// // ******************************************************************** // * License and Disclaimer * // * * // * The Geant4 software is copyright of the Copyright Holders of * // * the Geant4 Collaboration. It is provided under the terms and * // * conditions of the Geant4 Software License, included in the file * // * LICENSE and available at http://cern.ch/geant4/license . These * // * include a list of copyright holders. * // * * // * Neither the authors of this software system, nor their employing * // * institutes,nor the agencies providing financial support for this * // * work make any representation or warranty, express or implied, * // * regarding this software system or assume any liability for its * // * use. Please see the license in the file LICENSE and URL above * // * for the full disclaimer and the limitation of liability. * // * * // * This code implementation is the result of the scientific and * // * technical work of the GEANT4 collaboration. * // * By using, copying, modifying or distributing the software (or * // * any work based on the software) you agree to acknowledge its * // * use in resulting scientific publications, and indicate your * // * acceptance of all terms of the Geant4 Software license. * // ******************************************************************** // // G4GeomTools // // Class description: // // A collection of utilities which can be helpful for a wide range // of geometry-related tasks // Author: Evgueni Tcherniaev (CERN), 10.10.2016 // -------------------------------------------------------------------- #ifndef G4GEOMTOOLS_HH #define G4GEOMTOOLS_HH #include #include "G4TwoVector.hh" #include "G4ThreeVector.hh" using G4TwoVectorList = std::vector; using G4ThreeVectorList = std::vector; /** * @brief G4GeomTools is a collecting utilities which can be helpful * for a wide range of geometry-related tasks. */ class G4GeomTools { public: // ================================================================== // 2D Utilities // ------------------------------------------------------------------ /** * Functions to calculate the area of 2D triangle, returned value is * positive if the vertices of the triangle are given in anticlockwise * order, otherwise it is negative. */ static G4double TriangleArea(G4double Ax, G4double Ay, G4double Bx, G4double By, G4double Cx, G4double Cy); static G4double TriangleArea(const G4TwoVector& A, const G4TwoVector& B, const G4TwoVector& C); /** * Calculates the area of a 2D quadrilateral, returned value is positive if * the vertices of the quadrilateral are given in anticlockwise order, * otherwise it is negative. */ static G4double QuadArea(const G4TwoVector& A, const G4TwoVector& B, const G4TwoVector& C, const G4TwoVector& D); /** * Calculates the area of a 2D polygon, returned value is positive if * the vertices of the polygon are defined in anticlockwise order, * otherwise it is negative. */ static G4double PolygonArea(const G4TwoVectorList& polygon); /** * Decides if a point (Px,Py) is inside the triangle (Ax,Ay)(Bx,By)(Cx,Cy). */ static G4bool PointInTriangle(G4double Px, G4double Py, G4double Ax, G4double Ay, G4double Bx, G4double By, G4double Cx, G4double Cy); /** * Decides if a point P is inside the triangle ABC. */ static G4bool PointInTriangle(const G4TwoVector& P, const G4TwoVector& A, const G4TwoVector& B, const G4TwoVector& C); /** * Decides if a point P is inside the 'Polygon'. */ static G4bool PointInPolygon(const G4TwoVector& P, const G4TwoVectorList& Polygon); /** * Decides if a 2D 'polygon' is convex, i.e. if all internal angles are * less than pi. */ static G4bool IsConvex(const G4TwoVectorList& polygon); /** * Simple implementation of "ear clipping" algorithm for triangulation * of a simple contour/polygon, it places results in a std::vector as * triplets of vertices. If triangulation is successful the function * returns true, otherwise false. */ static G4bool TriangulatePolygon(const G4TwoVectorList& polygon, std::vector& result); /** * Same using the function above and returning as 'result' a list * of triangles. */ static G4bool TriangulatePolygon(const G4TwoVectorList& polygon, G4TwoVectorList& result); /** * Removes collinear and coincident points from a 2D 'polygon'. * Indices of removed points are available in 'iout'. * Allows to specify a 'tolerance'. */ static void RemoveRedundantVertices(G4TwoVectorList& polygon, std::vector& iout, G4double tolerance = 0.0); /** * Calculates the bounding rectangle of a disk sector. It returns false * if the input parameters do not meet the following criteria: * rmin >= 0 * rmax > rmin + kCarTolerance * delPhi > 0 + kCarTolerance. */ static G4bool DiskExtent(G4double rmin, G4double rmax, G4double startPhi, G4double delPhi, G4TwoVector& pmin, G4TwoVector& pmax); /** * Calculates the bounding rectangle of a disk sector. * Faster version without check of parameters. */ static void DiskExtent(G4double rmin, G4double rmax, G4double sinPhiStart, G4double cosPhiStart, G4double sinPhiEnd, G4double cosPhiEnd, G4TwoVector& pmin, G4TwoVector& pmax); /** * Computes the circumference (perimeter) of an ellipse. */ static G4double EllipsePerimeter(G4double a, G4double b); /** * Computes the lateral surface area of an elliptic cone. */ static G4double EllipticConeLateralArea(G4double a, G4double b, G4double h); // ================================================================== // 3D Utilities // ------------------------------------------------------------------ /** * Finds the normal to the plane of a 3D triangle ABC; * the length of the normal is equal to the area of the triangle. */ static G4ThreeVector TriangleAreaNormal(const G4ThreeVector& A, const G4ThreeVector& B, const G4ThreeVector& C); /** * Finds the normal to the plane of a 3D quadrilateral ABCD; * the length of the normal is equal to the area of the quadrilateral. */ static G4ThreeVector QuadAreaNormal(const G4ThreeVector& A, const G4ThreeVector& B, const G4ThreeVector& C, const G4ThreeVector& D); /** * Finds the normal to the plane of a 3D polygon; the length of the * normal is equal to the area of the polygon. */ static G4ThreeVector PolygonAreaNormal(const G4ThreeVectorList& polygon); /** * Calculates the distance between a point 'P' and line segment AB in 3D. */ static G4double DistancePointSegment(const G4ThreeVector& P, const G4ThreeVector& A, const G4ThreeVector& B); /** * Finds a point on a 3D line segment AB closest to point 'P'. */ static G4ThreeVector ClosestPointOnSegment(const G4ThreeVector& P, const G4ThreeVector& A, const G4ThreeVector& B); /** * Finds a point on a 3D triangle ABC closest to point 'P'. */ static G4ThreeVector ClosestPointOnTriangle(const G4ThreeVector& P, const G4ThreeVector& A, const G4ThreeVector& B, const G4ThreeVector& C); /** * Calculates the bounding box of a spherical sector, * @returns false if input parameters do not meet the following criteria: * rmin >= 0 * rmax > rmin + kCarTolerance * startTheta >= 0 && <= pi; * delTheta > 0 + kCarTolerance * delPhi > 0 + kCarTolerance. */ static G4bool SphereExtent(G4double rmin, G4double rmax, G4double startTheta, G4double delTheta, G4double startPhi, G4double delPhi, G4ThreeVector& pmin, G4ThreeVector& pmax); /** * Calculates the hyperbolic surface stereo. Stereo is a half angle at the * intersection point of the two lines in the tangent plane cross-section. */ static G4double HypeStereo(G4double r0, // radius at z = 0 G4double r, // radius at z = h G4double h); /** * Finds the XY-coordinates of the corners of a generic trap that bounds * specified twisted tube. * @param[in] twistAng The twist angle. * @param[in] endInnerRad The inner radius at z = halfZ. * @param[in] endOuterRad The outer radius at z = halfZ. * @param[in] dPhi Delta phi. * @param[in] vertices The corners of the generic trap. */ static void TwistedTubeBoundingTrap(G4double twistAng, G4double endInnerRad, G4double endOuterRad, G4double dPhi, G4TwoVectorList& vertices); /** * Calculate surface area of the hyperboloid between 'zmin' and 'zmax'. * @param[in] dphi Delta phi. * @param[in] r0 The radius at z = 0. * @param[in] tanstereo The tangent of the stereo angle. * @param[in] zmin Minimum Z. * @param[in] zmax Maximum Z. */ static G4double HyperboloidSurfaceArea(G4double dphi, G4double r0, G4double tanstereo, G4double zmin, G4double zmax); private: /** * Helper function for use by TriangulatePolygon(). */ static G4bool CheckSnip(const G4TwoVectorList& contour, G4int a, G4int b, G4int c, G4int n, const G4int* V); /** * Complete Elliptic Integral of the Second Kind. */ static G4double comp_ellint_2(G4double e); }; #endif