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

[Janne V. Kujala]

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Janne V. Kujala <address@hidden>        02/11/28 13:21:50

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

Log message:
        continuous

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.81&tr2=1.82&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.81 
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.82
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.81        Thu Nov 28 
13:03:08 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Thu Nov 28 13:21:50 2002
@@ -381,9 +381,9 @@
 where
 $A \cap B(y, r) = \emptyset$ implies $y \notin B$ and 
 $A \cap B(y, r) = B(y,r)$ implies $y \in B$.
-Additionally, slow movement of $A$ should result into small
-changes in $B$ so that the rippling is not too fast.
-XXX: continuous mapping?
+Additionally, the mapping from $A$'s to $B$'s should be continuous
+so that slow movement of $A$ results into ``rippling'' in $B$.
+Furthermore, the rippling should not be too fast.
 
 %
 %to start with the requirement that:
@@ -395,7 +395,7 @@
 %From this porperty, it follows that the mapping from $A$'s to $B$'s 
 %is actually defined by a point relation $R \subset (\mathbf{R}^2)^2$:
 %
-One way of defining such mapping is a relation 
+One way of defining such mapping is a continuous relation 
 $R \subset (\mathbf{R}^2)^2$ that identifies the points of $A$ 
 with points in $B$:
 \[
@@ -403,7 +403,6 @@
 \]
 If $d(x,y) \le r$ for all $x R y$, the maximum distortion requirement
 is satisfied. 
-Furthermore, $R$ should be continuous to create natural rippling.
 
 If $R$ is a continuous function, i.e., $x R y \Leftrightarrow y = G(x)$,
 the irregular shapes will be connected (if the original shape is connected), 
@@ -434,8 +433,7 @@
 but that is likely to not yield good performance if the shape has fine detail.
 Furthermore, intersections in the edge may cause additional problems.
 If the function is bijection, so as to avoid any intersections, we
-can just as well use the inverse function case by simply inverting 
-the function.
+can just as well use the invert it and use the inverse mapping.
 
 ---