From 9266bde5fb1dd18a36d54eea427a2e8d84839b18 Mon Sep 17 00:00:00 2001 From: Andreas Fabri Date: Thu, 5 Jul 2007 13:30:04 +0000 Subject: [PATCH] Fixed typos --- Ridges_3/doc_tex/Ridges_3/Ridges_3_user.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/Ridges_3/doc_tex/Ridges_3/Ridges_3_user.tex b/Ridges_3/doc_tex/Ridges_3/Ridges_3_user.tex index 489a50f3575..f63cca8a4bd 100644 --- a/Ridges_3/doc_tex/Ridges_3/Ridges_3_user.tex +++ b/Ridges_3/doc_tex/Ridges_3/Ridges_3_user.tex @@ -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