### 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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