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

[Janne V. Kujala]

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Janne V. Kujala <address@hidden>        02/11/17 07:15:45

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

Log message:
        fix eqs

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.48&tr2=1.49&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.48 
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.49
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.48        Sun Nov 17 
06:55:27 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Sun Nov 17 07:15:45 2002
@@ -318,7 +318,7 @@
 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 seen as computing the intersection of (the volume
-above) the surface $(p, f(p))$ and a \emph{cutting surface} $(E(s,g(t)), t)$, 
+below) the surface $(p, f(p))$ and a \emph{cutting surface} $(E(s,g(t)), t)$, 
 and then mapping the intersection on the envelope $E(s,t)$ 
 using the parametrization of the cutting surface.
 The function $g$ (actually its inverse) defines the profile of the 
@@ -355,18 +355,18 @@
 \subsection{Drawing the shape}
 
 Recall that the torn shape can be defined as the intersection
-of a surface $(p,f(p))$ and a cutting plane $E(s,g(t),t)$.
+of a surface $(p,f(p))$ and a cutting plane $(E(s,g(t)),t)$.
 Using the same parametrization for both surfaces, a point $E(s,t)$
 is inside the tear-out, iff
 \begin{equation}
-    f(E(s,g(t))) < t.
+    f(E(s,g(t))) \ge t.
 \end{equation}
 
 Because $E(s,t)$ and $E(s,g(t))$ are both affine functions,
 we can draw the section as a single QUAD with object position 
 interpolated as $E(s,t)$, texture coordinates as $E(s,g(t))$,
 and the alpha component of the primary color as $(1-t)$.
-The above inequality can be written as $f(E(s,g(t))) + (1-t) < 1$.
+The above inequality can be written as $f(E(s,g(t))) + (1-t) \ge 1$.
 The left side can be computed using texture environment mode ADD
 and an INTENSITY texture storing $f(p)$.
 The alpha output of the texture environment can then be tested