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0001 // This file is part of the Acts project. 0002 // 0003 // Copyright (C) 2016-2020 CERN for the benefit of the Acts project 0004 // 0005 // This Source Code Form is subject to the terms of the Mozilla Public 0006 // License, v. 2.0. If a copy of the MPL was not distributed with this 0007 // file, You can obtain one at http://mozilla.org/MPL/2.0/. 0008 0009 #pragma once 0010 0011 #include "Acts/Definitions/Algebra.hpp" 0012 #include "Acts/Definitions/Alignment.hpp" 0013 #include "Acts/Definitions/Tolerance.hpp" 0014 #include "Acts/Definitions/TrackParametrization.hpp" 0015 #include "Acts/Geometry/GeometryContext.hpp" 0016 #include "Acts/Geometry/Polyhedron.hpp" 0017 #include "Acts/Surfaces/BoundaryTolerance.hpp" 0018 #include "Acts/Surfaces/ConeBounds.hpp" 0019 #include "Acts/Surfaces/RegularSurface.hpp" 0020 #include "Acts/Surfaces/Surface.hpp" 0021 #include "Acts/Surfaces/SurfaceConcept.hpp" 0022 #include "Acts/Utilities/BinningType.hpp" 0023 #include "Acts/Utilities/Result.hpp" 0024 #include "Acts/Utilities/detail/RealQuadraticEquation.hpp" 0025 0026 #include <cmath> 0027 #include <cstddef> 0028 #include <memory> 0029 #include <string> 0030 0031 namespace Acts { 0032 0033 /// @class ConeSurface 0034 /// 0035 /// Class for a conical surface in the Tracking geometry. 0036 /// It inherits from Surface. 0037 /// 0038 /// The ConeSurface is special since no corresponding 0039 /// Track parameters exist since they're numerical instable 0040 /// at the tip of the cone. 0041 /// Propagations to a cone surface will be returned in 0042 /// curvilinear coordinates. 0043 0044 class ConeSurface : public RegularSurface { 0045 friend class Surface; 0046 0047 protected: 0048 /// Constructor form HepTransform and an opening angle 0049 /// 0050 /// @param transform is the transform to place to cone in a 3D frame 0051 /// @param alpha is the opening angle of the cone 0052 /// @param symmetric indicates if the cones are built to +/1 z 0053 ConeSurface(const Transform3& transform, double alpha, 0054 bool symmetric = false); 0055 0056 /// Constructor form HepTransform and an opening angle 0057 /// 0058 /// @param transform is the transform that places the cone in the global frame 0059 /// @param alpha is the opening angle of the cone 0060 /// @param zmin is the z range over which the cone spans 0061 /// @param zmax is the z range over which the cone spans 0062 /// @param halfPhi is the opening angle for cone ssectors 0063 ConeSurface(const Transform3& transform, double alpha, double zmin, 0064 double zmax, double halfPhi = M_PI); 0065 0066 /// Constructor from HepTransform and ConeBounds 0067 /// 0068 /// @param transform is the transform that places the cone in the global frame 0069 /// @param cbounds is the boundary class, the bounds must exit 0070 ConeSurface(const Transform3& transform, 0071 std::shared_ptr<const ConeBounds> cbounds); 0072 0073 /// Copy constructor 0074 /// 0075 /// @param other is the source cone surface 0076 ConeSurface(const ConeSurface& other); 0077 0078 /// Copy constructor - with shift 0079 /// 0080 /// @param gctx The current geometry context object, e.g. alignment 0081 /// @param other is the source cone surface 0082 /// @param shift is the additional transform applied after copying 0083 ConeSurface(const GeometryContext& gctx, const ConeSurface& other, 0084 const Transform3& shift); 0085 0086 public: 0087 ~ConeSurface() override = default; 0088 ConeSurface() = delete; 0089 0090 /// Assignment operator 0091 /// 0092 /// @param other is the source surface for the assignment 0093 ConeSurface& operator=(const ConeSurface& other); 0094 0095 /// The binning position method - is overloaded for r-type binning 0096 /// 0097 /// @param gctx The current geometry context object, e.g. alignment 0098 /// @param bValue defines the type of binning applied in the global frame 0099 /// 0100 /// @return The return type is a vector for positioning in the global frame 0101 Vector3 binningPosition(const GeometryContext& gctx, 0102 BinningValue bValue) const final; 0103 0104 /// Return the surface type 0105 SurfaceType type() const override; 0106 0107 /// Return the measurement frame - this is needed for alignment, in particular 0108 /// for StraightLine and Perigee Surface 0109 /// - the default implementation is the RotationMatrix3 of the transform 0110 /// 0111 /// @param gctx The current geometry context object, e.g. alignment 0112 /// @param position is the global position where the measurement frame is 0113 /// constructed 0114 /// @param direction is the momentum direction used for the measurement frame 0115 /// construction 0116 /// @return matrix that indicates the measurement frame 0117 RotationMatrix3 referenceFrame(const GeometryContext& gctx, 0118 const Vector3& position, 0119 const Vector3& direction) const final; 0120 0121 /// Return method for surface normal information 0122 /// 0123 /// @param gctx The current geometry context object, e.g. alignment 0124 /// @param lposition is the local position at normal vector request 0125 /// @return Vector3 normal vector in global frame 0126 Vector3 normal(const GeometryContext& gctx, 0127 const Vector2& lposition) const final; 0128 0129 /// Return method for surface normal information 0130 /// 0131 /// @param gctx The current geometry context object, e.g. alignment 0132 /// @param position is the global position as normal vector base 0133 /// @return Vector3 normal vector in global frame 0134 Vector3 normal(const GeometryContext& gctx, 0135 const Vector3& position) const final; 0136 0137 // Return method for the rotational symmetry axis 0138 /// 0139 /// @param gctx The current geometry context object, e.g. alignment 0140 /// 0141 // @return This returns the local z axis 0142 virtual Vector3 rotSymmetryAxis(const GeometryContext& gctx) const; 0143 0144 /// This method returns the ConeBounds by reference 0145 const ConeBounds& bounds() const final; 0146 0147 /// Local to global transformation 0148 /// 0149 /// @param gctx The current geometry context object, e.g. alignment 0150 /// @param lposition is the local position to be transformed 0151 /// 0152 /// @return The global position by value 0153 Vector3 localToGlobal(const GeometryContext& gctx, 0154 const Vector2& lposition) const final; 0155 0156 // Use overloads from `RegularSurface` 0157 using RegularSurface::globalToLocal; 0158 using RegularSurface::localToGlobal; 0159 using RegularSurface::normal; 0160 0161 /// Global to local transformation 0162 /// 0163 /// @param gctx The current geometry context object, e.g. alignment 0164 /// @param position is the global position to be transformed 0165 /// @param tolerance optional tolerance within which a point is considered 0166 /// valid on surface 0167 /// 0168 /// @return a Result<Vector2> which can be !ok() if the operation fails 0169 Result<Vector2> globalToLocal( 0170 const GeometryContext& gctx, const Vector3& position, 0171 double tolerance = s_onSurfaceTolerance) const final; 0172 0173 /// Straight line intersection schema from position/direction 0174 /// 0175 /// @param gctx The current geometry context object, e.g. alignment 0176 /// @param position The position to start from 0177 /// @param direction The direction at start 0178 /// @param boundaryTolerance the Boundary Check 0179 /// @param tolerance the tolerance used for the intersection 0180 /// 0181 /// If possible returns both solutions for the cylinder 0182 /// 0183 /// @return @c SurfaceMultiIntersection object (contains intersection & surface) 0184 SurfaceMultiIntersection intersect( 0185 const GeometryContext& gctx, const Vector3& position, 0186 const Vector3& direction, 0187 const BoundaryTolerance& boundaryTolerance = 0188 BoundaryTolerance::Infinite(), 0189 double tolerance = s_onSurfaceTolerance) const final; 0190 0191 /// The pathCorrection for derived classes with thickness 0192 /// 0193 /// @param gctx The current geometry context object, e.g. alignment 0194 /// @param position is the global potion at the correction point 0195 /// @param direction is the momentum direction at the correction point 0196 /// @return is the path correction due to incident angle 0197 double pathCorrection(const GeometryContext& gctx, const Vector3& position, 0198 const Vector3& direction) const final; 0199 0200 /// Return a Polyhedron for the surfaces 0201 /// 0202 /// @param gctx The current geometry context object, e.g. alignment 0203 /// @param lseg Number of segments along curved lines, it represents 0204 /// the full 2*M_PI coverange, if lseg is set to 1 only the extrema 0205 /// are given 0206 /// @note that a surface transform can invalidate the extrema 0207 /// in the transformed space 0208 /// 0209 /// @return A list of vertices and a face/facett description of it 0210 Polyhedron polyhedronRepresentation(const GeometryContext& gctx, 0211 std::size_t lseg) const override; 0212 0213 /// Return properly formatted class name for screen output 0214 std::string name() const override; 0215 0216 /// Calculate the derivative of path length at the geometry constraint or 0217 /// point-of-closest-approach w.r.t. alignment parameters of the surface (i.e. 0218 /// local frame origin in global 3D Cartesian coordinates and its rotation 0219 /// represented with extrinsic Euler angles) 0220 /// 0221 /// @param gctx The current geometry context object, e.g. alignment 0222 /// @param position global 3D position 0223 /// @param direction global 3D momentum direction 0224 /// 0225 /// @return Derivative of path length w.r.t. the alignment parameters 0226 AlignmentToPathMatrix alignmentToPathDerivative( 0227 const GeometryContext& gctx, const Vector3& position, 0228 const Vector3& direction) const final; 0229 0230 /// Calculate the derivative of bound track parameters local position w.r.t. 0231 /// position in local 3D Cartesian coordinates 0232 /// 0233 /// @param gctx The current geometry context object, e.g. alignment 0234 /// @param position The position of the parameters in global 0235 /// 0236 /// @return Derivative of bound local position w.r.t. position in local 3D 0237 /// cartesian coordinates 0238 ActsMatrix<2, 3> localCartesianToBoundLocalDerivative( 0239 const GeometryContext& gctx, const Vector3& position) const final; 0240 0241 protected: 0242 std::shared_ptr<const ConeBounds> m_bounds; ///< bounds (shared) 0243 0244 private: 0245 /// Implementation of the intersection solver 0246 /// 0247 /// <b>mathematical motivation:</b> 0248 /// 0249 /// The calculation will be done in the 3-dim frame of the cone, 0250 /// i.e. the symmetry axis of the cone is the z-axis, x- and y-axis are 0251 /// perpendicular 0252 /// to the z-axis. In this frame the cone is centered around the origin. 0253 /// Therefore the two points describing the line have to be first 0254 /// recalculated 0255 /// into the new frame. 0256 /// Suppose, this is done, the points of intersection can be 0257 /// obtained as follows:<br> 0258 /// 0259 /// The cone is described by the implicit equation 0260 /// @f$x^2 + y^2 = z^2 \tan \alpha@f$ 0261 /// where @f$\alpha@f$ is opening half-angle of the cone the and 0262 /// the line by the parameter equation (with @f$t@f$ the 0263 /// parameter and @f$x_1@f$ and @f$x_2@f$ are points on the line) 0264 /// @f$(x,y,z) = \vec x_1 + (\vec x_2 - \vec x_2) t @f$. 0265 /// The intersection is the given to the value of @f$t@f$ where 0266 /// the @f$(x,y,z)@f$ coordinates of the line satisfy the implicit 0267 /// equation of the cone. Inserting the expression for the points 0268 /// on the line into the equation of the cone and rearranging to 0269 /// the form of a gives (letting @f$ \vec x_d = \frac{\vec x_2 - \vec 0270 /// x_1}{|\vec x_2 - \vec x_1|} @f$): 0271 /// @f$t^2 (x_d^2 + y_d^2 - z_d^2 \tan^2 \alpha) + 2 t (x_1 x_d + 0272 /// y_1 y_d - z_1 z_d \tan^2 \alpha) + (x_1^2 + y_1^2 - z_1^2 0273 /// \tan^2 \alpha) = 0 @f$ 0274 /// Solving the above for @f$t@f$ and putting the values into the 0275 /// equation of the line gives the points of intersection. @f$t@f$ 0276 /// is also the length of the path, since we normalized @f$x_d@f$ 0277 /// to be unit length. 0278 /// 0279 /// @return the quadratic equation 0280 detail::RealQuadraticEquation intersectionSolver( 0281 const GeometryContext& gctx, const Vector3& position, 0282 const Vector3& direction) const; 0283 }; 0284 0285 static_assert(RegularSurfaceConcept<ConeSurface>, 0286 "ConeSurface does not fulfill RegularSurfaceConcept"); 0287 0288 } // namespace Acts
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