Commit 2e3e1758 authored by Guillaume Jacquenot's avatar Guillaume Jacquenot Committed by Guillaume Jacquenot

Update vtkCurvatures.h doc that poorly render with Doxygen

parent 82b68fc0
......@@ -21,31 +21,32 @@
*
* Gauss Curvature
* discrete Gauss curvature (K) computation,
* \f$K(vertex v) = 2*PI-\sum_{facet neighbs f of v} (angle_f at v)\f$
* The contribution of every facet is for the moment weighted by \f$Area(facet)/3\f$
* The units of Gaussian Curvature are \f$[1/m^2]\f$
* \f$K(\text{vertex v}) = 2*\pi - \sum_{\text{facet neighbs f of v}} (\text{angle_f at v})\f$.
* The contribution of every facet is for the moment weighted by \f$Area(facet)/3\f$.
* The units of Gaussian Curvature are \f$[1/m^2]\f$.
*
* Mean Curvature
* \f$H(vertex v) = average over edges neighbs e of H(e)\f$
* \f$H(edge e) = length(e)*dihedral_angle(e)\f$
* \f$H(vertex v) = \text{average over edges neighbs e of H(e)}\f$,
* \f$H(edge e) = length(e) * dihedral\_angle(e)\f$.
*
* NB: dihedral_angle is the ORIENTED angle between -PI and PI,
* this means that the surface is assumed to be orientable
* the computation creates the orientation
* The units of Mean Curvature are [1/m]
* the computation creates the orientation.
* The units of Mean Curvature are [1/m].
*
* Maximum (\f$k_max\f$) and Minimum (\f$k_min\f$) Principal Curvatures
* \f$k_max = H + sqrt(H^2 - K)\f$
* \f$k_min = H - sqrt(H^2 - K)\f$
* Excepting spherical and planar surfaces which have equal principal curvatures,
* the curvature at a point on a surface varies with the direction one "sets off"
* from the point. For all directions, the curvature will pass through two extrema:
* a minimum (\f$k_min\f$) and a maximum (\f$k_max\f$) which occur at mutually orthogonal
* directions to each other.
* Maximum (\f$k_\max\f$) and Minimum (\f$k_\min\f$) Principal Curvatures
* \f$k_\max = H + \sqrt{H^2 - K}\f$,
* \f$k_\min = H - \sqrt{H^2 - K}\f$
* Excepting spherical and planar surfaces which have equal principal
* curvatures, the curvature at a point on a surface varies with the direction
* one "sets off" from the point. For all directions, the curvature will pass
* through two extrema: a minimum (\f$k_\min\f$) and a maximum (\f$k_\max\f$)
* which occur at mutually orthogonal directions to each other.
*
* NB. The sign of the Gauss curvature is a geometric ivariant, it should be +ve
* when the surface looks like a sphere, -ve when it looks like a saddle,
* however, the sign of the Mean curvature is not, it depends on the
* convention for normals - This code assumes that normals point outwards (ie
* NB. The sign of the Gauss curvature is a geometric invariant, it should be
* positive when the surface looks like a sphere, negative when it looks like a
* saddle, however the sign of the Mean curvature is not, it depends on the
* convention for normals. This code assumes that normals point outwards (i.e.
* from the surface of a sphere outwards). If a given mesh produces curvatures
* of opposite senses then the flag InvertMeanCurvature can be set and the
* Curvature reported by the Mean calculation will be inverted.
......
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