[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 08:13:27

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

Log message:
        continuity

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.37&tr2=1.38&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.37 
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.38
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.37        Wed Nov 13 
08:06:53 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Wed Nov 13 08:13:27 2002
@@ -268,6 +268,7 @@
 
 
 Edge shapes: attached and sprinkled and intermediates.
+TOPOLOGY!
 
 Finally, there is the question of what should happen when the viewport reaches 
the edge
 of the canvas.
@@ -282,6 +283,16 @@
 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
 for the algorithm.
+
+To start off, assume that we are drawing the torn edge around a given 
+smooth parametric curve $C = (x(t), y(t))$. The thickness of the roughness of 
the
+edge is assumed to be small compared
+to the curvature of $C$.
+
+Locally, we can approximate the curve by a point and a normal vector.
+The resulting shape of the edge should be continuous w.r.t.~both the local
+point and normal vector.
+
 
 - 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