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