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

[Tuomas J. Lukka]

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Tuomas J. Lukka <address@hidden>        02/11/13 08:26:11

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

Log message:
        fix algo

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.39&tr2=1.40&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.39 
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.40
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.39        Wed Nov 13 
08:20:12 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Wed Nov 13 08:26:11 2002
@@ -299,11 +299,18 @@
 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 $C$.
+again using a function $f(p)$ of location $p$, a given point is {\em inside} 
the curve,
+iff $f(p) < |p - n_C(p)|$, where $n_C(p)$ is the nearest point to $p$ on the 
curve $C$.
+
+Although these algorithms seem different and produce different results, there 
is 
+actually a reasonable generalization which yields to a visual explanation.
+Both algorithms can be represented as
+$$
+    f(g(p)) < |p-n_C(p)|
+$$
+where $g(p) = p$ for the sprinkled case and $g(p) = n_C(p)$ 
+for the attached case. 
 
-- 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
   is visible as the ``rippling speed''