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Fixed typos

This commit is contained in:
Andreas Fabri 2007-07-05 13:30:04 +00:00
parent 35dbad809c
commit 9266bde5fb
1 changed files with 3 additions and 3 deletions
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6
Ridges_3/doc_tex/Ridges_3/Ridges_3_user.tex
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@ -255,7 +255,7 @@ See \cite{cgal:cp-tdare-05} for a detailed discussion of {\em
compliant} meshes. \medskip
As 0-level set of the extremality coefficients $b_0$ and $b_3$, ridges
are extracted by a marching triangles algorithm \footnote{A marching
are extracted by a marching triangles algorithm.\footnote{A marching
triangles algorithm is similar to a 2d marching cubes algorithm (or
marching rectangles algorithm), excepted that a one-manifold is
reported on a two-manifold tessellated by triangles.}
@ -308,7 +308,7 @@ triangle are less likely to be regular and the detection of ridges
cannot be relevant by this method. This is why we propose another
method to detect umbilics independently.
\paragraph{Non compliant meshes : filtering ridges on {\em
\paragraph{Non compliant meshes: filtering ridges on {\em
strength} and {\em sharpness}.}
%%
For real world applications dealing with coarse meshes, or meshes
@ -325,7 +325,7 @@ zero crossings of $b_0$ and $b_3$, one can expect erroneous detections
as long as these coefficients remain small. In order to select the
most prominent ridge points, we focus on points where the variation of
the curvature is fast along the curvature line. One can observe that,
at a ridge point, according to equation
at a ridge point, according to Equation
\ref{eq:taylor_along_line}, the second derivative of $k_1$ along its
curvature line satisfies $k_1^{''}(0) = P_1/(k_1-k_2)$. Using this
observation, one can define the {\em sharpness of a ridge} as the