Fixup dox: Clarify upper/lower indices and add \param.

src/ApparentHorizons/StrahlkorperFunctions.hpp

@@ -29,6 +29,10 @@ namespace StrahlkorperFunctions {
 /*!
  * \f$(\theta,\phi)\f$ on the Strahlkorper surface.
  * Doesn't depend on the shape of the surface.
+ *
+ * We need to choose upper vs lower indices for theta_phi; it doesn't
+ * matter because these are coordinates and not geometric objects, so
+ * we choose lower indices arbitrarily.
  */
 template <typename Fr>
 tnsr::i<DataVector, 2, ::Frame::Spherical<Fr>> theta_phi(
@@ -43,8 +47,12 @@ void theta_phi(
 
 /// @{
 /*!
- * `r_hat(i)` is \f$\hat{r}^i = x_i/\sqrt{x^2+y^2+z^2}\f$ on the
+ * `r_hat(i)` is \f$\hat{r}_i = x_i/\sqrt{x^2+y^2+z^2}\f$ on the
  * Strahlkorper surface.  Doesn't depend on the shape of the surface.
+ *
+ * We need to choose upper vs lower indices for rhat; it doesn't
+ * matter because rhat is a quantity defined with a Euclidean metric,
+ * so we choose the lower index arbitrarily.
  */
 template <typename Fr>
 tnsr::i<DataVector, 3, Fr> rhat(
@@ -125,9 +133,10 @@ void radius(const gsl::not_null<Scalar<DataVector>*> result,
  * `cartesian_coords(i)` is \f$x_{\rm surf}^i\f$, the vector of \f$(x,y,z)\f$
  * coordinates of each point on the Strahlkorper surface.
  *
- * `radius` is the radius as a function of angle, as returned by
- * `StrahlkorperFunctions::radius`, and `r_hat` is the Euclidean
- * radial unit vector as returned by `StrahlkorperFunctions::rhat`.
+ * \param radius The radius as a function of angle, as returned by
+ * `StrahlkorperFunctions::radius`.
+ * \param r_hat The Euclidean radial unit vector as returned by
+ * `StrahlkorperFunctions::rhat`.
  */
 template <typename Fr>
 tnsr::I<DataVector, 3, Fr> cartesian_coords(
@@ -150,8 +159,10 @@ void cartesian_coords(const gsl::not_null<tnsr::I<DataVector, 3, Fr>*> coords,
  * considered a function of Cartesian coordinates
  * \f$f=f(\theta(x,y,z),\phi(x,y,z))\f$ for this operation.
  *
- * `radius_of_strahlkorper` is the radius of the Strahlkorper at each
+ * \param radius_of_strahlkorper The radius of the Strahlkorper at each
  * point, as returned by `StrahlkorperFunctions::radius`.
+ * \param inv_jac The inverse Jacobian as returned by
+ * `StrahlkorperFunctions::inv_jacobian`
  */
 template <typename Fr>
 tnsr::i<DataVector, 3, Fr> cartesian_derivs_of_scalar(
@@ -176,7 +187,7 @@ void cartesian_derivs_of_scalar(
  * function of Cartesian coordinates
  * \f$f=f(\theta(x,y,z),\phi(x,y,z))\f$ for this operation.
  *
- * `radius_of_strahlkorper` is the radius of the Strahlkorper at each
+ * \param radius_of_strahlkorper The radius of the Strahlkorper at each
  * point, as returned by `StrahlkorperFunctions::radius`.
  */
 template <typename Fr>
@@ -203,6 +214,9 @@ void cartesian_second_derivs_of_scalar(
  * independent of the radial coordinate. \f$f\f$ is considered a
  * function of Cartesian coordinates
  * \f$f=f(\theta(x,y,z),\phi(x,y,z))\f$ for this operation.
+ *
+ * \param radius_of_strahlkorper The radius of the Strahlkorper at each
+ * point, as returned by `StrahlkorperFunctions::radius`.
  */
 template <typename Fr>
 Scalar<DataVector> laplacian_of_scalar(
@@ -233,6 +247,12 @@ void laplacian_of_scalar(
  * `tangents(i,1)` are not necessarily orthogonal to each other,
  * since orthogonality between 2 vectors (as opposed to a vector and
  * a one-form) is metric-dependent.
+ *
+ * \param radius The radius of the Strahlkorper at each
+ * point, as returned by `StrahlkorperFunctions::radius`.
+ * \param r_hat The radial unit vector as returned by
+ * `StrahlkorperFunctions::rhat`.
+ * \param jac The jacobian as returned by `StrahlkorperFunctions::jacobian`.
  */
 template <typename Fr>
 StrahlkorperTags::aliases::Jacobian<Fr> tangents(
@@ -259,6 +279,12 @@ void tangents(
  * Note on the word "normal": \f$s_i\f$ points in the correct direction
  * (it is "normal" to the surface), but it does not have unit length
  * (it is not "normalized"; normalization requires a metric).
+ *
+ * \param dx_radius The Cartesian derivatives of the radius, as
+ * returned by StrahlkorperFunctions::cartesian_derivs_of_scalar with
+ * `StrahlkorperFunctions::radius` passed in as the scalar.
+ * \param r_hat The radial unit vector as returned by
+ * `StrahlkorperFunctions::rhat`.
  */
 template <typename Fr>
 tnsr::i<DataVector, 3, Fr> normal_one_form(