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Remove usage of boldsymbol in formulas (#7455)
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Only on a few places the `\boldsymbol` is used in formulas, this has
been removed to make it consistent with other packages.
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sloriot authored May 25, 2023
2 parents 898e452 + 13ea7e9 commit 54b1fb6
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Expand Up @@ -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

<center>
\f$\Delta \boldsymbol{b} = \boldsymbol{0}\f$
\f$\Delta b = 0\f$
</center>

subject to suitable Dirichlet boundary conditions. Harmonic coordinates are the only coordinates
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Expand Up @@ -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

<center>\f$U(\boldsymbol{x}) = (1 - \lambda) D(\boldsymbol{x}) + \lambda V(\boldsymbol{x})\f$,</center>
<center>\f$U(x) = (1 - \lambda) D(x) + \lambda V(x)\f$,</center>

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
Expand All @@ -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
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