mirror of https://github.com/CGAL/cgal
Errors in bibliography and incorrect usage of `\f[` command
- The `&` in the bibliography has to be escaped
- the doxygen command `\f[` should not be used to directly change the environment, for this the doxygen command `\f{` exists.
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@ -1355,7 +1355,7 @@ Teillaud"
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@article{cgal:lrt-ccm-22,
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@article{cgal:lrt-ccm-22,
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author = {Jacques-Olivier Lachaud and Pascal Romon and Boris Thibert},
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author = {Jacques-Olivier Lachaud and Pascal Romon and Boris Thibert},
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journal = {Discrete & Computational Geometry},
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journal = {Discrete \& Computational Geometry},
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title = {Corrected Curvature Measures},
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title = {Corrected Curvature Measures},
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volume = {68},
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volume = {68},
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pages = {477-524},
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pages = {477-524},
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@ -142522,7 +142522,7 @@ of geometric optics."
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title = {{Fast and Robust QEF Minimization using Probabilistic Quadrics}},
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title = {{Fast and Robust QEF Minimization using Probabilistic Quadrics}},
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author = {Trettner, Philip and Kobbelt, Leif},
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author = {Trettner, Philip and Kobbelt, Leif},
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year = {2020},
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year = {2020},
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publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
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publisher = {The Eurographics Association and John Wiley \& Sons Ltd.},
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ISSN = {1467-8659},
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ISSN = {1467-8659},
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DOI = {10.1111/cgf.13933}
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DOI = {10.1111/cgf.13933}
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}
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}
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@ -996,15 +996,13 @@ to derive new closed-form equations for the corrected curvature measures. These
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curvature measures are the first step for computing the curvatures. For a triangle \f$ \tau_{ijk} \f$,
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curvature measures are the first step for computing the curvatures. For a triangle \f$ \tau_{ijk} \f$,
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with vertices \a i, \a j, \a k:
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with vertices \a i, \a j, \a k:
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\f[
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\f{align*}{
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\begin{align*}
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\mu^{(0)}(\tau_{ijk}) = &\frac{1}{2} \langle \bar{\mathbf{u}} \mid (\mathbf{x}_j - \mathbf{x}_i) \times (\mathbf{x}_k - \mathbf{x}_i) \rangle, \\
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\mu^{(0)}(\tau_{ijk}) = &\frac{1}{2} \langle \bar{\mathbf{u}} \mid (\mathbf{x}_j - \mathbf{x}_i) \times (\mathbf{x}_k - \mathbf{x}_i) \rangle, \\
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\mu^{(1)}(\tau_{ijk}) = &\frac{1}{2} \langle \bar{\mathbf{u}} \mid (\mathbf{u}_k - \mathbf{u}_j) \times \mathbf{x}_i + (\mathbf{u}_i - \mathbf{u}_k) \times \mathbf{x}_j + (\mathbf{u}_j - \mathbf{u}_i) \times \mathbf{x}_k \rangle, \\
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\mu^{(1)}(\tau_{ijk}) = &\frac{1}{2} \langle \bar{\mathbf{u}} \mid (\mathbf{u}_k - \mathbf{u}_j) \times \mathbf{x}_i + (\mathbf{u}_i - \mathbf{u}_k) \times \mathbf{x}_j + (\mathbf{u}_j - \mathbf{u}_i) \times \mathbf{x}_k \rangle, \\
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\mu^{(2)}(\tau_{ijk}) = &\frac{1}{2} \langle \mathbf{u}_i \mid \mathbf{u}_j \times \mathbf{u}_k \rangle, \\
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\mu^{(2)}(\tau_{ijk}) = &\frac{1}{2} \langle \mathbf{u}_i \mid \mathbf{u}_j \times \mathbf{u}_k \rangle, \\
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\mu^{\mathbf{X},\mathbf{Y}}(\tau_{ijk}) = & \frac{1}{2} \big\langle \bar{\mathbf{u}} \big| \langle \mathbf{Y} | \mathbf{u}_k -\mathbf{u}_i \rangle \mathbf{X} \times (\mathbf{x}_j - \mathbf{x}_i) \big\rangle
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\mu^{\mathbf{X},\mathbf{Y}}(\tau_{ijk}) = & \frac{1}{2} \big\langle \bar{\mathbf{u}} \big| \langle \mathbf{Y} | \mathbf{u}_k -\mathbf{u}_i \rangle \mathbf{X} \times (\mathbf{x}_j - \mathbf{x}_i) \big\rangle
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-\frac{1}{2} \big\langle \bar{\mathbf{u}} \big| \langle \mathbf{Y} | \mathbf{u}_j -\mathbf{u}_i \rangle \mathbf{X} \times (\mathbf{x}_k - \mathbf{x}_i) \big\rangle,
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-\frac{1}{2} \big\langle \bar{\mathbf{u}} \big| \langle \mathbf{Y} | \mathbf{u}_j -\mathbf{u}_i \rangle \mathbf{X} \times (\mathbf{x}_k - \mathbf{x}_i) \big\rangle,
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\end{align*}
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\f}
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\f]
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where \f$ \langle \cdot \mid \cdot \rangle \f$ denotes the usual scalar product,
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where \f$ \langle \cdot \mid \cdot \rangle \f$ denotes the usual scalar product,
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\f$ \bar{\mathbf{u}}=\frac{1}{3}( \mathbf{u}_i + \mathbf{u}_j + \mathbf{u}_k )\f$.
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\f$ \bar{\mathbf{u}}=\frac{1}{3}( \mathbf{u}_i + \mathbf{u}_j + \mathbf{u}_k )\f$.
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