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

[Janne V. Kujala]

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Janne V. Kujala <address@hidden>        02/11/19 12:07:08

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

Log message:
        bugfix

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.56&tr2=1.57&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.56 
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.57
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.56        Tue Nov 19 
08:33:58 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Tue Nov 19 12:07:08 2002
@@ -657,17 +657,19 @@
 tying ripple shape to canvas positions.
 
 The problem can be fully solved with a vector valued ripple function 
-${\bf F}({\bf p})$,
+${\bf F}({\bf p})$, $\Vert{\bf F}({\bf p})\Vert \le 1$,
 using $f({\bf p}) = (1 + {\bf d}\cdot {\bf F}({\bf p}))/2$, 
 where ${\bf d}$ is the unit normal
 of the envelope. The dot product automatically inverts the 
 function for a 180 degree rotation.
-This function can be directly used with the
-pre-computed borders method by pre-computing the dot product
-when computing the outer surfaces. As a bonus, the scattered
-case, too, then needs to store only a span of 180 degrees.
-The texture shader version can also use vector valued ripple function
-with no additional cost.
+
+The texture shader version can directly use the vector valued ripple function.
+It can also be used with the
+pre-computed borders method by pre-computing the dot product, too,
+when computing the outer surfaces. 
+However, even the connected case then requires a full 360 span
+of pre-computed outer surfaces.
+
 
 \if0
 Content drawn using stencil.