diff --git a/Documentation/doc/biblio/cgal_manual.bib b/Documentation/doc/biblio/cgal_manual.bib index 3f0f258a870..d1600747b48 100644 --- a/Documentation/doc/biblio/cgal_manual.bib +++ b/Documentation/doc/biblio/cgal_manual.bib @@ -1355,7 +1355,7 @@ Teillaud" @article{cgal:lrt-ccm-22, author = {Jacques-Olivier Lachaud and Pascal Romon and Boris Thibert}, - journal = {Discrete & Computational Geometry}, + journal = {Discrete \& Computational Geometry}, title = {Corrected Curvature Measures}, volume = {68}, pages = {477-524}, diff --git a/Documentation/doc/biblio/geom.bib b/Documentation/doc/biblio/geom.bib index f92a1b5cbd5..88f05c78f7f 100644 --- a/Documentation/doc/biblio/geom.bib +++ b/Documentation/doc/biblio/geom.bib @@ -142522,7 +142522,7 @@ of geometric optics." title = {{Fast and Robust QEF Minimization using Probabilistic Quadrics}}, author = {Trettner, Philip and Kobbelt, Leif}, year = {2020}, - publisher = {The Eurographics Association and John Wiley & Sons Ltd.}, + publisher = {The Eurographics Association and John Wiley \& Sons Ltd.}, ISSN = {1467-8659}, DOI = {10.1111/cgf.13933} } diff --git a/Polygon_mesh_processing/doc/Polygon_mesh_processing/Polygon_mesh_processing.txt b/Polygon_mesh_processing/doc/Polygon_mesh_processing/Polygon_mesh_processing.txt index e532de3e728..08d8d798f41 100644 --- a/Polygon_mesh_processing/doc/Polygon_mesh_processing/Polygon_mesh_processing.txt +++ b/Polygon_mesh_processing/doc/Polygon_mesh_processing/Polygon_mesh_processing.txt @@ -996,15 +996,13 @@ to derive new closed-form equations for the corrected curvature measures. These curvature measures are the first step for computing the curvatures. For a triangle \f$ \tau_{ijk} \f$, with vertices \a i, \a j, \a k: -\f[ - \begin{align*} +\f{align*}{ \mu^{(0)}(\tau_{ijk}) = &\frac{1}{2} \langle \bar{\mathbf{u}} \mid (\mathbf{x}_j - \mathbf{x}_i) \times (\mathbf{x}_k - \mathbf{x}_i) \rangle, \\ \mu^{(1)}(\tau_{ijk}) = &\frac{1}{2} \langle \bar{\mathbf{u}} \mid (\mathbf{u}_k - \mathbf{u}_j) \times \mathbf{x}_i + (\mathbf{u}_i - \mathbf{u}_k) \times \mathbf{x}_j + (\mathbf{u}_j - \mathbf{u}_i) \times \mathbf{x}_k \rangle, \\ \mu^{(2)}(\tau_{ijk}) = &\frac{1}{2} \langle \mathbf{u}_i \mid \mathbf{u}_j \times \mathbf{u}_k \rangle, \\ \mu^{\mathbf{X},\mathbf{Y}}(\tau_{ijk}) = & \frac{1}{2} \big\langle \bar{\mathbf{u}} \big| \langle \mathbf{Y} | \mathbf{u}_k -\mathbf{u}_i \rangle \mathbf{X} \times (\mathbf{x}_j - \mathbf{x}_i) \big\rangle -\frac{1}{2} \big\langle \bar{\mathbf{u}} \big| \langle \mathbf{Y} | \mathbf{u}_j -\mathbf{u}_i \rangle \mathbf{X} \times (\mathbf{x}_k - \mathbf{x}_i) \big\rangle, - \end{align*} -\f] +\f} where \f$ \langle \cdot \mid \cdot \rangle \f$ denotes the usual scalar product, \f$ \bar{\mathbf{u}}=\frac{1}{3}( \mathbf{u}_i + \mathbf{u}_j + \mathbf{u}_k )\f$.