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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/BoundaryCheck.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/Concepts.hpp" 0024 #include "Acts/Utilities/Result.hpp" 0025 #include "Acts/Utilities/detail/RealQuadraticEquation.hpp" 0026 0027 #include <cmath> 0028 #include <cstddef> 0029 #include <memory> 0030 #include <string> 0031 0032 namespace Acts { 0033 0034 /// @class ConeSurface 0035 /// 0036 /// Class for a conical surface in the Tracking geometry. 0037 /// It inherits from Surface. 0038 /// 0039 /// The ConeSurface is special since no corresponding 0040 /// Track parameters exist since they're numerical instable 0041 /// at the tip of the cone. 0042 /// Propagations to a cone surface will be returned in 0043 /// curvilinear coordinates. 0044 0045 class ConeSurface : public RegularSurface { 0046 friend class Surface; 0047 0048 protected: 0049 /// Constructor form HepTransform and an opening angle 0050 /// 0051 /// @param transform is the transform to place to cone in a 3D frame 0052 /// @param alpha is the opening angle of the cone 0053 /// @param symmetric indicates if the cones are built to +/1 z 0054 ConeSurface(const Transform3& transform, double alpha, 0055 bool symmetric = false); 0056 0057 /// Constructor form HepTransform and an opening angle 0058 /// 0059 /// @param transform is the transform that places the cone in the global frame 0060 /// @param alpha is the opening angle of the cone 0061 /// @param zmin is the z range over which the cone spans 0062 /// @param zmax is the z range over which the cone spans 0063 /// @param halfPhi is the opening angle for cone ssectors 0064 ConeSurface(const Transform3& transform, double alpha, double zmin, 0065 double zmax, double halfPhi = M_PI); 0066 0067 /// Constructor from HepTransform and ConeBounds 0068 /// 0069 /// @param transform is the transform that places the cone in the global frame 0070 /// @param cbounds is the boundary class, the bounds must exit 0071 ConeSurface(const Transform3& transform, 0072 std::shared_ptr<const ConeBounds> cbounds); 0073 0074 /// Copy constructor 0075 /// 0076 /// @param other is the source cone surface 0077 ConeSurface(const ConeSurface& other); 0078 0079 /// Copy constructor - with shift 0080 /// 0081 /// @param gctx The current geometry context object, e.g. alignment 0082 /// @param other is the source cone surface 0083 /// @param shift is the additional transform applied after copying 0084 ConeSurface(const GeometryContext& gctx, const ConeSurface& other, 0085 const Transform3& shift); 0086 0087 public: 0088 ~ConeSurface() override = default; 0089 ConeSurface() = delete; 0090 0091 /// Assignment operator 0092 /// 0093 /// @param other is the source surface for the assignment 0094 ConeSurface& operator=(const ConeSurface& other); 0095 0096 /// The binning position method - is overloaded for r-type binning 0097 /// 0098 /// @param gctx The current geometry context object, e.g. alignment 0099 /// @param bValue defines the type of binning applied in the global frame 0100 /// 0101 /// @return The return type is a vector for positioning in the global frame 0102 Vector3 binningPosition(const GeometryContext& gctx, 0103 BinningValue bValue) const final; 0104 0105 /// Return the surface type 0106 SurfaceType type() const override; 0107 0108 /// Return the measurement frame - this is needed for alignment, in particular 0109 /// for StraightLine and Perigee Surface 0110 /// - the default implementation is the RotationMatrix3 of the transform 0111 /// 0112 /// @param gctx The current geometry context object, e.g. alignment 0113 /// @param position is the global position where the measurement frame is 0114 /// constructed 0115 /// @param direction is the momentum direction used for the measurement frame 0116 /// construction 0117 /// @return matrix that indicates the measurement frame 0118 RotationMatrix3 referenceFrame(const GeometryContext& gctx, 0119 const Vector3& position, 0120 const Vector3& direction) const final; 0121 0122 /// Return method for surface normal information 0123 /// 0124 /// @param gctx The current geometry context object, e.g. alignment 0125 /// @param lposition is the local position at normal vector request 0126 /// @return Vector3 normal vector in global frame 0127 Vector3 normal(const GeometryContext& gctx, 0128 const Vector2& lposition) const final; 0129 0130 /// Return method for surface normal information 0131 /// 0132 /// @param gctx The current geometry context object, e.g. alignment 0133 /// @param position is the global position as normal vector base 0134 /// @return Vector3 normal vector in global frame 0135 Vector3 normal(const GeometryContext& gctx, 0136 const Vector3& position) const final; 0137 0138 // Return method for the rotational symmetry axis 0139 /// 0140 /// @param gctx The current geometry context object, e.g. alignment 0141 /// 0142 // @return This returns the local z axis 0143 virtual Vector3 rotSymmetryAxis(const GeometryContext& gctx) const; 0144 0145 /// This method returns the ConeBounds by reference 0146 const ConeBounds& bounds() const final; 0147 0148 /// Local to global transformation 0149 /// 0150 /// @param gctx The current geometry context object, e.g. alignment 0151 /// @param lposition is the local position to be transformed 0152 /// 0153 /// @return The global position by value 0154 Vector3 localToGlobal(const GeometryContext& gctx, 0155 const Vector2& lposition) const final; 0156 0157 // Use overloads from `RegularSurface` 0158 using RegularSurface::globalToLocal; 0159 using RegularSurface::localToGlobal; 0160 using RegularSurface::normal; 0161 0162 /// Global to local transformation 0163 /// 0164 /// @param gctx The current geometry context object, e.g. alignment 0165 /// @param position is the global position to be transformed 0166 /// @param tolerance optional tolerance within which a point is considered 0167 /// valid on surface 0168 /// 0169 /// @return a Result<Vector2> which can be !ok() if the operation fails 0170 Result<Vector2> globalToLocal( 0171 const GeometryContext& gctx, const Vector3& position, 0172 double tolerance = s_onSurfaceTolerance) const final; 0173 0174 /// Straight line intersection schema from position/direction 0175 /// 0176 /// @param gctx The current geometry context object, e.g. alignment 0177 /// @param position The position to start from 0178 /// @param direction The direction at start 0179 /// @param bcheck the Boundary Check 0180 /// @param tolerance the tolerance used for the intersection 0181 /// 0182 /// If possible returns both solutions for the cylinder 0183 /// 0184 /// @return @c SurfaceMultiIntersection object (contains intersection & surface) 0185 SurfaceMultiIntersection intersect( 0186 const GeometryContext& gctx, const Vector3& position, 0187 const Vector3& direction, 0188 const BoundaryCheck& bcheck = BoundaryCheck(false), 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 ACTS_STATIC_CHECK_CONCEPT(RegularSurfaceConcept, ConeSurface); 0286 0287 } // namespace Acts
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