%***********************************************************************
\section{sAm[̃XN[̌vZ}

ѐXN[o[ERg[̐ݒƁCʂ̕`ԂƂ̊֌W
߂邽߂̌vZ@qׂD

\begin{figure}[h]
  \begin{center}
    \begin{overpic}[scale=1.0]{tech_memo_scroll.eps}
      \put(55, 99){\scriptsize ${\rm vsq.TotalClocks} \cdot {\rm scaleX} + {\rm pictPianoRoll.Width}$}
      \put(24, 92){\scriptsize startToDrawX}
      \put(69, 92){\scriptsize pictPianoRoll.Width}

      \put(122, 71){\scriptsize 0}
      \put(122, 49){\scriptsize vScroll.Value}
      \put(122, 43){\scriptsize vScroll.Maximum -}
      \put(129, 40){\scriptsize vScroll.LargeChange}

      \put(14, 73){\rotatebox{90}{\scriptsize startToDrawY}}
      \put(14, 36){\rotatebox{90}{\scriptsize pictPianoRoll.Height}}
      \put(5, 29){\rotatebox{90}{\scriptsize $128 \cdot \lfloor 100 \cdot {\rm scaleY} \rfloor$}}

      \put(43, 19){\scriptsize \textcolor{red}{0}}
      \put(59, 19){\scriptsize \textcolor{red}{hScroll.Value}}
      \put(82, 19){\scriptsize \textcolor{red}{${\rm hScroll.Maximum} - {\rm hScroll.LargeChange}$}}

      \put(45, 68){\color[rgb]{1.,0,0}{Viewport}}
      \put(25, 80){\color[rgb]{0,0,1.}{zXN[}}
    \end{overpic}
  \end{center}
  \label{}FXN[T}}
\end{figure}

}̂悤ɁCr[|[g̃ItZbg${\rm startToDrawX}$${\rm startToDrawX}$Œ`D
܂CXN[ERg[${\rm hScroll}$${\rm Value}$vpeB[̒PʂclockC
XN[ERg[${\rm vScroll}$${\rm Value}$vpeB[̒PʂcentłD
sAm[̉ʏ̉̕\{${\rm scaleX [pixel/clock]}$Cc̕\{${\rm scaleY [pixel/cent]}$ƂD
\par
${\rm startToDrawX}$C${\rm startToDrawY}$͎Œ`F
\begin{equation}
  \left\{
  \begin{array}{l}
    {\rm startToDrawX} = {\rm hScroll.Value} \cdot {\rm scaleX},
  \\
    {\rm startToDrawY} = {\rm vScroll.Value} \cdot {\rm scaleY}.
  \end{array} \right.
\end{equation}

%-----------------------------------------------------------------------
\subsection{XN[o[}
${\rm startToDrawX}$̍őlэŏl͎̂悤Ɍ߂.
\begin{eqnarray}
  \max ({\rm startToDrawX}) &=& {\rm vsq.TotalClocks} \cdot {\rm scaleX},
  \\
  \min ({\rm startToDrawX}) &=& 0.
\end{eqnarray}

XN[o[ԉEɃXN[ꂽƂɁChScroll.ValueőlƂ˂΂ȂȂC
startToDrawX̍őlscaleXŊ̂ChScroll.Value̍őlƂȂ悤ɂD
܂CXN[o[̓̎dlhScroll.Value̍ől
${\rm hScroll.Maximum} - {\rm hScroll.LargeChange}$
ł̂ŁC̎藧D
\begin{equation}
  \frac{\max( {\rm startToDrawX} )}{ {\rm scaleX} } = {\rm hScroll.Maximum} - {\rm hScroll.LargeChange}
  \label{eq:hscroll_max_limitation}
\end{equation}

ɁCOϏXN[o[̉“͈͂ƃXN[{bNX̔̕䂪CzXN[ƃr[|[g̔̕
łƔςǂ̂ŁC̎藧‚悤ɂD
\begin{equation}
  \frac{\rm pictPianoRoll.Width}{{\rm vsq.TotalClocks} \cdot {\rm scaleX} + {\rm pictPianoRoll.Width}} = \frac{\rm hScroll.LargeChange}{\rm hScroll.Maximum}
  \label{eq:hscroll_viewport-ratio_limitation}
\end{equation}

(\ref{eq:hscroll_max_limitation})Ǝ(\ref{eq:hscroll_viewport-ratio_limitation})AĉƁChScroll.MaximumhScroll.LargeChange͎Œ܂D

\begin{eqnarray}
   {\rm hScroll.Maximum}     &=& {\rm vsq.TotalClocks} + \frac{\rm pictPianoRoll.Width}{\rm scaleX},\label{eq:hscroll_maximum}
   \\
   {\rm hScroll.LargeChange} &=& \frac{\rm pictPianoRoll.Width}{\rm scaleX}.\label{eq:hscroll_largechange}
\end{eqnarray}

ŁCXN[{bNX̎ۂ̕\ɂȂ邩𒲂ׂD
XN[o[̍\͂}̂悤ɂȂĂD

\begin{figure}[h]
  \begin{center}
    \begin{overpic}[width=160mm]{tech_memo_scroll_abstract.eps}
      \put(3, 6){\scriptsize thumbWidth}
      \put(140, 6){\scriptsize thumbWidth}
      \put(84, 6){\scriptsize boxWidth}
      \put(70, 22){\scriptsize hScroll.Width}
    \end{overpic}
  \end{center}
\end{figure}

XN[o[̓̎dlC藧D

\begin{equation}
  \frac{\rm boxWidth}{{\rm hScroll.Width} - 2 \cdot {\rm thumbWidth}} = \frac{\rm hScroll.LargeChange}{\rm hScroll.Maximum}.
\end{equation}

]āC

\begin{equation}
  {\rm boxWidth} = \frac{\rm hScroll.LargeChange}{\rm hScroll.Maximum} ({\rm hScroll.Width} - 2 \cdot {\rm thumbWidth}).\label{eq:hscroll_boxwidth_limitation}
\end{equation}

boxWidth́C(\ref{eq:hscroll_maximum})Ǝ(\ref{eq:hscroll_largechange})ɂ茈܂邪C
̑傫lȉɂȂƔɈÂ炭ȂƍlD
ŁCboxWidth̍ŏl$\min({\rm boxWidth})$ƂC(\ref{eq:hscroll_maximum})Ǝ(\ref{eq:hscroll_largechange})
߂l̒l菬Ȃꍇ́Cȉ̗v̂ŌvZ邱ƂɂD

\par

boxWidthl$\min({\rm boxWidth})$̒萔ƂĈD
ƁC(\ref{eq:hscroll_viewport-ratio_limitation})͐藧ȂȂ邪C͎dȂD
ڂCXN[{bNX삵ɂƂ̕ʖڂƎvłD
]čŏ(\ref{eq:hscroll_max_limitation})Ǝ(\ref{eq:hscroll_viewport-ratio_limitation})AĉɁC
(\ref{eq:hscroll_max_limitation})Ǝ(\ref{eq:hscroll_boxwidth_limitation})AĉD
́C

\begin{eqnarray}
  {\rm hScroll.Maximum}     &=& \frac{{\rm vsq.TotalClocks}\left({\rm hScroll.Width - 2 \cdot {\rm thumbWidth}}\right)}{\left({\rm hScroll.Width - 2 \cdot {\rm thumbWidth}}\right) - {\rm boxWidth}},\\
  {\rm hScroll.LargeChange} &=& \frac{{\rm vsq.TotalClocks} \cdot {\rm boxWidth}}{\left({\rm hScroll.Width - 2 \cdot {\rm thumbWidth}}\right) - {\rm boxWidth}},
\end{eqnarray}

ƂȂD

%-----------------------------------------------------------------------
\subsection{XN[o[}

startToDrawY̍őlэŏl͎̂悤Ɍ߂D

\begin{eqnarray}
  \max( {\rm startToDrawY} ) &=& 128 \cdot \lfloor 100 \cdot {\rm scaleY} \rfloor - {\rm pictPianoRoll.Height},
  \\
  \min( {\rm startToDrawY} ) &=& 0.
\end{eqnarray}

XN[o[ԉɃXN[ꂽƂɁCvScroll.ValueőlƂ˂΂ȂȂC
startToDrawY̍őlscaleYŊ̂CvScroll.Value̍őlƂȂ悤ɂD
܂CXN[o[̓̎dlvScroll.Value̍ől
${\rm vScroll.Maximum} - {\rm vScroll.LargeChange}$ł̂ŁC̎藧D

\begin{equation}
  \frac{\max( {\rm startToDrawY} )}{\rm scaleY} = {\rm vScroll.Maximum} - {\rm vScroll.LargeChange}.
  \label{eq:vscroll_max_limitation}
\end{equation}

ɁCOϏXN[o[̉ғ͈͂ƃXN[{bNX̍̔䂪CzXN[ƃr[|[g̍̔
łƔςǂ̂ŁC̎藧‚悤ɂD

\begin{equation}
  \frac{\rm pictPianoRoll.Height}{128 \cdot \lfloor 100 \cdot {\rm scaleY} \rfloor} = \frac{\rm vScroll.LargeChange}{\rm vScroll.Maximum}.
  \label{eq:vscroll_viewport-ratio_limitation}
\end{equation}

(\ref{eq:vscroll_max_limitation})Ǝ(\ref{eq:vscroll_viewport-ratio_limitation})AĉƁC
vScroll.MaximumvScroll.LargeChange͎Œ܂D

\begin{eqnarray}
  {\rm vScroll.Maximum}     &=& \frac{128 \cdot \lfloor 100 \cdot {\rm scaleY} \rfloor}{\rm scaleY},
  \\
  {\rm vScroll.LargeChange} &=& \frac{\rm pictPianoRoll.Height}{\rm scaleY}.
\end{eqnarray}

ŁCXN[{bNX̎ۂ̕\ɂȂ邩𒲂ׂD
XN[o[̏ꍇƑ̓ł̂ŁCXN[{bNX̍${\rm boxHeight}$ɂ‚āC藧D

\begin{equation}
  {\rm boxHeight} = \frac{\rm vScroll.LargeChange}{\rm vScroll.Maximum}({\rm vScroll.Height} - 2 \cdot {\rm thumbHeight}).
  \label{eq:vscroll_boxheight_limitation}
\end{equation}

XN[o[̂ƂƓlɁCboxHeightClmin(boxHeight)̒萔ƂĈD
(\ref{eq:vscroll_max_limitation})Ǝ(\ref{eq:vscroll_boxheight_limitation})AĉD́C

\begin{eqnarray}
  {\rm vScroll.Maximum}     &=& \frac{128 \cdot \lfloor 100 \cdot {\rm scaleY} \rfloor - {\rm pictPianoRoll.Height}}{\rm scaleY} \times \nonumber\\
                            & & \hspace{1.0em}\frac{{\rm vScroll.Height - 2 \cdot {\rm thumbHeight}}}{{\rm vScroll.Height - 2 \cdot {\rm thumbHeight} - {\rm boxHeight}}},
  \\
  {\rm vScroll.LargeChange} &=& \frac{128 \cdot \lfloor 100 \cdot {\rm scaleY} \rfloor - {\rm pictPianoRoll.Height}}{\rm scaleY} \times \nonumber\\
                            & & \hspace{1.0em}\frac{\rm boxHeight}{{\rm vScroll.Height - 2 \cdot {\rm thumbHeight} - {\rm boxHeight}}},
\end{eqnarray}

ƂȂD