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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 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 https://mozilla.org/MPL/2.0/.
 
 #pragma once
 
 #include "Acts/Definitions/Algebra.hpp"
 #include "Acts/Definitions/Tolerance.hpp"
 
 #include <algorithm>
 #include <cmath>
 #include <numbers>
 #include <span>
 #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 value
 /// @param phiMax The second phi value
 /// @param phiRef is a vector of reference phi values to be included as well
 /// @param quarterSegments number of segments used to approximate a segment quarter
 ///
 /// @return a vector of generated phi values
 std::vector<double> phiSegments(double phiMin = -std::numbers::pi,
                                 double phiMax = std::numbers::pi,
                                 const std::vector<double>& phiRefs = {},
                                 unsigned int quarterSegments = 2u);
 
 /// Helper method to create a regular 2 or 3 D segment
 /// between two phi values with a given number of segments
 ///
 /// It will insert the phi at extrema points and reference points, it uses
 /// a minimum approximation of a circle with 8 segments
 ///
 /// @tparam vertex_t Type of vertex to be applied
 /// @tparam transform_t Optional transform
 ///
 /// @param rXY The radius description if first +/= second: ellipse
 /// @param phiMin the minimum phi value
 /// @param phiMax the second phi value
 /// @param phiRef is a vector of reference phi values to be included as well
 /// @param quarterSegments number of segments used to approximate a segment quarter
 /// @param offset The out of plane offset position of the bow
 /// @param transform The transform applied (optional)
 ///
 /// @return a vector of vertices
 template <typename vertex_t, typename transform_t>
 std::vector<vertex_t> segmentVertices(
     std::pair<double, double> rXY, double phiMin, double phiMax,
     const std::vector<double>& phiRefs = {}, unsigned int quarterSegments = 2u,
     const vertex_t& offset = vertex_t::Zero(),
     const transform_t& transform = transform_t::Identity()) {
   std::vector<vertex_t> vertices;
   std::vector<double> phis =
       phiSegments(phiMin, phiMax, phiRefs, quarterSegments);
   for (double phi : phis) {
     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);
   }
   return vertices;
 }
 
 /// 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 of the ellipse
 /// @param quarterSegments number of segments used to approximate a segment quarter
 ///
 /// @return a vector of 2d-vectors
 std::vector<Vector2> ellipsoidVertices(double innerRx, double innerRy,
                                        double outerRx, double outerRy,
                                        double avgPhi = 0.,
                                        double halfPhi = std::numbers::pi,
                                        unsigned int quarterSegments = 2u);
 
 /// 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 quarterSegments number of segments used to approximate a segment quarter
 ///
 /// @return a vector of 2d-vectors
 std::vector<Vector2> circularVertices(double innerR, double outerR,
                                       double avgPhi = 0.,
                                       double halfPhi = std::numbers::pi,
                                       unsigned int quarterSegments = 2u);
 
 /// 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,
                   double tolerance = s_onSurfaceTolerance);
 
 /// Calculate the closest point on the polygon.
 inline Vector2 computeClosestPointOnPolygon(const Vector2& point,
                                             std::span<const Vector2> vertices,
                                             const SquareMatrix2& metric) {
   auto squaredNorm = [&](const Vector2& x) {
     return (x.transpose() * metric * x).value();
   };
 
   // calculate the closest position on the segment between `ll0` and `ll1` to
   // the point as measured by the metric induced by the metric matrix
   auto closestOnSegment = [&](auto&& ll0, auto&& ll1) {
     // normal vector and position of the closest point along the normal
     auto n = ll1 - ll0;
     auto n_transformed = metric * n;
     auto f = n.dot(n_transformed);
     auto u = std::isnormal(f)
                  ? (point - ll0).dot(n_transformed) / f
                  : 0.5;  // ll0 and ll1 are so close it doesn't matter
     // u must be in [0, 1] to still be on the polygon segment
     return ll0 + std::clamp(u, 0.0, 1.0) * n;
   };
 
   auto iv = std::begin(vertices);
   Vector2 l0 = *iv;
   Vector2 l1 = *(++iv);
   Vector2 closest = closestOnSegment(l0, l1);
   auto closestDist = squaredNorm(closest - point);
   // Calculate the closest point on other connecting lines and compare distances
   for (++iv; iv != std::end(vertices); ++iv) {
     l0 = l1;
     l1 = *iv;
     Vector2 current = closestOnSegment(l0, l1);
     auto currentDist = squaredNorm(current - point);
     if (currentDist < closestDist) {
       closest = current;
       closestDist = currentDist;
     }
   }
   // final edge from last vertex back to the first vertex
   Vector2 last = closestOnSegment(l1, *std::begin(vertices));
   if (squaredNorm(last - point) < closestDist) {
     closest = last;
   }
   return closest;
 }
 
 /// Calculate the closest point on the box
 inline Vector2 computeEuclideanClosestPointOnRectangle(
     const Vector2& point, const Vector2& lowerLeft, const Vector2& upperRight) {
   /*
    *
    *        |                 |
    *   IV   |       V         | I
    *        |                 |
    *  ------------------------------
    *        |                 |
    *        |                 |
    *   VIII |     INSIDE      | VI
    *        |                 |
    *        |                 |
    *  ------------------------------
    *        |                 |
    *   III  |      VII        | II
    *        |                 |
    *
    */
 
   double l0 = point[0], l1 = point[1];
   double loc0Min = lowerLeft[0], loc0Max = upperRight[0];
   double loc1Min = lowerLeft[1], loc1Max = upperRight[1];
 
   // check if inside
   if (loc0Min <= l0 && l0 < loc0Max && loc1Min <= l1 && l1 < loc1Max) {
     // INSIDE
     double dist = std::abs(loc0Max - l0);
     Vector2 cls(loc0Max, l1);
 
     double test = std::abs(loc0Min - l0);
     if (test <= dist) {
       dist = test;
       cls = {loc0Min, l1};
     }
 
     test = std::abs(loc1Max - l1);
     if (test <= dist) {
       dist = test;
       cls = {l0, loc1Max};
     }
 
     test = std::abs(loc1Min - l1);
     if (test <= dist) {
       return {l0, loc1Min};
     }
     return cls;
   } else {
     // OUTSIDE, check sectors
     if (l0 > loc0Max) {
       if (l1 > loc1Max) {  // I
         return {loc0Max, loc1Max};
       } else if (l1 <= loc1Min) {  // II
         return {loc0Max, loc1Min};
       } else {  // VI
         return {loc0Max, l1};
       }
     } else if (l0 < loc0Min) {
       if (l1 > loc1Max) {  // IV
         return {loc0Min, loc1Max};
       } else if (l1 <= loc1Min) {  // III
         return {loc0Min, loc1Min};
       } else {  // VIII
         return {loc0Min, l1};
       }
     } else {
       if (l1 > loc1Max) {  // V
         return {l0, loc1Max};
       } else {  // l1 <= loc1Min # VII
         return {l0, loc1Min};
       }
       // third case not necessary, see INSIDE above
     }
   }
 }
 
 }  // namespace Acts::detail::VerticesHelper

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