/********************************************************************************
 *                                                                              *
 * This file is part of IfcOpenShell.                                           *
 *                                                                              *
 * IfcOpenShell is free software: you can redistribute it and/or modify         *
 * it under the terms of the Lesser GNU General Public License as published by  *
 * the Free Software Foundation, either version 3.0 of the License, or          *
 * (at your option) any later version.                                          *
 *                                                                              *
 * IfcOpenShell is distributed in the hope that it will be useful,              *
 * but WITHOUT ANY WARRANTY; without even the implied warranty of               *
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the                 *
 * Lesser GNU General Public License for more details.                          *
 *                                                                              *
 * You should have received a copy of the Lesser GNU General Public License     *
 * along with this program. If not, see <http://www.gnu.org/licenses/>.         *
 *                                                                              *
 ********************************************************************************/

#include "mapping.h"
#define mapping POSTFIX_SCHEMA(mapping)
using namespace ifcopenshell::geometry;

#ifdef SCHEMA_HAS_IfcCurveSegment

#include "../profile_helper.h"

#include <boost/mpl/vector.hpp>
#include <boost/mpl/for_each.hpp>

// @todo use std::numbers::pi when upgrading to C++ 20
#define PI 3.1415926535897932384626433832795


namespace
{
	// trapezoid rule integration
	// @todo is there a well established math library we can use instead of
	// creating our own integrator?
	double integrate(double a, double b, unsigned n, std::function<double(double)> fn)
	{
		double area = 0;
		double h = (b - a) / n;
		auto x1 = a;
		auto f1 = fn(x1);
		for (auto i = 1; i <= n; i++)
		{
			auto x2 = a + h * i;
			auto f2 = fn(x2);
			area += h * (f1 + f2) / 2.0;

			x1 = x2;
			f1 = f2;
		}
		return area;
	}
}

// types of entities that can be IfcCurveSegment.ParentCurve
typedef boost::mpl::vector<
	IfcSchema::IfcLine
#ifdef SCHEMA_HAS_IfcClothoid
	, IfcSchema::IfcClothoid
#endif
#if defined SCHEMA_HAS_IfcSecondOrderPolynomialSpiral
	, IfcSchema::IfcSecondOrderPolynomialSpiral
#endif
	, IfcSchema::IfcPolyline
	, IfcSchema::IfcCircle
> curve_seg_types;

class curve_segment_evaluator {
private:
	mapping* mapping_;
	double length_unit_;
	double start_;
	double length_;
	IfcSchema::IfcCurve* curve_;

	std::optional<std::function<Eigen::Vector3d(double)>> eval_;

public:
	// First constructor, takes parameters from IfcCurveSegment
	curve_segment_evaluator(mapping* mapping,double length_unit, IfcSchema::IfcCurve* curve, IfcSchema::IfcCurveMeasureSelect* st, IfcSchema::IfcCurveMeasureSelect* le)
		: mapping_(mapping)
		, length_unit_(length_unit)
		, curve_(curve)
	{
		// @todo in IFC4X3_ADD2 this needs to be length measure
		
		if (!st->as<IfcSchema::IfcLengthMeasure>() || !le->as<IfcSchema::IfcLengthMeasure>()) {
			// @nb Parameter values are forbidden in the specification until parametrization is provided for all spirals
			throw std::runtime_error("Unsupported curve measure type");
		}
		
		start_ = *st->as<IfcSchema::IfcLengthMeasure>() * length_unit;
		length_ = *le->as<IfcSchema::IfcLengthMeasure>() * length_unit;
	}

// Clothoid using Taylor Series approximation
#ifdef SCHEMA_HAS_IfcClothoid
	// Then initialize Function(double) -> Vector3, by means of IfcCurve subtypes
	void operator()(IfcSchema::IfcClothoid* c) {
		// @todo verify
		auto sign = [](double v)->int{return v < 0 ? -1 : (0 < v ? 1 : 0); };
		auto sign_s = sign(start_);
		auto sign_l = sign(length_);
		double L = 0;
		if (sign_s == 0) L = fabs(length_);
		else if (sign_s == sign_l) L = fabs(start_ + length_);
		else L = fabs(start_);

		auto A = c->ClothoidConstant();
		auto R = A * A / L;
		auto RL = (A < 0 ? -1.0 : 1.0) * R * L;

		auto position = c->Position();
		auto placement = position->as<IfcSchema::IfcAxis2Placement2D>();
		auto ref_direction = placement->RefDirection();
		double theta = 0.0; // angle the circle's placement X-axis makes with respect to global X axis
		if (ref_direction)
		{
			auto dr = ref_direction->DirectionRatios();
			auto dx = dr[0];
			auto dy = dr[1];
			theta = atan2(dy, dx);
		}

		auto C = placement->Location();
		if (!C->as<IfcSchema::IfcCartesianPoint>())
		{
			throw std::runtime_error("Only IfcCartesianPoint is supported for center of IfcCircle");
			// @todo add support for other IfcPoint subtypes
		}
		auto Cx = C->as<IfcSchema::IfcCartesianPoint>()->Coordinates()[0];
		auto Cy = C->as<IfcSchema::IfcCartesianPoint>()->Coordinates()[1];

		eval_ = [RL,Cx,Cy,theta](double u) {
			// coordinate along clothoid is local coordinates
			auto xterm_1 = u;
			auto xterm_2 = std::pow(u, 5) / (40 * std::pow(RL, 2));
			auto xterm_3 = std::pow(u, 9) / (3456 * std::pow(RL, 4));
			auto xterm_4 = std::pow(u, 13) / (599040 * std::pow(RL, 6));
			auto xl = xterm_1 - xterm_2 + xterm_3 - xterm_4;

			auto yterm_1 = std::pow(u, 3) / (6 * RL);
			auto yterm_2 = std::pow(u, 7) / (336 * std::pow(RL, 3));
			auto yterm_3 = std::pow(u, 11) / (42240 * std::pow(RL, 5));
			auto yterm_4 = std::pow(u, 15) / (9676800 * std::pow(RL, 7));
			auto yl = yterm_1 - yterm_2 + yterm_3 - yterm_4;

			// transform point into clothoid's coodinate system
			auto x = xl * cos(theta) - yl * sin(theta) + Cx;
			auto y = xl * sin(theta) + yl * cos(theta) + Cy;
			return Eigen::Vector3d(x, y, 0.0);
		};
	}
#endif

	void set_spiral_functor(mapping* mapping,IfcSchema::IfcSpiral* s, std::function<double(double)> signX,std::function<double(double)> fnX, std::function<double(double)> signY, std::function<double(double)> fnY)
	{
		// determine the length of the spiral from the local origin to the end point
		auto binary_sign = [](double v)->int {return v < 0 ? -1 : (0 < v ? 1 : 0); }; // returns -1, 0, or 1
		auto sign_s = binary_sign(start_);
		auto sign_l = binary_sign(length_);
		double L = 0;
		if (sign_s == 0) L = fabs(length_); // start_ is at zero so length_ is the L
		else if (sign_s == sign_l) L = fabs(start_ + length_); // start_ and length_ are additive
		else L = fabs(start_); // start_ and length_ are in opposite directions so start_ is furthest from the origin

		//const auto& transformation_matrix = taxonomy::cast<taxonomy::matrix4>(mapping->map(s->Position()))->ccomponents();
		auto transformation_matrix = taxonomy::cast<taxonomy::matrix4>(mapping->map(s->Position()))->ccomponents();

		eval_ = [L, transformation_matrix, signX, fnX, signY, fnY](double u) {
			// integration limits, integrate from a to b
			// from 8.9.3.19.1, integration limits are 0.0 to u where u is a normalized parameter
			auto a = 0.0;
			auto b = fabs(u / L);

			auto n = 10; // use 10 steps in the numeric integration

			auto x = signX(u)*integrate(a, b, n, fnX);
			auto y = signY(u)*integrate(a, b, n, fnY);

			// transform point into clothoid's coodinate system
			auto result = transformation_matrix * Eigen::Vector4d(x, y, 0.0, 1.0);
			return Eigen::Vector3d(result(0),result(1),result(2));
			};
	}

// Clothoid using numerical integration
//#ifdef SCHEMA_HAS_IfcClothoid
//// Then initialize Function(double) -> Vector3, by means of IfcCurve subtypes
//	void operator()(IfcSchema::IfcClothoid* c) {
//
//		auto A = c->ClothoidConstant();
//
//		// the integration is for the +X, +Y quadrant - need to adjust the signs of the resulting X and Y values
//		// so that the results are in the correct quadrant.
//		// A > 0 and u > 0 -> +X, +Y
//		// A < 0 and u > 0 -> +X, -Y
//		// A > 0 and u < 0 -> -X, -Y
//		// A < 0 and u < 0 -> -X, +Y
//		// X depends only on u, Y depends on u and A.
//		auto sign = [](double v)->int {return v < 0 ? -1 : 1; }; // returns -1 or 1
//		auto sign_x = [sign](double t) {return sign(t); };
//		auto sign_y = [sign, A](double t) {return sign(t) == sign(A) ? 1.0 : -1.0; };
//		auto fn_x = [A](double t)->double {return A * sqrt(PI) * cos(PI * A * t * t / (2 * fabs(A))); };
//		auto fn_y = [A](double t)->double {return A * sqrt(PI) * sin(PI * A * t * t / (2 * fabs(A))); };
//
//		set_spiral_functor(mapping_,c->as<IfcSchema::IfcSpiral>(), sign_x, fn_x, sign_y, fn_y);
//	}
//#endif

#ifdef SCHEMA_HAS_IfcSecondOrderPolynomialSpiral
	void operator()(IfcSchema::IfcSecondOrderPolynomialSpiral* s)
	{
		// @todo verify - this is an example implementation of a different kind of spiral - lots of clean up needed
		auto A0 = s->ConstantTerm();
		auto A1 = s->LinearTerm();
		auto A2 = s->QuadraticTerm();

		auto theta = [A0, A1, A2](double t)
			{
				auto a0 = A0.has_value() ? t / A0.value() : 0.0;
				auto a1 = A1.has_value() ? A1.value() * std::pow(t, 2) / (2 * fabs(std::pow(A1.value(), 3))) : 0.0;
				auto a2 = std::pow(t, 3) / (3 * std::pow(A2, 3));
				return a0 + a1 + a2;
			};

		auto sign = [](double v)->int {return v < 0 ? -1 : 1; }; // returns -1 or 1
		auto sign_x = [sign](double t) {return sign(t); };
		auto sign_y = [sign](double t) {return sign(t); }; // @todo fix - not sure about sign_y yet, need to find some plots of this spiral

		auto fn_x = [theta](double t)->double {return cos(theta(t)); };
		auto fn_y = [theta](double t)->double {return sin(theta(t)); };

		set_spiral_functor(mapping_, s->as<IfcSchema::IfcSpiral>(), sign_x, fn_x, sign_y, fn_y);
	}
#endif

	void operator()(IfcSchema::IfcCircle* c)
	{
		auto R = c->Radius();
		//const auto& transformation_matrix = taxonomy::cast<taxonomy::matrix4>(mapping_->map(c->Position()))->ccomponents();
		auto transformation_matrix = taxonomy::cast<taxonomy::matrix4>(mapping_->map(c->Position()))->ccomponents();

		eval_ = [R, transformation_matrix](double u)
			{
				auto angle = u / R; // angle subtended by arc length u

				// compute point on circle centered at (0,0) with x-axis horizontal and y-axis vertical
				auto x = R * cos(angle);
				auto y = R * sin(angle);

				// transform point into circle's coodinate system
				auto result = transformation_matrix * Eigen::Vector4d(x, y, 0.0, 1.0);
				return Eigen::Vector3d(result(0), result(1), result(2));
			};
	}

	void operator()(IfcSchema::IfcPolyline* pl)
	{
		auto points = taxonomy::cast<taxonomy::loop>(mapping_->map_impl(pl));

		struct Range
		{
			double u_start;
			double u_end;
			std::function<bool(double, double, double)> compare;
			bool operator<(const Range& r) const { return u_start < r.u_start; }
		};
		using Function = std::function<std::pair<double, double>(double u)>;
		std::map<Range, Function> fns;

		auto std_compare = [](double u_start, double u, double u_end) {return u_start <= u && u < u_end; };
		auto end_compare = [](double u_start, double u, double u_end) {return u_start <= u && u <= (u_end+0.001); };

		auto iter = points->children.begin();
		auto end = points->children.end();
		auto last = std::prev(end);
		auto u = 0.0;
		for (; iter != end; iter++)
		{
			auto edge(*iter);
			auto& start_point = boost::get<taxonomy::point3::ptr>(edge->start);
			auto p1x = start_point->components_->x();
			auto p1y = start_point->components_->y();

			auto& end_point = boost::get<taxonomy::point3::ptr>(edge->end);
			auto p2x = end_point->components_->x();
			auto p2y = end_point->components_->y();

			auto dx = p2x - p1x;
			auto dy = p2y - p1y;
			auto l = sqrt(dx * dx + dy * dy);
			if (l == 0.0)
			{
				// @todo use closeness tolerance instead of absolute 0.0
				throw std::runtime_error("invalid polyline - points must not be coincident");
			}

			dx /= l;
			dy /= l;

			auto fn = [p1x, p1y, dx, dy](double u) { return std::make_pair(p1x + u * dx, p1y + u * dy); };

			fns.insert(std::make_pair(Range{ u, u + l,iter == last ? end_compare : std_compare }, fn));

			u = u + l;
		}

		eval_ = [fns](double u) {
			auto iter = std::find_if(fns.cbegin(), fns.cend(), [=](const auto& fn)
				{
					auto [u_start, u_end, compare] = fn.first;
					return compare(u_start, u, u_end);
				});
			
			if (iter == fns.end()) throw std::runtime_error("invalid distance from start"); // this should never happen, but just in case it does
			
			auto [u_start, u_end, compare] = iter->first;
			auto [x,y] = (iter->second)(u - u_start); // (u - u_start) is distance from start of this segment of the polyline
			return Eigen::Vector3d(x, y, 0);
			};
	}

	void operator()(IfcSchema::IfcLine* l) {
		auto s = l->Pnt();
		auto c = s->Coordinates();
		auto v = l->Dir();
		auto dr = v->Orientation()->DirectionRatios();
		auto m = v->Magnitude();
		auto px = c[0];
		auto py = c[1];
		auto dx = dr[0] / m;
		auto dy = dr[1] / m;

		eval_ = [px, py, dx, dy](double u) {
			auto x = px + u * dx;
			auto y = py + u * dy;
			return Eigen::Vector3d(x, y, 0);
			};
	}

	// Take the boost::type value from mpl::for_each and test it against our curve instance
	template <typename T>
	void operator()(boost::type<T>) {
		if (curve_->as<T>()) {
			(*this)(curve_->as<T>());
		}
	}

	// Then, with function populated based on IfcCurve subtype, we can evaluate to points
	Eigen::Vector3d operator()(double u) {
		if (eval_) {
			return (*eval_)((u + start_) * length_unit_);
		} else {
			throw std::runtime_error(curve_->declaration().name() + " not implemented");
		}
	}

	double length() const {
		return length_;
	}
};

taxonomy::ptr mapping::map_impl(const IfcSchema::IfcCurveSegment* inst) {
	// @todo fixed number of segments or fixed interval?
	// @todo placement
	// @todo figure out what to do with the zero length segments at the end of compound curves

	static int NUM_SEGMENTS = 64;
	curve_segment_evaluator cse(this, length_unit_, inst->ParentCurve(), inst->SegmentStart(), inst->SegmentLength());
	boost::mpl::for_each<curve_seg_types, boost::type<boost::mpl::_>>(std::ref(cse));

	std::vector<taxonomy::point3::ptr> polygon;

	// @todo - for some reason this isn't working, the matrix gets all messed up
	//const auto& transformation_matrix = taxonomy::cast<taxonomy::matrix4>(map(inst->Placement()))->ccomponents();
	auto transformation_matrix = taxonomy::cast<taxonomy::matrix4>(map(inst->Placement()))->ccomponents();

	// @todo - is there a better way to deal with tolerance and "nearly zero" values?
	auto length = cse.length();
	if (0.001 < fabs(length))
	{
		for (int i = 0; i <= NUM_SEGMENTS; ++i) {
			auto u = length * i / NUM_SEGMENTS;
		
			auto p = cse(u);
			auto result =  transformation_matrix * Eigen::Vector4d(p(0),p(1),p(2), 1.);
			polygon.push_back(taxonomy::make<taxonomy::point3>(result(0),result(1),result(2)));
		}
	}

	return polygon_from_points(polygon);
}

#endif