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

[Janne V. Kujala]

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Janne V. Kujala <address@hidden>        02/11/30 02:59:28

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

Log message:
        reorg, comment out stuff

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.97&tr2=1.98&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.97 
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.98
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.97        Fri Nov 29 
14:27:10 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Sat Nov 30 02:59:28 2002
@@ -478,6 +478,7 @@
 And more importantly, texture shading is not implemented on low-end
 hardware.
 XXX: we want to be able to draw connected tear-out shapes.
+XXX: ebbing?
 
 \if 0
 We split the edge of the original shape to multiple pieces, 
@@ -569,24 +570,17 @@
 and the undistorted shape $A$ is the region inside the spine $E(x,1/2)$.
 
 Although these algorithms seem different and produce different results, 
-there is actually a general formulation in the one-dimensional case.
-Both algorithms can be seen as computing the intersection of a
-\emph{ripple volume}, the volume below the surface $(\p, f(\p))$,
- and a \emph{cutting surface} $(E(x,g(y)), y)$, 
-and then mapping the intersection on the envelope $E(x,y)$ 
-using the parameters of the cutting surface.
-
-The function $g$ (actually its inverse) defines the profile of the 
-cutting surface, with $g(y) = y$ for the scattered case and $g(y) = 1/2$,
-i.e., a vertical surface, for the connected case. 
-Other choices for $g$ are possible, but not very useful, because they
-correspond to just different distortions of the same basic shape.
-
-Using the same parametrization for both surfaces, a point $E(x,y)$
+they can both be formulated as offsetting in the one-dimensional case:
+a point $E(x,y)$
 is inside the tear-out, iff
 \begin{equation} \label{eq:inside}
-    f(E(x,g(y))) \ge y.
+    f(E(x,g(y))) \ge y,
 \end{equation}
+where $g(y) = y$ for the scattered case and $g(y) = 1/2$.
+The function $g(y)$ specifies how the ``offset texture'' is mapped.
+Other choices for $g$ are possible, but not very useful, because they
+correspond to just different distortions of the same basic shape.
+
 For more variation on edge shapes, the inequality can be 
 generalized to
 \begin{equation} \label{eq:inside2}
@@ -752,6 +746,20 @@
 
 \subsubsection{Pre-computed borders}
 
+XXX:
+
+Both algorithms can be seen as computing the intersection of a
+\emph{ripple volume}, the volume below the surface $(\p, f(\p))$,
+ and a \emph{cutting surface} $(E(x,g(y)), y)$, 
+and then mapping the intersection on the envelope $E(x,y)$ 
+using the parameters of the cutting surface.
+
+The function $g$ (actually its inverse) defines the profile of the 
+cutting surface, with $g(y) = y$ for the scattered case and $g(y) = 1/2$,
+i.e., a vertical surface, for the connected case. 
+
+Using the same parametrization for both surfaces, 
+
 Recall that the torn shape can be defined as the intersection
 of the ripple volume, i.e., the volume below $(x,y,f(x,y))$, 
 and a cutting surface $(x,g(y),y)$,
@@ -839,6 +847,9 @@
 The edge texture can be one texel wide (if the image of the 
 edge is drawn horizontally), allowing for large height and
 so non-photorealistic scaling to large scales.
+Note that it still has to be a 2D texture for the mipmapping trick
+to work.
+
 Increasing the border width scaling exponent from 0 makes the
 border width less consistent with sloped offset.
 
@@ -918,6 +929,7 @@
 inverts the torn shape between them, breaking the principle of
 tying ripple shape to canvas location.
 
+\if0
 The problem can be fully solved with a vector valued ripple function 
 $F({\p})$, $\Vert F({\p})\Vert \le 1$,
 using $f({\p}) = (1 + N \cdot F({\p}))/2$, 
@@ -932,7 +944,7 @@
 pre-computed borders method by pre-computing the dot product, too.
 However, even the connected case then requires a full 360 degree span
 of pre-computed outer surfaces.
-
+\fi
 
 \if0
 Content drawn using stencil.