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Fixes to distort tag.

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Originally committed to SVN as r1410.
This commit is contained in:
Rodrigo Braz Monteiro 2007-07-11 03:22:29 +00:00
parent cb8fc119ff
commit 2c5a42e347
2 changed files with 14 additions and 7 deletions
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@ -271,7 +271,9 @@ Styles work in a very different way from the way they did on previous formats (w
of ASS3, which actually implements this very same style based on this format, as ``StyleEx''). of ASS3, which actually implements this very same style based on this format, as ``StyleEx'').
Instead of setting multiple parameters across many commas, you simply specify override tags. When a line Instead of setting multiple parameters across many commas, you simply specify override tags. When a line
uses a style, it's as if the overrides of the style were inserted right before the start of the line uses a style, it's as if the overrides of the style were inserted right before the start of the line
contents. contents, with one exception: certain tags without parameters revert to the style default. For example,
\textbackslash c will revert the primary colour to the one specified in style. Such use of tags is invalid
in the style definition, and \must\ be ignored if found in them.
Also, a style can inherit from another style, and define new overrides which are then appended to those Also, a style can inherit from another style, and define new overrides which are then appended to those
of the parent style. The parent style \must\ have been declared \emph{BEFORE} the style trying to use of the parent style. The parent style \must\ have been declared \emph{BEFORE} the style trying to use
@ -442,6 +444,7 @@ imagery.
\textbf{Usage:} \textbf{Usage:}
\begin{verbatim} \begin{verbatim}
\distort(x1,y1,x2,y2,x3,y3) \distort(x1,y1,x2,y2,x3,y3)
\distort
\end{verbatim} \end{verbatim}
\textbf{Description:} \textbf{Description:}
@ -453,6 +456,7 @@ $P_0$ is the origin, $P_1 = (x1,y1)$ is the corner at the end of the baseline fo
$P_2 = (x2,y2)$ is the point above that, and $P_3 = (x3,y3)$ is the point above $P_0$. That is, they $P_2 = (x2,y2)$ is the point above that, and $P_3 = (x3,y3)$ is the point above $P_0$. That is, they
are listed clockwise from origin ($P_0$). are listed clockwise from origin ($P_0$).
If the parameter list is ommitted, the distort reverts to the style's default (none by default).
This tag can be animated with \textbackslash t. This tag can be animated with \textbackslash t.
\textbf{Implementation:} \textbf{Implementation:}
@ -462,12 +466,15 @@ In order to transform a given (x,y) coordinate pair to it:
\begin{enumerate} \begin{enumerate}
\item Normalize the (x,y) coordinates to a (u,v) system, so that $P_0$ = (0,0) and $P_2$ = (1,1). \item Normalize the (x,y) coordinates to a (u,v) system, so that $P_0$ = (0,0) and $P_2$ = (1,1).
This can be done by dividing x by the block's baseline length (bl) and y by the block height (h). This can be done by dividing x by the block's baseline length (bl) and y by the block height (h).
The matrix for this operation is:\\ The affine 3D transformation matrix for this operation is:\\
\[ \left[\begin{array}{ c c } \[ \left[\begin{array}{ c c c c }
\frac{1}{bl} & 0 \\ \frac{1}{bl} & 0 & 0 & -\frac{P_{0x}}{bl} \\
0 & \frac{1}{h} 0 & \frac{1}{h} & 0 & -\frac{P_{0y}}{h} \\
\end{array} \right]\] 0 & 0 & 1 & 0 \\
\item Apply the following formula: $P = P_0 + (P_1-P_0) u + (P_3-P_0) v + (P_0+P_2-P_1-P_3) u v$\\ 0 & 0 & 0 & 1
\end{array} \right]\]\\
That is, $u = \frac{P_x - P_{0x}}{bl}; v = \frac{P_y - P_{0y}}{h}$.
\item Apply the following formula: $P = P_0 + (P_1-P_0) u + (P_3-P_0) v + (P_0+P_2-P_1-P_3) u v$.\\
This can be interpreted as simple vector operations, that is, apply that once using the x coordinates This can be interpreted as simple vector operations, that is, apply that once using the x coordinates
and another using the y coordinates. Since the four points are constant, the coeficients can be and another using the y coordinates. Since the four points are constant, the coeficients can be
precalculated, resulting in a very fast transformation.\\ precalculated, resulting in a very fast transformation.\\