/*========================================================================= Program: Visualization Toolkit Module: vtkCurvatures.h Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen All rights reserved. See Copyright.txt or http://www.kitware.com/Copyright.htm for details. This software is distributed WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the above copyright notice for more information. =========================================================================*/ /** * @class vtkCurvatures * @brief compute curvatures (Gauss and mean) of a Polydata object * * vtkCurvatures takes a polydata input and computes the curvature of the * mesh at each point. Four possible methods of computation are available : * * Gauss Curvature * discrete Gauss curvature (K) computation, * \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$H(vertex v) = \text{average over edges neighbs e of H(e)}\f$, * \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]. * * 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 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. * * @par Thanks: * Philip Batchelor philipp.batchelor@kcl.ac.uk for creating and contributing * the class and Andrew Maclean a.maclean@acfr.usyd.edu.au for cleanups and * fixes. Thanks also to Goodwin Lawlor for contributing patch to calculate * principal curvatures * * * */ #ifndef vtkCurvatures_h #define vtkCurvatures_h #include "vtkFiltersGeneralModule.h" // For export macro #include "vtkPolyDataAlgorithm.h" #define VTK_CURVATURE_GAUSS 0 #define VTK_CURVATURE_MEAN 1 #define VTK_CURVATURE_MAXIMUM 2 #define VTK_CURVATURE_MINIMUM 3 class VTKFILTERSGENERAL_EXPORT vtkCurvatures : public vtkPolyDataAlgorithm { public: vtkTypeMacro(vtkCurvatures,vtkPolyDataAlgorithm); void PrintSelf(ostream& os, vtkIndent indent) override; /** * Construct with curvature type set to Gauss */ static vtkCurvatures *New(); //@{ /** * Set/Get Curvature type * VTK_CURVATURE_GAUSS: Gaussian curvature, stored as * DataArray "Gauss_Curvature" * VTK_CURVATURE_MEAN : Mean curvature, stored as * DataArray "Mean_Curvature" */ vtkSetMacro(CurvatureType,int); vtkGetMacro(CurvatureType,int); void SetCurvatureTypeToGaussian() { this->SetCurvatureType(VTK_CURVATURE_GAUSS); } void SetCurvatureTypeToMean() { this->SetCurvatureType(VTK_CURVATURE_MEAN); } void SetCurvatureTypeToMaximum() { this->SetCurvatureType(VTK_CURVATURE_MAXIMUM); } void SetCurvatureTypeToMinimum() { this->SetCurvatureType(VTK_CURVATURE_MINIMUM); } //@} //@{ /** * Set/Get the flag which inverts the mean curvature calculation for * meshes with inward pointing normals (default false) */ vtkSetMacro(InvertMeanCurvature,vtkTypeBool); vtkGetMacro(InvertMeanCurvature,vtkTypeBool); vtkBooleanMacro(InvertMeanCurvature,vtkTypeBool); //@} protected: vtkCurvatures(); // Usual data generation method int RequestData(vtkInformation *, vtkInformationVector **, vtkInformationVector *) override; /** * discrete Gauss curvature (K) computation, * cf http://www-ipg.umds.ac.uk/p.batchelor/curvatures/curvatures.html */ void GetGaussCurvature(vtkPolyData *output); // discrete Mean curvature (H) computation, // cf http://www-ipg.umds.ac.uk/p.batchelor/curvatures/curvatures.html void GetMeanCurvature(vtkPolyData *output); /** * Maximum principal curvature \f$k_max = H + sqrt(H^2 -K)\f$ */ void GetMaximumCurvature(vtkPolyData *input, vtkPolyData *output); /** * Minimum principal curvature \f$k_min = H - sqrt(H^2 -K)\f$ */ void GetMinimumCurvature(vtkPolyData *input, vtkPolyData *output); // Vars int CurvatureType; vtkTypeBool InvertMeanCurvature; private: vtkCurvatures(const vtkCurvatures&) = delete; void operator=(const vtkCurvatures&) = delete; }; #endif