Points are
labeled as $\pp_i$, Triangles as $T_i$. Write down the
corresponding off-file (ignore $z$-coordinates).

\begin{figure}
    \epsfig{file=triangulation.ps,height=2in}
    \caption{A triangulation.}
      \label{fig:triang}
\end{figure}

\vspace{4cm}

 {\bf 7.} Let $\pp$ be a point on an object and let
$\nn$ be the corresponding normal. Let $\ee$ be the eye position
of the viewer. What condition do $\pp$, $\nn$, and $\ee$ have to
satisfy such that $\pp$ is on a silhouette?

\vspace{2cm}

{\bf 8.} What is the convex hull of a tetrahedron?

\vspace{2cm}

{\bf 9.} What is ``cel shading"?

 \vspace{3cm}

{\bf 10.} Let a texture be defined by the letter ``X" drawn into a
square. Draw schematically how the RGB structure of the mipmap
levels are stored using three levels of mipmap depth.

\vspace{4cm}




 \vspace{4cm}















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