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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'').
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
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
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:}
\begin{verbatim}
\distort(x1,y1,x2,y2,x3,y3)
\distort
\end{verbatim}
\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
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.
\textbf{Implementation:}
@ -462,12 +466,15 @@ In order to transform a given (x,y) coordinate pair to it:
\begin{enumerate}
\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).
The matrix for this operation is:\\
\[ \left[\begin{array}{ c c }
\frac{1}{bl} & 0 \\
0 & \frac{1}{h}
\end{array} \right]\]
\item Apply the following formula: $P = P_0 + (P_1-P_0) u + (P_3-P_0) v + (P_0+P_2-P_1-P_3) u v$\\
The affine 3D transformation matrix for this operation is:\\
\[ \left[\begin{array}{ c c c c }
\frac{1}{bl} & 0 & 0 & -\frac{P_{0x}}{bl} \\
0 & \frac{1}{h} & 0 & -\frac{P_{0y}}{h} \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{array} \right]\]\\
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
and another using the y coordinates. Since the four points are constant, the coeficients can be
precalculated, resulting in a very fast transformation.\\