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

[Tuomas J. Lukka]

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Tuomas J. Lukka <address@hidden>        02/11/30 13:25:10

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

Log message:
        Sugg

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.114&tr2=1.115&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.114 
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.115
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.114       Sat Nov 30 
12:55:34 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Sat Nov 30 13:25:10 2002
@@ -583,14 +583,18 @@
 
 XXX figs for all these shapes!
 
+\subsubsection{2D offset texture}
+
 The type of offsetting in Eq.(\ref{eqoffset}) is implemented 
 in modern texture shading hardware, such as the NV25 architecture.
 The image of the undistorted shape can be stored in a texture and accessed
 with texture coordinates offset by (read from) another texture.
 This is called an offset (dependent) texture access.
 
-On hardware without such capabilities, such as the NV10, we can
-obtain a similar effect by constraining the offset
+\subsubsection{Polygonal XXX}
+
+On hardware without texture shading capabilities, such as the NV10, we can
+obtain a suitable shape by constraining the offset
 in the direction of the normal. This can be done by rendering
 into a texture a function which is 1 inside the undistorted shape and
 falls off linearly with distance. The hardware is capable of adding
@@ -866,57 +870,57 @@
 ending up on screen.
 That stencil bit is then used to draw borders for the torn edges.
 
-If a canvas is torn into multiple pieces, the above methods
-produce edges that do not fit together: the edges of adjacent
-pieces have opposing ripples.
-The problem is partly solved by inverting (i.e., $1-f(\p)$) 
-the ripple function for either one of each pair of facing sides.
-But then a 180 degree rotation of a pair of fitting pieces 
-inverts the torn shape between them, breaking the principle of
-tying ripple shape to canvas location.
-
-\if0
-The problem can be fully solved with a vector valued ripple function 
-$F({\p})$, $\Vert F({\p})\Vert \le 1$,
-using $f({\p}) = (1 + N \cdot F({\p}))/2$, 
-where $N$ is the unit normal
-of the envelope. The dot product automatically inverts the 
-function for a 180 degree rotation.
-XXX: equivalent to drawing each envelope section by real 2D-offsetting 
-of a half-plane
-
-The texture shader version can directly use the vector valued ripple function.
-It can also be used with the
-pre-computed borders method by pre-computing the dot product, too.
-However, even the connected case then requires a full 360 degree span
-of pre-computed outer surfaces.
-\fi
-
-\if0
-Content drawn using stencil.
-Inside only needs to be drawn twice. ???
-Can create ``outside'' stencil and draw inside only once.
-
-Curved lines: \\
-- dicing \\
-- non-rectangular segments need projective texture mapping for
-  the connected case: rectangular sections are stretched together \\
-
-Corners: \\
-- motion problem with connected edge on non-rectangular segments 
-  on a straight line
-  (the ripples ``rotate'' when the tearout shape moves)  \\
-- rounded corners to make segments more rectangular \\
-- possible problem with self-intersecting envelope \\
-- could move spine to the inner edge with the spine-normal definition \\
-- creating corners by intersecting two straight lines with stencil \\
-
-
-Jigsaw puzzle problems: \\
-- tear-out pieces do not fit together \\
-- partially solved using inverted version of the texture \\
-- better solution by using a two-component texture
-\fi
+% If a canvas is torn into multiple pieces, the above methods
+% produce edges that do not fit together: the edges of adjacent
+% pieces have opposing ripples.
+% The problem is partly solved by inverting (i.e., $1-f(\p)$) 
+% the ripple function for either one of each pair of facing sides.
+% But then a 180 degree rotation of a pair of fitting pieces 
+% inverts the torn shape between them, breaking the principle of
+% tying ripple shape to canvas location.
+% 
+% \if0
+% The problem can be fully solved with a vector valued ripple function 
+% $F({\p})$, $\Vert F({\p})\Vert \le 1$,
+% using $f({\p}) = (1 + N \cdot F({\p}))/2$, 
+% where $N$ is the unit normal
+% of the envelope. The dot product automatically inverts the 
+% function for a 180 degree rotation.
+% XXX: equivalent to drawing each envelope section by real 2D-offsetting 
+% of a half-plane
+% 
+% The texture shader version can directly use the vector valued ripple 
function.
+% It can also be used with the
+% pre-computed borders method by pre-computing the dot product, too.
+% However, even the connected case then requires a full 360 degree span
+% of pre-computed outer surfaces.
+% \fi
+% 
+% \if0
+% Content drawn using stencil.
+% Inside only needs to be drawn twice. ???
+% Can create ``outside'' stencil and draw inside only once.
+% 
+% Curved lines: \\
+% - dicing \\
+% - non-rectangular segments need projective texture mapping for
+%   the connected case: rectangular sections are stretched together \\
+% 
+% Corners: \\
+% - motion problem with connected edge on non-rectangular segments 
+%   on a straight line
+%   (the ripples ``rotate'' when the tearout shape moves)  \\
+% - rounded corners to make segments more rectangular \\
+% -%  possible problem with self-intersecting envelope \\
+% - could move spine to the inner edge with the spine-normal definition \\
+% - creating corners by intersecting two straight lines with stencil \\
+% 
+% 
+% Jigsaw puzzle problems: \\
+% - tear-out pieces do not fit together \\
+% - partially solved using inverted version of the texture \\
+% - better solution by using a two-component texture
+% \fi
 
 \section{Example applications}