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 // This file is part of the Acts project.
 //
 // Copyright (C) 2020 CERN for the benefit of the Acts project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
 #pragma once
 
 #include "Acts/Definitions/Algebra.hpp"
 #include "Acts/Definitions/Tolerance.hpp"
 
 #include <algorithm>
 #include <cmath>
 #include <utility>
 #include <vector>
 
 /// Helper methods for polyhedron vertices drawing and inside/outside checks.
 namespace Acts::detail::VerticesHelper {
 
 /// A method that inserts the cartesian extrema points and segments
 /// a curved segment into sub segments
 ///
 /// @param phiMin the minimum Phi of the bounds object
 /// @param phiMax the maximum Phi of the bounds object
 /// @param phiRef is a vector of reference phi values to be included as well
 /// @param phiTolerance is the tolerance for reference phi insertion
 /// @return a vector
 std::vector<ActsScalar> phiSegments(ActsScalar phiMin = -M_PI,
                                     ActsScalar phiMax = M_PI,
                                     const std::vector<ActsScalar>& phiRefs = {},
                                     ActsScalar phiTolerance = 1e-6);
 
 /// Helper method to create a regular 2 or 3 D segment
 ///  between two phi values
 ///
 /// @tparam vertex_t Type of vertex to be applied
 /// @tparam transform_t Optional transform
 ///
 /// @param vertices [in,out] The 3D vertices to be filled
 /// @param rxy The radius description if first +/= second: ellipse
 /// @param phi1 The first phi value
 /// @param phi2 The second phi value
 /// @param lseg The number of segments for full 2*PI
 /// @param addon The additional segments to be built
 /// @param offset The out of plane offset position of the bow
 /// @param transform The transform applied (optional)
 template <typename vertex_t, typename transform_t>
 void createSegment(std::vector<vertex_t>& vertices,
                    std::pair<ActsScalar, ActsScalar> rxy, ActsScalar phi1,
                    ActsScalar phi2, unsigned int lseg, int addon = 0,
                    const vertex_t& offset = vertex_t::Zero(),
                    const transform_t& transform = transform_t::Identity()) {
   // Calculate the number of segments - 1 is the minimum
   unsigned int segs =
       static_cast<unsigned int>(std::abs(phi2 - phi1) / (2 * M_PI) * lseg);
   segs = segs > 0 ? segs : 1;
   ActsScalar phistep = (phi2 - phi1) / segs;
   // Create the segments
   for (unsigned int iphi = 0; iphi < segs + addon; ++iphi) {
     ActsScalar phi = phi1 + iphi * phistep;
     vertex_t vertex = vertex_t::Zero();
     vertex(0) = rxy.first * std::cos(phi);
     vertex(1) = rxy.second * std::sin(phi);
 
     vertex = vertex + offset;
     vertices.push_back(transform * vertex);
   }
 }
 
 /// Construct vertices on an ellipse-like bound object.
 ///
 /// @param innerRx The radius of the inner ellipse (in x), 0 if sector
 /// @param innerRy The radius of the inner ellipse (in y), 0 if sector
 /// @param outerRx The radius of the outer ellipse (in x)
 /// @param outerRy The radius of the outer ellipse (in y)
 /// @param avgPhi The phi direction of the center if sector
 /// @param halfPhi The half phi sector if sector
 /// @param lseg The number of segments for for a full 2*pi segment
 /// @return a vector of 2d-vectors
 std::vector<Vector2> ellipsoidVertices(ActsScalar innerRx, ActsScalar innerRy,
                                        ActsScalar outerRx, ActsScalar outerRy,
                                        ActsScalar avgPhi = 0.,
                                        ActsScalar halfPhi = M_PI,
                                        unsigned int lseg = 1);
 
 /// Construct vertices on an disc/wheel-like bound object.
 ///
 /// @param innerR The radius of the inner circle (sector)
 /// @param outerR The radius of the outer circle (sector)
 /// @param avgPhi The phi direction of the center if sector
 /// @param halfPhi The half phi sector if sector
 /// @param lseg The number of segments for for a full 2*pi segment
 /// @return a vector of 2d-vectors
 std::vector<Vector2> circularVertices(ActsScalar innerR, ActsScalar outerR,
                                       ActsScalar avgPhi = 0.,
                                       ActsScalar halfPhi = M_PI,
                                       unsigned int lseg = 1);
 /// Check if the point is inside the polygon w/o any tolerances.
 ///
 /// @tparam vertex_container_t is an iterable container
 ///
 /// @param point is the Vector2Type to check
 /// @param vertices Forward iterable container of convex polygon vertices.
 ///                 Calling `std::begin`/ `std::end` on the container must
 ///                 return an iterator where `*it` must be convertible to
 ///                 an `Vector2Type`.
 /// @return bool for inside/outside
 template <typename vertex_t, typename vertex_container_t>
 bool isInsidePolygon(const vertex_t& point,
                      const vertex_container_t& vertices) {
   // when we move along the edges of a convex polygon, a point on the inside of
   // the polygon will always appear on the same side of each edge.
   // a point on the outside will switch sides at least once.
 
   // returns which side of the connecting line between `ll0` and `ll1` the point
   // `p` is on. computes the sign of the z-component of the cross-product
   // between the line normal vector and the vector from `ll0` to `p`.
   auto lineSide = [&](auto&& ll0, auto&& ll1) {
     auto normal = ll1 - ll0;
     auto delta = point - ll0;
     return std::signbit((normal[0] * delta[1]) - (normal[1] * delta[0]));
   };
 
   auto iv = std::begin(vertices);
   auto l0 = *iv;
   auto l1 = *(++iv);
   // use vertex0 to vertex1 to define reference sign and compare w/ all edges
   auto reference = lineSide(l0, l1);
   for (++iv; iv != std::end(vertices); ++iv) {
     l0 = l1;
     l1 = *iv;
     if (lineSide(l0, l1) != reference) {
       return false;
     }
   }
   // manual check for last edge from last vertex back to the first vertex
   if (lineSide(l1, *std::begin(vertices)) != reference) {
     return false;
   }
   // point was always on the same side. point must be inside.
   return true;
 }
 
 /// Check if the point is inside the rectangle.
 ///
 /// @tparam vertex_t is vector with [0],[1] access
 ///
 /// @param point is the Vector2Type to check
 /// @param vertices Forward iterable container of convex polygon vertices.
 ///                 Calling `std::begin`/ `std::end` on the container must
 ///                 return an iterator where `*it` must be convertible to
 ///                 an `Vector2Type`.
 /// @return bool for inside/outside
 template <typename vertex_t>
 bool isInsideRectangle(const vertex_t& point, const vertex_t& lowerLeft,
                        const vertex_t& upperRight) {
   return (lowerLeft[0] <= point[0]) && (point[0] < upperRight[0]) &&
          (lowerLeft[1] <= point[1]) && (point[1] < upperRight[1]);
 }
 
 /// This method checks if a cloud of points are on 2D hyper-plane in 3D space.
 ///
 /// @param vertices The list of vertices to test
 /// @param tolerance The allowed out of plane tolerance
 /// @return boolean to indicate if all points are inside/outside
 bool onHyperPlane(const std::vector<Vector3>& vertices,
                   ActsScalar tolerance = s_onSurfaceTolerance);
 
 }  // namespace Acts::detail::VerticesHelper

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