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 //------------------------------- -*- C++ -*- -------------------------------//
 // Copyright Celeritas contributors: see top-level COPYRIGHT file for details
 // SPDX-License-Identifier: (Apache-2.0 OR MIT)
 //---------------------------------------------------------------------------//
 //! \file orange/surf/Involute.hh
 //---------------------------------------------------------------------------//
 #pragma once
 
 #include <cassert>
 #include <cmath>
 
 #include "corecel/Constants.hh"
 #include "corecel/Types.hh"
 #include "corecel/cont/Array.hh"
 #include "corecel/cont/Span.hh"
 #include "corecel/math/Algorithms.hh"
 #include "corecel/math/ArrayUtils.hh"
 #include "orange/OrangeTypes.hh"
 
 #include "detail/InvolutePoint.hh"
 #include "detail/InvoluteSolver.hh"
 
 namespace celeritas
 {
 //---------------------------------------------------------------------------//
 /*!
  * Z-aligned circular involute.
  *
  * An involute is a curve created by unwinding a chord from a shape.
  * The involute implemented here is constructed from a circle and can be made
  * to be clockwise (negative) or anti-clockwise (positive).
  * This involute is the same type of that found in HFIR, and is necessary for
  * building accurate models.
  *
  * While the parameters define the curve itself have no restriction, except for
  * the radius of involute being positive, the involute needs to be bounded for
  * there to be finite solutions to the roots of the intersection points.
  * Additionally this bound cannot exceed an interval of size of 2 to be able to
  * determine if whether a particle is in, out, or on the involute surface.
  * Lastly the involute geometry is fixed to be z-aligned.
  *
  * \f[
  *   x = r_b (\cos(t+a) + t \sin(t+a)) + x_0
  * \f]
  * \f[
  *   y = r_b (\sin(t+a) - t \cos(t+a)) + y_0
  * \f]
  *
  * where \em t is the normal angle of the tangent to the circle of involute
  * with radius \em r_b from a starting angle of \em a (\f$r/h\f$ for a finite
  * cone.
  */
 class Involute
 {
   public:
     //@{
     //! \name Type aliases
     using Intersections = Array<real_type, 3>;
     using StorageSpan = Span<real_type const, 6>;
     using Real2 = Array<real_type, 2>;
     //@}
 
   public:
     //// CLASS ATTRIBUTES ////
 
     // Surface type identifier
     static CELER_CONSTEXPR_FUNCTION SurfaceType surface_type()
 
     {
         return SurfaceType::inv;
     }
 
     //! Safety cannot be trivially calculated
     static CELER_CONSTEXPR_FUNCTION bool simple_safety() { return false; }
 
   public:
     //// CONSTRUCTORS ////
 
     explicit Involute(Real2 const& origin,
                       real_type radius,
                       real_type displacement,
                       Chirality sign,
                       real_type tmin,
                       real_type tmax);
 
     // Construct from raw data
     template<class R>
     explicit inline CELER_FUNCTION Involute(Span<R, StorageSpan::extent>);
 
     //// ACCESSORS ////
 
     //! X-Y center of the circular base of the involute
     CELER_FUNCTION Real2 const& origin() const { return origin_; }
 
     //! Involute circle's radius
     CELER_FUNCTION real_type r_b() const { return std::fabs(r_b_); }
 
     //! Displacement angle
     CELER_FUNCTION real_type displacement_angle() const { return a_; }
 
     // Orientation of the involute curve
     inline CELER_FUNCTION Chirality sign() const;
 
     //! Get bounds of the involute
     CELER_FUNCTION real_type tmin() const { return tmin_; }
     CELER_FUNCTION real_type tmax() const { return tmax_; }
 
     //! Get a view to the data for type-deleted storage
     CELER_FUNCTION StorageSpan data() const { return {&origin_[0], 6}; }
 
     //// CALCULATION ////
 
     // Determine the sense of the position relative to this surface
     inline CELER_FUNCTION SignedSense calc_sense(Real3 const& pos) const;
 
     // Calculate all possible straight-line intersections with this surface
     inline CELER_FUNCTION Intersections calc_intersections(
         Real3 const& pos, Real3 const& dir, SurfaceState on_surface) const;
 
     // Calculate outward normal at a position
     inline CELER_FUNCTION Real3 calc_normal(Real3 const& pos) const;
 
   private:
     // Location of the center of circle of involute
     Real2 origin_;
 
     // Involute parameters
     real_type r_b_;  // Radius, negative if "clockwise" (flipped)
     real_type a_;
 
     // Bounds
     real_type tmin_;
     real_type tmax_;
 };
 
 //---------------------------------------------------------------------------//
 // INLINE DEFINITIONS
 //---------------------------------------------------------------------------//
 /*!
  * Construct from raw data.
  */
 template<class R>
 CELER_FUNCTION Involute::Involute(Span<R, StorageSpan::extent> data)
     : origin_{data[0], data[1]}
     , r_b_{data[2]}
     , a_{data[3]}
     , tmin_{data[4]}
     , tmax_{data[5]}
 {
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Orientation of the involute curve.
  */
 CELER_FUNCTION auto Involute::sign() const -> Chirality
 {
     return r_b_ > 0 ? Chirality::left : Chirality::right;
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Determine the sense of the position relative to this surface.
  *
  * This is performed by first checking if the particle is outside the bounding
  * circles given by tmin and tmax.
  *
  * Then position is compared to a point on the involute at the same radius from
  * the origin.
  *
  * Next the point is determined to be inside if an involute that passes it,
  * has an \em t that is within the bounds and an \em a greater than the
  * involute being tested for. To do this, the tangent to the involute must be
  * determined by calculating the intercepts of the circle of involute and
  * circle centered at the midpoint of the origin and the point being tested for
  * that extends to the origin. After which the angle of tangent point can be
  * determined and used to calculate \em a via: \f[
  * a = angle - t_point
  * \f]
  *
  * To calculate the intercept of two circles it is assumed that the two circles
  * are \em x_prime axis. The coordinate along \em x_prime originating from the
  * center of one of the circles is given by: \f[ x_prime = (d^2 - r^2 +
  * R^2)/(2d) \f] Where \em d is the distance between the center of the two
  * circles, \em r is the radius of the displaced circle, and \em R is the
  * radius of the circle at the origin. Then the point \em y_prime can be
  * obatined from: \f[ y_prime = \pm sqrt(R^2 - x_prime^2) \f] Then to convert (
  * \em x_prime , \em y_prime ) to ( \em x, \em y ) the following rotation is
  * applied:\f[ x = x_prime*cos(theta) - y_prime*sin(theta) y =
  * y_prime*cos(theta) + x_prime*sin(theta) \f] Where \em theta is the angle
  * between the \em x_prime axis and the \em x axis.
  */
 CELER_FUNCTION SignedSense Involute::calc_sense(Real3 const& pos) const
 {
     using constants::pi;
 
     Real2 xy;
     xy[0] = pos[0] - origin_[0];
     xy[1] = pos[1] - origin_[1];
 
     if (this->sign() == Chirality::right)
     {
         xy[0] = negate(xy[0]);
     }
 
     // Calculate distance to origin and obtain t value for distance.
     real_type const t_point_sq = dot_product(xy, xy) / ipow<2>(r_b_) - 1;
 
     // Check if point is in defined bounds.
     if (t_point_sq < ipow<2>(tmin_))
     {
         return SignedSense::outside;
     }
     if (t_point_sq > ipow<2>(tmax_))
     {
         return SignedSense::outside;
     }
 
     // Check if Point is on involute.
     detail::InvolutePoint calc_point{this->r_b(), a_};
     Real2 point = calc_point(clamp_to_nonneg(t_point_sq));
 
     if (xy == point)
     {
         return SignedSense::on;
     }
 
     // Check if point is in interval
 
     // Calculate tangent point
     // TODO: check that compiler avoids recomputing trig functions
     real_type x_prime = ipow<2>(r_b_) / norm(xy);
     real_type y_prime = std::sqrt(ipow<2>(r_b_) - ipow<2>(x_prime));
 
     // TODO: check that compiler avoids recomputing trig functions
     point[0] = (x_prime * xy[0] - y_prime * xy[1]) / norm(xy);
     point[1] = (y_prime * xy[0] + x_prime * xy[1]) / norm(xy);
 
     // Calculate angle of tangent
     real_type theta = std::acos(point[0] / norm(point));
     if (point[1] < 0)
     {
         theta = 2 * pi - theta;
     }
     // Count number of positive rotations around involute
     using namespace celeritas::literals;
     theta += max<real_type>(0_r, std::floor((tmax_ + a_ - theta) / (2 * pi)))
              * 2 * pi;
 
     // Calculate the displacement angle of the point
     real_type a1 = theta - std::sqrt(clamp_to_nonneg(t_point_sq));
 
     // Check if point is inside bounds
     if (theta < tmax_ + a_ && a1 > a_)
     {
         return SignedSense::inside;
     }
 
     return SignedSense::outside;
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Calculate all possible straight-line intersections with this surface.
  */
 CELER_FUNCTION auto Involute::calc_intersections(
     Real3 const& pos, Real3 const& dir, SurfaceState on_surface) const
     -> Intersections
 {
     // Expand translated positions into 'xyz' coordinate system
     Real3 rel_pos{pos};
     rel_pos[0] -= origin_[0];
     rel_pos[1] -= origin_[1];
 
     detail::InvoluteSolver solve(this->r_b(), a_, this->sign(), tmin_, tmax_);
 
     return solve(rel_pos, dir, on_surface);
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Calculate outward normal at a position on the surface.
  *
  * This is done by taking the derivative of the involute equation : \f[
  * n = {\sin(t+a) - \cos(t+a), 0}
  * \f]
  */
 CELER_FORCEINLINE_FUNCTION Real3 Involute::calc_normal(Real3 const& pos) const
 {
     Real2 xy;
     xy[0] = pos[0] - origin_[0];
     xy[1] = pos[1] - origin_[1];
 
     // Calculate normal
     real_type const angle
         = std::sqrt(clamp_to_nonneg(dot_product(xy, xy) / ipow<2>(r_b_) - 1))
           + a_;
     Real3 normal_ = {std::sin(angle), -std::cos(angle), 0};
 
     if (this->sign() == Chirality::right)
     {
         normal_[0] = negate(normal_[0]);
     }
 
     return normal_;
 }
 
 //---------------------------------------------------------------------------//
 }  // namespace celeritas

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