From 13ea7e90eeefbce6e95ea7bcd7f9713f13dca15b Mon Sep 17 00:00:00 2001 From: albert-github Date: Thu, 18 May 2023 12:46:58 +0200 Subject: [PATCH] Remove usage of boldsymbol in formulas Only on a few places the `\boldsymbol` is used in formulas, this has been removed to make it consistent with other packages. --- .../Barycentric_coordinates_2.txt | 2 +- .../doc/Shape_regularization/Shape_regularization.txt | 10 +++++----- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/Barycentric_coordinates_2/doc/Barycentric_coordinates_2/Barycentric_coordinates_2.txt b/Barycentric_coordinates_2/doc/Barycentric_coordinates_2/Barycentric_coordinates_2.txt index 7b937fec3bd..53a7a11bcda 100644 --- a/Barycentric_coordinates_2/doc/Barycentric_coordinates_2/Barycentric_coordinates_2.txt +++ b/Barycentric_coordinates_2/doc/Barycentric_coordinates_2/Barycentric_coordinates_2.txt @@ -584,7 +584,7 @@ one should be cautious when using the unnormalized mean value weights. In that c The harmonic coordinates are computed by solving the Laplace equation
-\f$\Delta \boldsymbol{b} = \boldsymbol{0}\f$ +\f$\Delta b = 0\f$
subject to suitable Dirichlet boundary conditions. Harmonic coordinates are the only coordinates diff --git a/Shape_regularization/doc/Shape_regularization/Shape_regularization.txt b/Shape_regularization/doc/Shape_regularization/Shape_regularization.txt index 684d7eded87..88620e3fef6 100644 --- a/Shape_regularization/doc/Shape_regularization/Shape_regularization.txt +++ b/Shape_regularization/doc/Shape_regularization/Shape_regularization.txt @@ -456,12 +456,12 @@ This framework follows Section 3 from \cgalCite{cgal:bl-kippi-18}, however the a from that paper was extended and generalized. The idea behind the main algorithm is to minimize the energy -
\f$U(\boldsymbol{x}) = (1 - \lambda) D(\boldsymbol{x}) + \lambda V(\boldsymbol{x})\f$,
+
\f$U(x) = (1 - \lambda) D(x) + \lambda V(x)\f$,
-where \f$\boldsymbol{x} = (x_1, \dots, x_n)\f$ is a configuration of perturbations operated -on \f$n\f$ input items, \f$D(\boldsymbol{x})\f$ and \f$V(\boldsymbol{x})\f$ represent a data +where \f$x = (x_1, \dots, x_n)\f$ is a configuration of perturbations operated +on \f$n\f$ input items, \f$D(x)\f$ and \f$V(x)\f$ represent a data term and pairwise potential respectively, and \f$\lambda \in [0, 1]\f$ is a parameter weighting -these two terms. By setting up the correct types of \f$D(\boldsymbol{x})\f$ and \f$V(\boldsymbol{x})\f$, +these two terms. By setting up the correct types of \f$D(x)\f$ and \f$V(x)\f$, the problem can be reformulated into a quadratic optimization problem with \f$(n + m)\f$ variables and \f$2(n + m)\f$ linear constraints, where \f$m\f$ is the number of unique pairs formed by connecting an item to one of its closest neighbors. Let us explain how it all works when the input items @@ -475,7 +475,7 @@ segment and \f$j\f$ is the index of the jth segment is inserted in the graph whe This way each pair is inserted only once. The neighbors are found via the \ref QP_Regularization_Segments_Delaunay "Delaunay Neighbor Query". -When we have the graph, we fill in the terms \f$D(\boldsymbol{x})\f$ and \f$V(\boldsymbol{x})\f$ +When we have the graph, we fill in the terms \f$D(x)\f$ and \f$V(x)\f$ via the concept `RegularizationType`. First, we obtain a maximum perturbation bound for each segment via the method `RegularizationType::bound()`. Since we want to rotate segments, we return here the maximum allowed angle deviation for each segment with respect to its original orientation, lets