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## [Gzz-commits] gzz/Documentation/Manuscripts/Irregu irregu.tex

 From: Tuomas J. Lukka Subject: [Gzz-commits] gzz/Documentation/Manuscripts/Irregu irregu.tex Date: Sat, 30 Nov 2002 05:42:02 -0500

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Tuomas J. Lukka <address@hidden>        02/11/30 05:42:02

Modified files:
Documentation/Manuscripts/Irregu: irregu.tex

Log message:
HW

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.109&tr2=1.110&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.109
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.110
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.109       Sat Nov 30
05:39:23 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Sat Nov 30 05:42:02 2002
@@ -595,6 +595,8 @@
the value of such a texture and a noise texture and using that (through
alpha test) as a condition for drawing the fragment.

+[ XXX: OpenGL 1.3 or GL\_EXT\_texture\_env\_add required ]
+
We stress that this implementation is not necessarily any worse than
the offset texture implementation:
all its effects are within the options described in Section~\ref{secoptions}.
@@ -604,56 +606,39 @@
falling value, to avoid using the second texture unit and rendering
the shape to a texture.

-To obtain ebbing with displacement mapping, a similar approach
-can be used
-
-The shape is given by Eq.~(\ref{eq:inside}), which under the
-assumptions can be written as a point $(x,y)$ being inside the tearout,
-iff
-$- f(x,g(y)) + (1-y) \ge 1, -$
-where $g(y) = y$ or $g(y) = 1/2$.
-We can draw the section of the envelope as a single rectangle
-with texture coordinates interpolated as $(x,g(y))$
-and the alpha component of the primary color as $(1-y)$.
-The left side of the inequality can be computed using
-texture environment mode ADD and an INTENSITY texture storing $f(\p)$.
-The alpha output of the texture environment can then be tested
-against $1$ using ALPHA\_TEST to discard fragments outside
-the tear-out.
-
-[ XXX: OpenGL 1.3 or GL\_EXT\_texture\_env\_add required ]
-
-Using two texture units and register combiners,
-it is also possible to compute the generalized case given by
-Eq.~(\ref{eq:inside2}) with interpolation parameter of the
-form $\alpha(y) = a y + b$.
-This formulation also allows an infinite non-repeating area of
-different shapes by making
-the ripple functions $f_1$ and $f_2$ repeat at non-rationally
-related periods.
-On the other hand, the generalized formulation brakes most of the border
-drawing algorithms discussed below.
-
-
-\if0
-\subsection{A shape with the correct type of motion}
-
-Drawing a shape with the correct properties is relatively
-simple: drawing a single polygon with $\alpha=0$ at $x=0$ and
-$\alpha=1$ at $x=1$, using ALPHA\_TEST with the cutoff set close to one,
-and adding a texture value to the incoming fragment alpha value
-achieves this.
-
-The texture coordinates determine whether the edge will be attached
-or sprinkled: for sprinkled edges, simply use the current point's
-paper coordinates as texture coordinates. For attached edges,
-project the points to a line at $x=.5$ along the $x$-axis
-and use those texture coordinates.
-\fi
+To obtain ebbing with a kind of displacement mapping, a similar approach
+can be used: instead of accessing the noise texture at the pixel
+location of the paper, the noise texture is accessed at the location
+of the undistorted edge. This
+
+% The shape is given by Eq.~(\ref{eq:inside}), which under the
+% assumptions can be written as a point $(x,y)$ being inside the tearout,
+% iff
+% $+% f(x,g(y)) + (1-y) \ge 1, +%$
+% where $g(y) = y$ or $g(y) = 1/2$.
+% We can draw the section of the envelope as a single rectangle
+% with texture coordinates interpolated as $(x,g(y))$
+% and the alpha component of the primary color as $(1-y)$.
+
+% The left side of the inequality can be computed using
+% texture environment mode ADD and an INTENSITY texture storing $f(\p)$.
+% The alpha output of the texture environment can then be tested
+% against $1$ using ALPHA\_TEST to discard fragments outside
+% the tear-out.
+
+% Using two texture units and register combiners,
+% it is also possible to compute the generalized case given by
+% Eq.~(\ref{eq:inside2}) with interpolation parameter of the
+% form $\alpha(y) = a y + b$.
+% This formulation also allows an infinite non-repeating area of
+% different shapes by making
+% the ripple functions $f_1$ and $f_2$ repeat at non-rationally
+% related periods.
+% On the other hand, the generalized formulation brakes most of the border
+% drawing algorithms discussed below.

-IMAGE

\subsection{Drawing the edge}



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