[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 08:20:12

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