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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: Wed, 13 Nov 2002 08:20:12 -0500

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Tuomas J. Lukka <address@hidden>        02/11/13 08:20:12

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

Log message:
More algo

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.38&tr2=1.39&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.38
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.39
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.38        Wed Nov 13
08:13:27 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Wed Nov 13 08:20:12 2002
@@ -281,7 +281,9 @@
\subsection{Algorithm How?''}

In this subsection, we formulate the design criteria of the preceding section
mathematically
-to obtain a simple algorithm with the desired properties and an interesting
graphical explanation
+and discuss
+a simple algorithm for a shape with the desired properties
+and an interesting graphical explanation
for the algorithm.

To start off, assume that we are drawing the torn edge around a given
@@ -293,6 +295,13 @@
The resulting shape of the edge should be continuous w.r.t.~both the local
point and normal vector.

+For the attached edge, we can obtain the final curve by simply shifting the
original
+smooth curve to its normal direction by a function which only depends on the
location $(x, y)$.
+
+The sprinkled case, on the other hand, can be obtained through a decision
process:
+again using a function of location $f(x,y)$, a given point is {\em inside} the
curve,
+iff $f(x,y) < d_C(x,y)$, where $d_C(x,y)$ is the distance of the point $(x,y)$
from
+the contents of the curve $C$.

- the torn shape of a point on an edge should be a continuous function of the
point's location on the paper\\
- the function should change slowly enough so that the dot product of movement
direction and edge normal