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

[Tuomas J. Lukka]

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Tuomas J. Lukka <address@hidden>        02/11/30 13:44:09

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

Log message:
        oops

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Irregu/irregu.tex.diff?tr1=1.119&tr2=1.120&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Irregu/irregu.tex
diff -u gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.119 
gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.120
--- gzz/Documentation/Manuscripts/Irregu/irregu.tex:1.119       Sat Nov 30 
13:38:04 2002
+++ gzz/Documentation/Manuscripts/Irregu/irregu.tex     Sat Nov 30 13:44:09 2002
@@ -618,9 +618,9 @@
 
 \subsubsection{Explicit undistorted shape}
 
-Naturally, the undistorted shape can also be drawn by by OpenGL primitives, 
+Naturally, the undistorted shape can also be drawn by OpenGL primitives, 
 by drawing polygons enveloping the widest variation in the torn shape
-and
+and using
 the smooth shading interpolation in OpenGL to obtain the linearly
 falling value. This avoids the use of the second texture unit.
 
@@ -633,9 +633,9 @@
 Corners can cause problems in this approach: for large angles,
 the deviation from the normal direction is not noticeable but 
 for angles approaching $90\deg$, the results are not satisfactory.
-There are several possible solutions: rounding the corners, using 
+There are at least two possible solutions: rounding the corners or using 
 the stencil buffer to render the two edges separately and taking
-the intersection,
+the intersection.
 
 
 
@@ -667,36 +667,36 @@
 % On the other hand, the generalized formulation brakes most of the border 
 % drawing algorithms discussed below.
 
-Curved envelopes can be approximated by dicing to linear pieces.
-In the connected case, the sections are drawn as if they were
-rectangles of such lengths that the spines of the adjacent sections meet. 
-Projective texture mapping is used to shear together the sides of the 
-adjacent rectangles.
-In the scattered case, the sections are drawn simply 
-as overlapping rectangles, 
-but clipped along a normal of the envelope so that no part is drawn twice.
-Both of these methods yield the same set of polygons, with
-the only difference in the texture coordinates.
-
-Corners can be problematic, because the envelope must not intersect
-itself. For the scattered case, corners can be drawn by simply
-connecting the envelopes of the sides on a diagonal line.
-For the connected case, the stretching of the texture
-causes an undesireble side effect: the ripples are directed radially
-outward between the directions of the corners, making
-the ripples rotate if the tear-out shape is moved along its side.
-
-A simple solution to the problem is rounding. 
-For example, 
-a higher order ellipse can be used to obtain a rectangle 
-with rounded corners and thus more rectangular sections.
-
-If rounding is not desired, the corners can be drawn as
-intersections of torn-edged half-planes.
-The border of the intersection shape is obtained
-as a similar intersection using the half-planes corresponding to
-the outer edges of the borders.
-The intersection can be implemented using stencil operations.
+% Curved envelopes can be approximated by dicing to linear pieces.
+% In the connected case, the sections are drawn as if they were
+% rectangles of such lengths that the spines of the adjacent sections meet. 
+% Projective texture mapping is used to shear together the sides of the 
+% adjacent rectangles.
+% In the scattered case, the sections are drawn simply 
+% as overlapping rectangles, 
+% but clipped along a normal of the envelope so that no part is drawn twice.
+% Both of these methods yield the same set of polygons, with
+% the only difference in the texture coordinates.
+% 
+% Corners can be problematic, because the envelope must not intersect
+% itself. For the scattered case, corners can be drawn by simply
+% connecting the envelopes of the sides on a diagonal line.
+% For the connected case, the stretching of the texture
+% causes an undesireble side effect: the ripples are directed radially
+% outward between the directions of the corners, making
+% the ripples rotate if the tear-out shape is moved along its side.
+% 
+% A simple solution to the problem is rounding. 
+% For example, 
+% a higher order ellipse can be used to obtain a rectangle 
+% with rounded corners and thus more rectangular sections.
+% 
+% If rounding is not desired, the corners can be drawn as
+% intersections of torn-edged half-planes.
+% The border of the intersection shape is obtained
+% as a similar intersection using the half-planes corresponding to
+% the outer edges of the borders.
+% The intersection can be implemented using stencil operations.
 
 %by drawing the outside
 %to the stencil buffer for each side of the shape.