From 4f25ac64bb9c1285dd2c3ea2c8d1aa80fabca668 Mon Sep 17 00:00:00 2001 From: Timo Heister Date: Fri, 16 Sep 2016 17:30:44 -0400 Subject: [PATCH] fix doxygen formula typesetting --- include/deal.II/grid/manifold_lib.h | 15 +++++++-------- 1 file changed, 7 insertions(+), 8 deletions(-) diff --git a/include/deal.II/grid/manifold_lib.h b/include/deal.II/grid/manifold_lib.h index f9583582bd..eb25ca1040 100644 --- a/include/deal.II/grid/manifold_lib.h +++ b/include/deal.II/grid/manifold_lib.h @@ -135,27 +135,26 @@ private: * While PolarManifold reflects the usual notion of polar coordinates, * it may not be suitable for domains that contain either the north or * south poles. Consider for instance the pair of points - * \f$x_1=(1,\pi/3,0)\f$ and \f$x_2=(1,\pi/3,\pi)\f$ in polar + * $x_1=(1,\pi/3,0)$ and $x_2=(1,\pi/3,\pi)$ in polar * coordinates (lying on the surface of a sphere with radius one, on * a parallel at at height $\pi/3$). In this case connecting the points * with a straight line in polar coordinates would take the long road * around the globe, without passing through the north pole. * * These two points would be connented (using a PolarManifold) by the curve - * \$[ - * \begin{align} + * @f{align*}{ * s: [0,1] & \rightarrow & \mathbb S^3 \\ * t & \mapsto & (1,\pi/3,0) + (0,0,t\pi) - * \$] + * @f} * This curve is not a geodesic on the sphere, and it is not how we * would connect those two points. A better curve, would be the one * passing through the North pole: - * \[ + * @f[ * s(t) = x_1 \cos(\alpha(t)) + \kappa \times x_1 \sin(\alpha(t)) + * \kappa ( \kappa \cdot x_1) (1-\cos(\alpha(t))). - * \] - * where $\kappa = \frac{x_1 \times \x_2}{\Vert x_1 \times \x_2 \Vert}$ - * and $\alpha(t) = t * \arccos(x_1 * x_2) $ for $t\in[0,1]$. + * @f] + * where $\kappa = \frac{x_1 \times x_2}{\Vert x_1 \times x_2 \Vert}$ + * and $\alpha(t) = t \cdot \arccos(x_1 \cdot x_2)$ for $t\in[0,1]$. * Indeed, this is a geodesic, and it is the natural choice when * connecting points on the surface of the sphere. In the examples above, * the PolarManifold class implements the first way of connecting two -- 2.39.5