maszyna/editor/editorRoad.cpp

/*
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/.
*/

#include "stdafx.h"
#include "editor/editorRoad.hpp"

#include "editor/editorTrack.hpp"
#include "world/Track.h"
#include "scene/scene.h"
#include "scene/scenelayers.h"
#include "simulation/simulation.h"
#include "utilities/Globals.h"
#include "utilities/utilities.h"

#include <algorithm>
#include <cmath>
#include <filesystem>
#include <set>

namespace
{

double const kSamePoint{0.25}; // ends of two pieces this close are taken for joined
double const kPieceLength{50.0}; // longest piece the planner makes
double const kPieceTurn{glm::radians(30.0)}; // largest turn of a single piece
double const kShortestRoad{2.0};
double const kTightestRadius{6.0};

void add_unique(std::vector<road_node *> &Roads, road_node *Road)
{
	if (Road != nullptr && std::find(Roads.begin(), Roads.end(), Road) == Roads.end())
		Roads.emplace_back(Road);
}

glm::dvec3 axis_end(road_node::state const &State, bool const Atend)
{
	return State.axis.points[Atend ? segment_data::point::end : segment_data::point::start];
}

// roads other than the specified one, with an end at specified point
std::vector<road_node *> roads_at(glm::dvec3 const &Point, road_node const *Exclude)
{
	std::vector<road_node *> result;
	for (auto *road : simulation::Roads.sequence())
	{
		if (road == nullptr || road == Exclude || road->m_editorremoved)
			continue;
		for (auto const atend : {false, true})
		{
			if (glm::distance(axis_end(road->definition(), atend), Point) < kSamePoint)
			{
				result.emplace_back(road);
				break;
			}
		}
	}
	return result;
}

// junctions with an arm at specified point
std::vector<junction_node *> junctions_at(glm::dvec3 const &Point)
{
	std::vector<junction_node *> result;
	for (auto *junction : simulation::Junctions.sequence())
	{
		if (junction == nullptr || junction->m_editorremoved)
			continue;
		for (auto const &arm : junction->definition().arms)
		{
			if (glm::distance(arm.position, Point) < kSamePoint)
			{
				result.emplace_back(junction);
				break;
			}
		}
	}
	return result;
}

void add_unique(std::vector<junction_node *> &Junctions, junction_node *Junction)
{
	if (Junction != nullptr && std::find(Junctions.begin(), Junctions.end(), Junction) == Junctions.end())
		Junctions.emplace_back(Junction);
}

// part of a path between two values of its curve parameter
segment_data subpath(segment_data const &Path, double const From, double const To)
{
	segment_data part{Path};
	auto const &p0{Path.points[segment_data::point::start]};
	auto const &p3{Path.points[segment_data::point::end]};
	part.rolls = {static_cast<float>(Path.rolls[0] + (Path.rolls[1] - Path.rolls[0]) * From), static_cast<float>(Path.rolls[0] + (Path.rolls[1] - Path.rolls[0]) * To)};
	if (Path.points[segment_data::point::control1] == glm::dvec3{0.0} && Path.points[segment_data::point::control2] == glm::dvec3{0.0})
	{
		part.points[segment_data::point::start] = glm::mix(p0, p3, From);
		part.points[segment_data::point::end] = glm::mix(p0, p3, To);
		return part;
	}
	auto const p1{p0 + Path.points[segment_data::point::control1]};
	auto const p2{p3 + Path.points[segment_data::point::control2]};
	auto const point = [&](double const T) {
		auto const u{1.0 - T};
		return u * u * u * p0 + 3.0 * u * u * T * p1 + 3.0 * u * T * T * p2 + T * T * T * p3;
	};
	auto const derivative = [&](double const T) {
		auto const u{1.0 - T};
		return 3.0 * u * u * (p1 - p0) + 6.0 * u * T * (p2 - p1) + 3.0 * T * T * (p3 - p2);
	};
	// a part of a cubic curve is a cubic curve, with the tangents scaled to the part of the parameter range it takes
	part.points[segment_data::point::start] = point(From);
	part.points[segment_data::point::end] = point(To);
	part.points[segment_data::point::control1] = derivative(From) * ((To - From) / 3.0);
	part.points[segment_data::point::control2] = derivative(To) * (-(To - From) / 3.0);
	return part;
}

// true if there's a vehicle on any of the paths turning the traffic back at the loose ends of the road
bool turning(road_node const &Road)
{
	for (auto const *turn : Road.turns())
		if (turn != nullptr && false == turn->Dynamics.empty())
			return true;
	return false;
}

void retire(std::vector<TTrack *> const &Tracks)
{
	for (auto *track : Tracks)
		if (track != nullptr)
			editor_track::retire(*track);
}

// smallest radius of the bend made by a bezier curve, seen from above; 0 if the curve is practically straight
double tightest_radius(segment_data const &Path)
{
	auto const &p0{Path.points[segment_data::point::start]};
	auto const &p3{Path.points[segment_data::point::end]};
	auto const p1{p0 + Path.points[segment_data::point::control1]};
	auto const p2{p3 + Path.points[segment_data::point::control2]};
	double curvature{0.0};
	for (int i = 0; i <= 16; ++i)
	{
		auto const t{i / 16.0};
		auto const u{1.0 - t};
		auto const first{3.0 * u * u * (p1 - p0) + 6.0 * u * t * (p2 - p1) + 3.0 * t * t * (p3 - p2)};
		auto const second{6.0 * u * (p2 - 2.0 * p1 + p0) + 6.0 * t * (p3 - 2.0 * p2 + p1)};
		auto const speedsquared{first.x * first.x + first.z * first.z};
		if (speedsquared < 1e-9)
			continue;
		curvature = std::max(curvature, std::abs(second.x * first.z - second.z * first.x) / (speedsquared * std::sqrt(speedsquared)));
	}
	return curvature > 1e-5 ? 1.0 / curvature : 0.0;
}

}

bool editor_road::available(std::string *Reason)
{
	if (Global.NvRenderer)
	{
		if (Reason != nullptr)
			*Reason = "Geometry of the roads can't be rebuilt with the experimental renderer";
		return false;
	}
	if (simulation::Region == nullptr)
	{
		if (Reason != nullptr)
			*Reason = "No scenery is loaded";
		return false;
	}
	return true;
}

bool editor_road::can_edit(road_node const &Road, std::string *Reason)
{
	std::string reason;
	if (false == available(&reason))
	{
		// reason was filled by the call
	}
	else if (Road.merged())
	{
		reason = "the scenery wasn't opened for editing (-edit), geometry of the roads it came with can't be taken apart";
	}
	else if (false == scene::Layers.editable(&Road, &reason))
	{
		// reason was filled by the call
	}
	else if (Road.occupied())
	{
		reason = "there are vehicles on it";
	}
	else
	{
		// the paths made to turn the vehicles back at the loose ends of the neighbours go away too
		for (auto const *neighbour : neighbours(Road))
			for (auto const *turn : neighbour->turns())
				if (turn != nullptr && false == turn->Dynamics.empty())
					reason = "there are vehicles turning back next to it";
	}
	if (reason.empty())
	{
		// so do the ways through the junctions it leads to
		for (auto const atend : {false, true})
			for (auto const *junction : junctions_at(axis_end(Road.definition(), atend)))
				if (junction->occupied())
					reason = "there are vehicles on the junction it leads to";
	}
	if (false == reason.empty() && Reason != nullptr)
		*Reason = reason;
	return reason.empty();
}

bool editor_road::can_edit(junction_node const &Junction, std::string *Reason)
{
	std::string reason;
	if (false == available(&reason))
	{
		// reason was filled by the call
	}
	else if (Junction.merged())
	{
		reason = "the scenery wasn't opened for editing (-edit), geometry of the junctions it came with can't be taken apart";
	}
	else if (false == scene::Layers.editable(&Junction, &reason))
	{
		// reason was filled by the call
	}
	else if (Junction.occupied())
	{
		reason = "there are vehicles on it";
	}
	else
	{
		// the roads attached to it get their loose ends closed anew
		for (auto const &arm : Junction.definition().arms)
			for (auto const *road : roads_at(arm.position, nullptr))
				if (turning(*road))
					reason = "there are vehicles turning back on the roads it leads to";
	}
	if (false == reason.empty() && Reason != nullptr)
		*Reason = reason;
	return reason.empty();
}

bool editor_road::can_join(loose_end const &End, std::string *Reason)
{
	// what gets attached takes the place of the paths made for the end as it was
	std::string reason;
	if (End.road != nullptr && turning(*End.road))
		reason = "there are vehicles turning back on the road";
	if (End.junction != nullptr)
	{
		if (End.junction->occupied())
			reason = "there are vehicles on the junction";
		for (auto const &arm : End.junction->definition().arms)
			for (auto const *road : roads_at(arm.position, nullptr))
				if (turning(*road))
					reason = "there are vehicles turning back on the roads the junction leads to";
	}
	if (false == reason.empty() && Reason != nullptr)
		*Reason = reason;
	return reason.empty();
}

std::vector<road_node *> editor_road::neighbours(road_node const &Road)
{
	std::vector<road_node *> result;
	if (Road.m_editorremoved)
		return result;
	for (auto const atend : {false, true})
		for (auto *road : roads_at(axis_end(Road.definition(), atend), &Road))
			add_unique(result, road);
	return result;
}

template <class Change_>
void editor_road::refresh(std::vector<road_node *> const &Roads, std::vector<junction_node *> const &Junctions, Change_ Change)
{
	// the pieces and junctions next to the changed ones keep their shape, but what they're joined with changes.
	// this takes down the paths made for the joints, so they can be made again once the change is done
	std::vector<road_node *> affected;
	std::vector<junction_node *> crossings;
	auto const gather = [&]() {
		std::vector<road_node *> roads{affected};
		std::vector<junction_node *> junctions{crossings};
		for (auto *road : Roads)
		{
			add_unique(roads, road);
			if (road->m_editorremoved)
				continue;
			for (auto *neighbour : neighbours(*road))
				add_unique(roads, neighbour);
			for (auto const atend : {false, true})
				for (auto *junction : junctions_at(axis_end(road->definition(), atend)))
					add_unique(junctions, junction);
		}
		for (auto *junction : Junctions)
			add_unique(junctions, junction);
		// a junction changes what the roads attached to it do at their ends
		for (auto *junction : junctions)
			if (false == junction->m_editorremoved)
				for (auto const &arm : junction->definition().arms)
					for (auto *road : roads_at(arm.position, nullptr))
						add_unique(roads, road);
		for (auto *road : roads)
		{
			if (std::find(affected.begin(), affected.end(), road) == affected.end())
			{
				retire(road->release_turns());
				affected.emplace_back(road);
			}
		}
		for (auto *junction : junctions)
		{
			if (std::find(crossings.begin(), crossings.end(), junction) == crossings.end())
			{
				retire(junction->release_links());
				crossings.emplace_back(junction);
			}
		}
	};
	gather();
	for (auto *road : Roads)
	{
		road->hide();
		retire(road->release_lanes());
	}
	for (auto *junction : Junctions)
		junction->hide();

	Change();

	// the change could have moved things next to other ones
	gather();
	std::vector<TTrack *> lanes;
	for (auto *road : Roads)
	{
		if (road->m_editorremoved)
			continue;
		road->create_lanes();
		road->show();
		lanes.insert(lanes.end(), road->tracks().begin(), road->tracks().end());
	}
	// joins the lanes with the lanes of the neighbours, by the ends they share
	editor_track::commit(lanes);
	for (auto *junction : Junctions)
		if (false == junction->m_editorremoved)
			junction->show();
	// the junctions take the lanes which end at them, what's left loose after that is closed by the roads
	for (auto *junction : crossings)
		if (false == junction->m_editorremoved)
			junction->create_links();
	for (auto *road : affected)
		if (false == road->m_editorremoved)
			road->close_ends();
}

std::vector<road_node *> editor_road::create(std::vector<road_node::state> const &States)
{
	static int counter{0};
	std::vector<road_node *> created;
	if (false == available())
		return created;
	for (auto const &state : States)
	{
		scene::node_data data;
		data.type = "road";
		data.range_max = -1.0;
		data.layer = scene::Layers.active(); // null_handle unless the scenery was opened for editing
		// the name is what the lanes are known by to the vehicles put on them, so each piece needs one of its own
		do
		{
			data.name = "road_" + std::to_string(++counter);
		} while (simulation::Roads.find(data.name) != nullptr);
		auto *road{new road_node(data)};
		road->define(state);
		road->mark_dirty();
		simulation::Roads.insert(road);
		scene::Layers.count(road->layer(), scene::layer_item::track);
		created.emplace_back(road);
	}
	refresh(created, {}, []() {});
	return created;
}

void editor_road::apply(std::vector<std::pair<road_node *, road_node::state>> const &Changes)
{
	std::vector<road_node *> roads;
	for (auto const &change : Changes)
		add_unique(roads, change.first);
	if (roads.empty())
		return;
	refresh(roads, {}, [&]() {
		for (auto const &change : Changes)
		{
			change.first->define(change.second);
			change.first->mark_dirty();
		}
	});
}

void editor_road::remove(std::vector<road_node *> const &Roads)
{
	std::vector<road_node *> roads;
	for (auto *road : Roads)
		if (road != nullptr && false == road->m_editorremoved)
			add_unique(roads, road);
	if (roads.empty())
		return;
	refresh(roads, {}, [&]() {
		for (auto *road : roads)
		{
			road->m_editorremoved = true;
			scene::Layers.count(road->layer(), scene::layer_item::track, -1);
		}
	});
}

void editor_road::revive(std::vector<road_node *> const &Roads)
{
	std::vector<road_node *> roads;
	for (auto *road : Roads)
		if (road != nullptr && road->m_editorremoved)
			add_unique(roads, road);
	if (roads.empty())
		return;
	refresh(roads, {}, [&]() {
		for (auto *road : roads)
		{
			road->m_editorremoved = false;
			road->mark_dirty();
			scene::Layers.count(road->layer(), scene::layer_item::track);
		}
	});
}

std::vector<junction_node *> editor_road::create(std::vector<junction_node::state> const &States)
{
	static int counter{0};
	std::vector<junction_node *> created;
	if (false == available())
		return created;
	for (auto const &state : States)
	{
		scene::node_data data;
		data.type = "junction";
		data.range_max = -1.0;
		data.layer = scene::Layers.active(); // null_handle unless the scenery was opened for editing
		do
		{
			data.name = "junction_" + std::to_string(++counter);
		} while (simulation::Junctions.find(data.name) != nullptr);
		auto *junction{new junction_node(data)};
		junction->define(state);
		junction->mark_dirty();
		simulation::Junctions.insert(junction);
		scene::Layers.count(junction->layer(), scene::layer_item::track);
		created.emplace_back(junction);
	}
	refresh({}, created, []() {});
	return created;
}

void editor_road::remove(std::vector<junction_node *> const &Junctions)
{
	std::vector<junction_node *> junctions;
	for (auto *junction : Junctions)
		if (junction != nullptr && false == junction->m_editorremoved)
			add_unique(junctions, junction);
	if (junctions.empty())
		return;
	refresh({}, junctions, [&]() {
		for (auto *junction : junctions)
		{
			junction->m_editorremoved = true;
			scene::Layers.count(junction->layer(), scene::layer_item::track, -1);
		}
	});
}

void editor_road::revive(std::vector<junction_node *> const &Junctions)
{
	std::vector<junction_node *> junctions;
	for (auto *junction : Junctions)
		if (junction != nullptr && junction->m_editorremoved)
			add_unique(junctions, junction);
	if (junctions.empty())
		return;
	refresh({}, junctions, [&]() {
		for (auto *junction : junctions)
		{
			junction->m_editorremoved = false;
			junction->mark_dirty();
			scene::Layers.count(junction->layer(), scene::layer_item::track);
		}
	});
}

road_node *editor_road::split(road_node &Road, double const T)
{
	if (T <= 0.001 || T >= 0.999)
		return nullptr;
	auto first{Road.definition()};
	auto second{first};
	auto const &path{Road.definition().axis};
	auto const p0{path.points[segment_data::point::start]};
	auto const p3{path.points[segment_data::point::end]};
	if (path.points[segment_data::point::control1] == glm::dvec3{0.0} && path.points[segment_data::point::control2] == glm::dvec3{0.0})
	{
		auto const middle{glm::mix(p0, p3, T)};
		first.axis.points[segment_data::point::end] = middle;
		second.axis.points[segment_data::point::start] = middle;
	}
	else
	{
		auto const p1{p0 + path.points[segment_data::point::control1]};
		auto const p2{p3 + path.points[segment_data::point::control2]};
		auto const p01{glm::mix(p0, p1, T)};
		auto const p12{glm::mix(p1, p2, T)};
		auto const p23{glm::mix(p2, p3, T)};
		auto const p012{glm::mix(p01, p12, T)};
		auto const p123{glm::mix(p12, p23, T)};
		auto const middle{glm::mix(p012, p123, T)};
		first.axis.points[segment_data::point::control1] = p01 - p0;
		first.axis.points[segment_data::point::control2] = p012 - middle;
		first.axis.points[segment_data::point::end] = middle;
		second.axis.points[segment_data::point::start] = middle;
		second.axis.points[segment_data::point::control1] = p123 - middle;
		second.axis.points[segment_data::point::control2] = p23 - p3;
	}
	auto const roll{static_cast<float>(path.rolls[0] + (path.rolls[1] - path.rolls[0]) * T)};
	first.axis.rolls[1] = roll;
	second.axis.rolls[0] = roll;
	apply({{&Road, first}});
	auto const created{create({second})};
	return created.empty() ? nullptr : created.front();
}

std::vector<road_node *> editor_road::chain(road_node &Road)
{
	std::vector<road_node *> result{&Road};
	for (std::size_t idx = 0; idx < result.size(); ++idx)
	{
		for (auto const atend : {false, true})
		{
			// a road goes on only where exactly two pieces meet
			auto const next{roads_at(axis_end(result[idx]->definition(), atend), result[idx])};
			if (next.size() == 1)
				add_unique(result, next.front());
		}
	}
	return result;
}

double editor_road::nearest_parameter(road_node::state const &State, glm::dvec3 const &Point)
{
	auto const distance = [&](double const T) {
		auto const position{State.point(T)};
		return glm::distance(glm::dvec2{position.x, position.z}, glm::dvec2{Point.x, Point.z});
	};
	double best{0.0};
	for (int i = 1; i <= 64; ++i)
		if (distance(i / 64.0) < distance(best))
			best = i / 64.0;
	double step{1.0 / 64.0};
	for (int i = 0; i < 24; ++i)
	{
		step *= 0.5;
		if (best - step >= 0.0 && distance(best - step) < distance(best))
			best -= step;
		else if (best + step <= 1.0 && distance(best + step) < distance(best))
			best += step;
	}
	return best;
}

road_node *editor_road::nearest(glm::dvec3 const &Point, double const Margin)
{
	road_node *result{nullptr};
	double best{std::numeric_limits<double>::max()};
	for (auto *road : simulation::Roads.sequence())
	{
		if (road == nullptr || road->m_editorremoved)
			continue;
		auto const &state{road->definition()};
		auto const reach{0.5 * state.width() + std::max(state.sides[0].width, state.sides[1].width) + Margin};
		if (glm::distance(road->location(), Point) > 0.5 * state.length() + reach + 10.0)
			continue;
		auto const position{state.point(nearest_parameter(state, Point))};
		auto const distance{glm::distance(glm::dvec2{position.x, position.z}, glm::dvec2{Point.x, Point.z})};
		// roads passing over or under the point don't count
		if (distance > reach || std::abs(position.y - Point.y) > 3.0)
			continue;
		if (distance < best)
		{
			best = distance;
			result = road;
		}
	}
	return result;
}

junction_node *editor_road::nearest_junction(glm::dvec3 const &Point)
{
	junction_node *result{nullptr};
	double best{std::numeric_limits<double>::max()};
	for (auto *junction : simulation::Junctions.sequence())
	{
		if (junction == nullptr || junction->m_editorremoved)
			continue;
		auto const &state{junction->definition()};
		// the junction takes the ground up to the ends of the roads it's made for
		double reach{0.0};
		for (auto const &arm : state.arms)
			reach = std::max(reach, glm::distance(glm::dvec2{arm.position.x, arm.position.z}, glm::dvec2{state.centre.x, state.centre.z}));
		auto const distance{glm::distance(glm::dvec2{state.centre.x, state.centre.z}, glm::dvec2{Point.x, Point.z})};
		if (distance > reach || std::abs(state.centre.y - Point.y) > 3.0 || distance > best)
			continue;
		best = distance;
		result = junction;
	}
	return result;
}

editor_road::loose_end editor_road::find_end(glm::dvec3 const &Point, double const Radius, bool const Junctions)
{
	loose_end result;
	double best{Radius};
	for (auto *road : simulation::Roads.sequence())
	{
		if (road == nullptr || road->m_editorremoved)
			continue;
		auto const &state{road->definition()};
		for (auto const atend : {false, true})
		{
			auto const position{axis_end(state, atend)};
			auto const distance{glm::distance(glm::dvec2{position.x, position.z}, glm::dvec2{Point.x, Point.z})};
			if (distance > best || std::abs(position.y - Point.y) > 3.0 || false == roads_at(position, road).empty() || false == junctions_at(position).empty())
				continue;
			best = distance;
			result = loose_end{};
			result.road = road;
			result.atend = atend;
			result.position = position;
			result.outwards = (atend ? state.tangent(1.0) : -state.tangent(0.0));
		}
	}
	if (false == Junctions)
		return result;
	for (auto *junction : simulation::Junctions.sequence())
	{
		if (junction == nullptr || junction->m_editorremoved)
			continue;
		for (auto const &arm : junction->definition().arms)
		{
			auto const distance{glm::distance(glm::dvec2{arm.position.x, arm.position.z}, glm::dvec2{Point.x, Point.z})};
			if (distance > best || std::abs(arm.position.y - Point.y) > 3.0 || false == roads_at(arm.position, nullptr).empty())
				continue;
			best = distance;
			result = loose_end{};
			result.junction = junction;
			result.position = arm.position;
			result.outwards = glm::dvec3{arm.direction.x, 0.0, arm.direction.y};
			// a road leading away from the junction has the lanes going out of it as the ones going along its axis
			result.forward = arm.outgoing;
			result.backward = arm.incoming;
			result.width = arm.width;
		}
	}
	return result;
}

std::vector<segment_data> editor_road::plan(glm::dvec3 const &Start, glm::dvec2 const *Direction, glm::dvec3 const &Target, glm::dvec2 const *Enddirection, bool const Straight, std::string &Error)
{
	std::vector<segment_data> pieces;
	glm::dvec2 const chord{Target.x - Start.x, Target.z - Start.z};
	auto const span{glm::length(chord)};
	if (span < kShortestRoad)
	{
		Error = "Too short";
		return pieces;
	}
	// straight road, cut into pieces of reasonable length
	auto const straight = [&](glm::dvec3 const &End) {
		auto const count{std::max(1, static_cast<int>(std::ceil(glm::distance(Start, End) / kPieceLength)))};
		for (int i = 0; i < count; ++i)
		{
			segment_data piece;
			piece.points[segment_data::point::start] = glm::mix(Start, End, static_cast<double>(i) / count);
			piece.points[segment_data::point::end] = glm::mix(Start, End, static_cast<double>(i + 1) / count);
			pieces.emplace_back(piece);
		}
	};

	if (Direction != nullptr && Enddirection != nullptr)
	{
		// both ends are tied, which leaves a single curve with the tangents set
		if (glm::dot(*Direction, chord) < 0.1 * span || glm::dot(*Enddirection, chord) < 0.1 * span)
		{
			Error = "The road would have to turn back to meet the end";
			return pieces;
		}
		auto const rise{(Target.y - Start.y) / 3.0};
		segment_data piece;
		piece.points[segment_data::point::start] = Start;
		piece.points[segment_data::point::end] = Target;
		piece.points[segment_data::point::control1] = glm::dvec3{Direction->x * span / 3.0, rise, Direction->y * span / 3.0};
		piece.points[segment_data::point::control2] = glm::dvec3{-Enddirection->x * span / 3.0, -rise, -Enddirection->y * span / 3.0};
		auto const radius{tightest_radius(piece)};
		if (radius == 0.0)
		{
			pieces.clear();
			straight(Target);
			return pieces;
		}
		if (radius < kTightestRadius)
		{
			Error = "The bend is too tight";
			return pieces;
		}
		piece.radius = static_cast<float>(radius);
		pieces.emplace_back(piece);
		return pieces;
	}
	if (Direction == nullptr && Enddirection != nullptr)
	{
		// only the far end is tied: the same road as the one leading back from there, turned around
		glm::dvec2 const back{-*Enddirection};
		auto reversed{plan(Target, &back, Start, nullptr, Straight, Error)};
		for (auto &piece : reversed)
		{
			std::swap(piece.points[segment_data::point::start], piece.points[segment_data::point::end]);
			std::swap(piece.points[segment_data::point::control1], piece.points[segment_data::point::control2]);
		}
		std::reverse(reversed.begin(), reversed.end());
		return reversed;
	}
	if (Direction == nullptr)
	{
		straight(Target);
		return pieces;
	}

	// the road leaves the start in set direction, and reaches the target with an arc
	auto const forward{*Direction};
	glm::dvec2 const left{forward.y, -forward.x};
	auto const along{glm::dot(chord, forward)};
	auto const side{glm::dot(chord, left)};
	if (Straight || std::abs(side) < 0.02 * span)
	{
		if (along < kShortestRoad)
		{
			Error = "The target is behind the start";
			return pieces;
		}
		straight(glm::dvec3{Start.x + forward.x * along, Target.y, Start.z + forward.y * along});
		return pieces;
	}
	auto const turn{2.0 * std::atan2(side, along)}; // positive to the left
	auto const radius{span * span / (2.0 * side)}; // likewise
	if (std::abs(turn) > glm::radians(170.0))
	{
		Error = "The road would have to turn back to reach the target";
		return pieces;
	}
	if (std::abs(radius) < kTightestRadius)
	{
		Error = "The bend is too tight";
		return pieces;
	}
	glm::dvec2 const start{Start.x, Start.z};
	auto const centre{start + left * radius};
	auto const count{std::max(1, static_cast<int>(std::ceil(std::max(std::abs(turn) / kPieceTurn, std::abs(radius * turn) / kPieceLength))))};
	auto const handle{4.0 / 3.0 * std::tan(std::abs(turn) / count / 4.0) * std::abs(radius)};
	auto const rise{(Target.y - Start.y) / count};
	for (int i = 0; i < count; ++i)
	{
		auto const angle0{turn * i / count};
		auto const angle1{turn * (i + 1) / count};
		auto const point0{centre - left * (radius * std::cos(angle0)) + forward * (radius * std::sin(angle0))};
		auto const point1{centre - left * (radius * std::cos(angle1)) + forward * (radius * std::sin(angle1))};
		auto const tangent0{forward * std::cos(angle0) + left * std::sin(angle0)};
		auto const tangent1{forward * std::cos(angle1) + left * std::sin(angle1)};
		segment_data piece;
		piece.points[segment_data::point::start] = glm::dvec3{point0.x, Start.y + rise * i, point0.y};
		piece.points[segment_data::point::end] = glm::dvec3{point1.x, Start.y + rise * (i + 1), point1.y};
		piece.points[segment_data::point::control1] = glm::dvec3{tangent0.x * handle, rise / 3.0, tangent0.y * handle};
		piece.points[segment_data::point::control2] = glm::dvec3{-tangent1.x * handle, -rise / 3.0, -tangent1.y * handle};
		piece.radius = static_cast<float>(std::abs(radius));
		pieces.emplace_back(piece);
	}
	// the arc is worked out from the start, make sure it ends exactly at the target
	pieces.back().points[segment_data::point::end] = Target;
	return pieces;
}

double editor_road::planar_length(segment_data const &Path)
{
	auto const whole{subpath(Path, 0.0, 1.0)};
	auto const &p0{whole.points[segment_data::point::start]};
	auto const &p3{whole.points[segment_data::point::end]};
	if (whole.points[segment_data::point::control1] == glm::dvec3{0.0} && whole.points[segment_data::point::control2] == glm::dvec3{0.0})
		return glm::distance(glm::dvec2{p0.x, p0.z}, glm::dvec2{p3.x, p3.z});
	auto const p1{p0 + whole.points[segment_data::point::control1]};
	auto const p2{p3 + whole.points[segment_data::point::control2]};
	double length{0.0};
	glm::dvec2 previous{p0.x, p0.z};
	for (int i = 1; i <= 32; ++i)
	{
		auto const t{i / 32.0};
		auto const u{1.0 - t};
		auto const point{u * u * u * p0 + 3.0 * u * u * t * p1 + 3.0 * u * t * t * p2 + t * t * t * p3};
		glm::dvec2 const current{point.x, point.z};
		length += glm::distance(previous, current);
		previous = current;
	}
	return length;
}

double editor_road::end_grade(segment_data const &Path)
{
	auto const &control{Path.points[segment_data::point::control2]};
	if (control != glm::dvec3{0.0})
	{
		auto const run{glm::length(glm::dvec2{control.x, control.z})};
		return run > 1e-6 ? -control.y / run : 0.0;
	}
	auto const length{planar_length(Path)};
	return length > 1e-6 ? (Path.points[segment_data::point::end].y - Path.points[segment_data::point::start].y) / length : 0.0;
}

std::vector<segment_data> editor_road::refine(std::vector<segment_data> const &Pieces, double const Length)
{
	std::vector<segment_data> result;
	for (auto const &piece : Pieces)
	{
		auto const count{std::max(1, static_cast<int>(std::ceil(planar_length(piece) / std::max(1.0, Length) - 0.01)))};
		for (int i = 0; i < count; ++i)
			result.emplace_back(count == 1 ? piece : subpath(piece, static_cast<double>(i) / count, static_cast<double>(i + 1) / count));
	}
	return result;
}

void editor_road::profile(std::vector<segment_data> &Pieces, std::vector<double> Heights, double const *Startgrade, double const *Endgrade)
{
	auto const count{Pieces.size()};
	if (count == 0 || Heights.size() != count + 1)
		return;
	std::vector<double> lengths(count);
	for (std::size_t i = 0; i < count; ++i)
		lengths[i] = std::max(0.01, planar_length(Pieces[i]));
	// the heights in between are evened out, so the road doesn't ride every dip. it's never lowered though,
	// as that would let the ground the heights were taken from come through the surface
	{
		auto const sampled{Heights};
		for (std::size_t i = 1; i < count; ++i)
			Heights[i] = std::max(sampled[i], 0.25 * sampled[i - 1] + 0.5 * sampled[i] + 0.25 * sampled[i + 1]);
	}
	std::vector<double> slopes(count);
	for (std::size_t i = 0; i < count; ++i)
		slopes[i] = (Heights[i + 1] - Heights[i]) / lengths[i];
	// slope at each joint is shared by the pieces on both its sides, which is what rounds the profile
	std::vector<double> grades(count + 1);
	grades.front() = (Startgrade != nullptr ? *Startgrade : slopes.front());
	grades.back() = (Endgrade != nullptr ? *Endgrade : slopes.back());
	for (std::size_t i = 1; i < count; ++i)
	{
		auto const before{slopes[i - 1]};
		auto const after{slopes[i]};
		if (before * after <= 0.0)
		{
			// a crest or a bottom
			grades[i] = 0.0;
			continue;
		}
		auto grade{(before * lengths[i] + after * lengths[i - 1]) / (lengths[i - 1] + lengths[i])};
		// kept from overshooting the heights the road is led through
		auto const limit{3.0 * std::min(std::abs(before), std::abs(after))};
		grades[i] = std::clamp(grade, -limit, limit);
	}
	for (std::size_t i = 0; i < count; ++i)
	{
		auto &piece{Pieces[i]};
		auto &start{piece.points[segment_data::point::start]};
		auto &end{piece.points[segment_data::point::end]};
		auto &control1{piece.points[segment_data::point::control1]};
		auto &control2{piece.points[segment_data::point::control2]};
		start.y = Heights[i];
		end.y = Heights[i + 1];
		if (control1 == glm::dvec3{0.0} && control2 == glm::dvec3{0.0})
		{
			if (std::abs(grades[i] - slopes[i]) < 1e-4 && std::abs(grades[i + 1] - slopes[i]) < 1e-4)
				continue; // even slope, the piece stays a plain straight
			// a straight needs its control points spelled out to bend up or down
			control1 = (end - start) / 3.0;
			control2 = (start - end) / 3.0;
		}
		control1.y = grades[i] * glm::length(glm::dvec2{control1.x, control1.z});
		control2.y = -grades[i + 1] * glm::length(glm::dvec2{control2.x, control2.z});
	}
}

double editor_road::junction_reach(int const Lanes, float const Width)
{
	// half of the road, and room for the corners
	return 0.5 * std::max(1, Lanes) * Width + 6.0;
}

junction_node::state editor_road::junction(junction_kind const Kind, glm::dvec3 const &Entry, glm::dvec2 const &Heading, int const Incoming, int const Outgoing, float const Width)
{
	junction_node::state state;
	auto const heading{glm::length(Heading) > 1e-6 ? glm::normalize(Heading) : glm::dvec2{0.0, 1.0}};
	glm::dvec2 const left{heading.y, -heading.x};
	auto const reach{junction_reach(Incoming + Outgoing, Width)};
	auto const spot = [&](glm::dvec2 const &Direction, double const Distance) { return glm::dvec3{Entry.x + Direction.x * Distance, Entry.y, Entry.z + Direction.y * Distance}; };
	state.centre = spot(heading, reach);
	auto const arm = [&](glm::dvec2 const &Direction, int const In, int const Out) {
		junction_node::arm_data data;
		data.position = glm::dvec3{state.centre.x + Direction.x * reach, Entry.y, state.centre.z + Direction.y * reach};
		data.direction = Direction;
		data.incoming = In;
		data.outgoing = Out;
		data.width = Width;
		state.arms.emplace_back(data);
	};
	// the road the junction is entered by, then the others: what comes in by one leaves by them
	arm(-heading, Incoming, Outgoing);
	if (Kind == junction_kind::cross || Kind == junction_kind::tee_left || Kind == junction_kind::tee_right)
		arm(heading, Outgoing, Incoming);
	if (Kind == junction_kind::cross || Kind == junction_kind::tee_sides || Kind == junction_kind::tee_left)
		arm(left, Outgoing, Incoming);
	if (Kind == junction_kind::cross || Kind == junction_kind::tee_sides || Kind == junction_kind::tee_right)
		arm(-left, Outgoing, Incoming);
	state.normalize();
	return state;
}

std::vector<std::string> const &editor_road::materials()
{
	static std::vector<std::string> names;
	static bool scanned{false};
	if (scanned)
		return names;
	scanned = true;
	std::set<std::string> found;
	std::error_code error;
	for (std::filesystem::directory_iterator file{Global.asCurrentTexturePath, std::filesystem::directory_options::skip_permission_denied, error}, end; file != end; file.increment(error))
	{
		if (error || false == file->is_regular_file(error))
			continue;
		auto extension{file->path().extension().string()};
		std::transform(extension.begin(), extension.end(), extension.begin(), [](unsigned char c) { return static_cast<char>(std::tolower(c)); });
		if (extension != ".mat" && extension != ".dds" && extension != ".tga" && extension != ".png" && extension != ".bmp" && extension != ".jpg" && extension != ".ktx" && extension != ".tex")
			continue;
		auto name{file->path().stem().string()};
		std::transform(name.begin(), name.end(), name.begin(), [](unsigned char c) { return static_cast<char>(std::tolower(c)); });
		// names with spaces can't be put in a scenery file
		if (name.empty() || name.find(' ') != std::string::npos)
			continue;
		found.emplace(name);
	}
	names.assign(found.begin(), found.end());
	return names;
}