--[[
This file is part of Courseplay (https://github.com/Courseplay/courseplay)
Copyright (C) 2018 Peter Vajko

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program 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
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.
]]

--
--  Geometry functions. No dependency on track/field/FS/courseplay
--  2D functions in the x,y plane
--


-- a point has the following attributes:
-- x
-- y
-- prevEdge : vector from the previous to this point
-- nextEdge : vector from this point to the next
-- tangent : the tangent vector of the curve at this point,
--           calculated as the vector between the 
--           the previous and next points
-- directionStats : edge lengths per direction range, used
--                  to figure out the longest edge, or, the
--                  optimum direction of tracks
--                  The key in this table is a 20 degree wide range
--                  between -180 and +180, the value is the total
--                  length of edges pointing in that range

-- TODO: make point a real class
local function pointToString(p)
	local fromAngle, toAngle = 'N/A', 'N/A'
	if p.nextEdge then
		toAngle = string.format('%.1f', math.deg(p.nextEdge.angle))
	end
	if p.prevEdge then
		fromAngle = string.format('%.1f', math.deg(p.prevEdge.angle))
	end
	local turn = p.turnStart and ' (start)' or ''
	turn = p.turnEnd and ' (end)' or turn
	return string.format('x=%.1f y=%.1f %s -> %s',
			p.x, p.y, fromAngle, toAngle) .. (p.reverse and '(rev)' or '' .. turn)
end

-- calculates the polar coordinates of x, y with some filtering
-- around pi/2 where tan is infinite
function toPolar( x, y )
	local length = math.sqrt( x * x + y * y )
	local bigEnough = 1000
	if ( x == 0 ) or ( math.abs( y/x ) > bigEnough ) then
		-- pi/2 or -pi/2
		if y >= 0 then
			return math.pi / 2, length  -- north
		else
			return - math.pi / 2, length -- south
		end
	else
		return math.atan2( y, x ), length
	end
end

function getDistanceBetweenPoints( p1, p2 )
	local dx = p2.x - p1.x
	local dy = p2.y - p1.y
	return math.sqrt( dx * dx + dy * dy )
end

--- Add a vector defined by polar coordinates to a point
-- @param point x and y coordinates of point
-- @param angle angle of polar vector
-- @param length length of polar vector
-- @return x and y of the resulting point
function addPolarVectorToPoint( point, angle, length )
	return { x = point.x + length * math.cos( angle ),
	         y = point.y + length * math.sin( angle )}
end

function normalizeAngle( a )
	return a >= 0 and a or 2 * math.pi + a
end
--- Get the average of two angles. 
-- Works fine even for the transition from -pi/2 to +pi/2
function getAverageAngle( a1, a2 )
	-- convert the 0 - -180 range into 180 - 360
	if math.abs( a1 - a2 ) > math.pi then
		a1 = normalizeAngle( a1 )
		a2 = normalizeAngle( a2 )
	end
	-- calculate average in this range
	local avg = ( a1 + a2 ) / 2
	-- convert back to 0 - -180 if necessary
	if avg > math.pi then avg = avg - 2 * math.pi end
	return avg
end

--- Get difference between two angles, even through 
-- -pi/2 and + pi/2
function getDeltaAngle( a1, a2 )
	-- convert the 0 - -180 range into 180 - 360
		if math.abs( a1 - a2 ) > math.pi then
		a1 = normalizeAngle( a1 )
		a2 = normalizeAngle( a2 )
	end
	-- calculate difference in this range
	return a2 - a1
end


function translatePoint(p, dx, dy)
	p.x = p.x + dx
	p.y = p.y + dy
end

function rotatePoint(p, angle)
	p.x, p.y = p.x * math.cos(angle) - p.y  * math.sin(angle), p.x * math.sin(angle) + p.y  * math.cos(angle)
end

-- TODO: put this into Polyline
--- This is kind of a low pass filter. If the 
-- direction change to the  next point is too big, 
-- the last point is removed
-- If the distance to the next point is less than distanceThreshold,
-- the current point is removed and the next one is replaced with a 
-- point between the current and the next.
function applyLowPassFilter( polygon, angleThreshold, distanceThreshold )
	local index = 1
	while index <= #polygon do
		local cp, np = polygon[ index], polygon[ index + 1 ]
		local isTooClose, isTooSharp = false, false
		if cp and np and cp.prevEdge and np.prevEdge then
			-- need to recalculate the edge length as we are moving points
			-- around here
			local angle, length = toPolar( np.x - cp.x, np.y - cp.y )
			isTooClose = length < distanceThreshold
			isTooSharp =  math.abs( getDeltaAngle( np.prevEdge.angle, cp.prevEdge.angle )) > angleThreshold
			if isTooClose or isTooSharp then
				-- replace current and next point with something in the middle
				polygon[ index + 1 ].x, polygon[ index + 1 ].y = getPointInTheMiddle( cp, np )
			end
		end
		if isTooSharp or isTooClose then
			table.remove( polygon, polygon:getIndex( index ))
			polygon:calculateData()
		else
			index = index + 1
		end
	end
end

-- TODO: put this into Polyline
--- make sure points in line are at least d apart
-- except in curves 
function space( line, angleThreshold, d )
	local result = Polyline:new({ line[ 1 ]})
	for i = 2, #line - 1 do
		local cp, pp = line[ i ], result[ #result ]
		local isCurve = math.abs( getDeltaAngle( cp.nextEdge.angle, pp.nextEdge.angle )) > angleThreshold
		if getDistanceBetweenPoints( cp, pp ) > d or isCurve then
			table.insert( result, cp )
		end
	end
	return result
end


--- Round corners of a polygon to turningRadius
--
function roundCorners( polygon, turnRadius )
	local needsArc = false
	local cIx = 1 -- current
	local nIx = cIx + 1 -- next
	while cIx <= #polygon do
		polygon[ cIx ].text = cIx
		local lookaheadDistance, lookbackDistance = 0, 0
		-- can we get from the current point to the next?
		while turnRadius > getTurningRadiusBetweenTwoPoints( polygon[ cIx ], polygon[ nIx ], turnRadius ) do
			nIx, lookaheadDistance, cIx, lookbackDistance = getNextWpPairToCheck( polygon, nIx, lookaheadDistance, cIx, lookbackDistance )
			if nIx > #polygon or cIx < 1 then
				-- don't want to deal with rollover, there'll be no rounding at the beginning/end of polygon for now
				needsArc = false
				break
			else
				needsArc = true
			end
		end
		if needsArc then
			needsArc = false
			nIx = polygon:replacePointsWithArc( cIx, nIx, turnRadius )
		end
		cIx = nIx
		nIx = cIx + 1 
	end
	polygon:calculateData()
	-- We have trouble with rounding tight S turns so clean up the resulting glitches.
	polygon:removeGlitches()
end

--- If we find that we can't drive to the next waypoint with our turning radius then we
-- check if we can drive to the one after the next or the one before the current. If that
-- still does not work then we go further forward and backwards, based on the distance from
-- the current wp.
function getNextWpPairToCheck( polygon, fwdIx, lookaheadDistance, backIx, lookbackDistance )
	local fD = polygon[ fwdIx ].nextEdge.length
	local bD = polygon[ backIx ].prevEdge.length
	if lookaheadDistance + fD < lookbackDistance + bD then
		-- extend our window forward
		return fwdIx + 1, lookaheadDistance + fD, backIx, lookbackDistance
	else
		-- extend our window backwards
		return fwdIx, lookaheadDistance, backIx - 1, lookbackDistance + bD
	end
end

-- get the theoretical turning radius we need to go from 'from' to 'to', 
-- starting in the from.prevEdge.angle direction and ending up in 
-- to.nextEdge.angle
function getTurningRadiusBetweenTwoPoints( from, to, targetRadius )
	local dA = getDeltaAngle( to.nextEdge.angle, from.prevEdge.angle )
	-- TODO: this is true only if the two points are nearly on the same line
	if math.abs( dA ) < math.rad( 5 ) then return math.huge end
	-- find intersection of the two edges, extend them by at least 5 m so they intersect even with
	-- very small radius
	local is = getIntersectionOfExtendedEdges( from.prevEdge, to.nextEdge, math.max(5, targetRadius * math.pi * 2 ))
	if is then
		local dFrom = getDistanceBetweenPoints( from, is )
		local dTo = getDistanceBetweenPoints( to, is )
		local r = math.abs( math.min( dFrom, dTo ) / math.tan( dA / 2 ))
		return r
	else
		return 0
	end
end

function addToDirectionStats( directionStats, angle, length )
	local width = 2
	-- normalize angle
	local a = math.deg( angle )
	a = a < 0 and ( a + 180 ) or a
	a = a % 180
	local range = math.floor( a / width ) * width + width / 2
	if directionStats[ range ] then
		directionStats[ range ].length = directionStats[ range ].length + length
		table.insert( directionStats[ range ].dirs, a )
	else
		directionStats[ range ] = { length=0, dirs={ a }}
	end
end

--- Trying to figure out in which direction 
-- the field is the longest.
function getBestDirection( directionStats )
	local best = { range = 0, length = 0 }
	-- find the angle range which has to most length
	for range, stats in pairs( directionStats ) do
		if stats.length > best.length then
			best.length = stats.length
			best.range = range
		end
	end
	local sum = 0
	-- calculate the average direction of the best range
	if directionStats[ best.range ] then
		for i, dir in ipairs( directionStats[ best.range ].dirs ) do
			sum = sum + dir
		end
		best.dir = math.floor( sum / #directionStats[ best.range ].dirs + 0.5 )
	end
	return best
end

--- Same as getIntersectionWithLine but returns all
-- intersections in a table
function getAllIntersectionsOfLineAndPolygon( polygon, p1, p2 )
	local intersections = {}
	-- loop through the polygon and check each vector from
	-- the current point to the next
	for i, cp in polygon:iterator() do
		local np = polygon[ i + 1 ]
		local intersectionPoint = getIntersection( cp.x, cp.y, np.x, np.y, p1.x, p1.y, p2.x, p2.y )
		if intersectionPoint then
			-- only add if this is not found already. Can happen if the p1-p2 goes right through
			-- a vertex of the polygon, so it getIntersection will be true for two edges of the polygon
			local found = false
			for i, p in ipairs( intersections ) do
				found = getDistanceBetweenPoints( p.point, intersectionPoint ) < 0.1
			end
			if not found then
				table.insert( intersections, { fromIx = i, toIx = polygon:getIndex( i + 1 ), point = intersectionPoint,
				                               d = getDistanceBetweenPoints( p1, intersectionPoint )})
			end
		end
	end
	-- now bubble sort the intersection points by they distance from p1 so the one closest
	-- to p1 is the first in the table
	for i = 1, #intersections -1 do
		if intersections[ i + 1 ].d < intersections[ i ].d then
			intersections[ i ], intersections[ i + 1 ] = intersections[ i + 1 ], intersections[ i ]
		end
	end
	return intersections
end

--- Find the points of an arc with radius r connecting to 
--  edges of a polygon.
--  e1, e2 are the edges like in calculatePolygonData
--  and we assume that as we walk around the polygon with increasing
--  vertice indexes, e1 comes first, then e2.
--  We want to use this to round sharp edges of polygon.
--
function findArcBetweenEdges( e1, e2, r )
	-- first, find the intersection of ab and cd. We most likely
	-- have to make them longer, as they are edges of a polygon
	-- lengthen ab forward and cd backwards by double radius
	-- calculate distance from 'is' to the point where a circle
	-- with r radius would touch ab/cd
	local is = getIntersectionOfExtendedEdges( e1, e2, 20 * r * math.pi )
	if is == nil then return nil end
	-- need to reverse one of the edges to get the correct angle between the two
	local alpha = getDeltaAngle( reverseAngle( e1.angle ), e2.angle )
	-- this is how far from 'is' the circle touches the e1 e2 lines
	local d = math.abs( r / math.tan( alpha / 2 ))
	-- our edges must be at least d distance from 'is' to be able
	-- to connect them with an arc
	local e1ToIs = getDistanceBetweenPoints( e1.to, is )
	local isToE2 = getDistanceBetweenPoints( is, e2.from )
	if lt( e1ToIs, d ) or lt( isToE2, d ) then
		return nil
	end
	-- start adding waypoints between e1.to and e2.from.
	-- first, go straight until we are exactly at d from is
	local delta = e1ToIs - d
	local points = Polyline:new()
	addStraightSectionToVertex( points, e1.to, e1.angle, delta )
	-- from here, go around in an arc until we are heading to e2.angle
	alpha = getDeltaAngle( e1.angle, e2.angle )
	-- do about x degree steps
	local nSteps = math.abs( math.floor( alpha * 30 / ( 2 * math.pi )))
	-- sanity check. Due to our lousy calculations we may end up here trying to generate an
	-- arc for just a few degree turn. This then results in weird artifacts like spikes. This
	-- is mainly becuase we don't handle cleanly the case where the intersection of e1 and e2
	-- is _behind_ e1.
	if math.abs(alpha) < math.pi / 12 then return nil end
	-- delta angle for one step
	local deltaAlpha = alpha / ( nSteps + 1 )
	-- length of a step, with a magic constant to cover up the calculation errors
	-- during the arc construction, without this we always seem to overshoot a bit
	local length = 2 * r * math.abs( math.sin( alpha / nSteps / 2 )) * 0.975
	local currentAlpha = e1.angle + deltaAlpha
	-- now walk around the arc
	local p = points[ #points ]
	for n = 1, nSteps, 1 do
		p = addPolarVectorToPoint( p, currentAlpha, length )
		table.insert( points, p )
		currentAlpha = currentAlpha + deltaAlpha
	end
	-- now add waypoints to the end if needed
	delta = isToE2 - d
	-- continue walking straight to the last wp if not close enough already
	if delta > CourseGenerator.waypointDistance / 4 then
		addStraightSectionToVertex( points, points[ #points ], currentAlpha, delta )
	end
	return points
end

-- lengthen an edge with delta. Make sure there's a waypoint
-- every CourseGenerator.waypointDistance meters.
function addStraightSectionToVertex( points, vertex, angle, delta )
	local d, n = delta, 1
	if delta > CourseGenerator.waypointDistance then
		n = math.floor( math.abs( delta ) / CourseGenerator.waypointDistance ) + 1
		d = delta / n
	end
	local dist = 0
	for i = 1, n do
		dist = dist + d
		local p = addPolarVectorToPoint( vertex, angle, dist )
		table.insert( points, p )
	end
end

-- Find the intersection of ab and cd. We extend them both with
-- extensionLength, ab forward, cd backwards as they are edges 
-- of a polygon
function getIntersectionOfExtendedEdges( e1, e2, extensionLength )
	local e1_to_x = e1.to.x + extensionLength * e1.dx / e1.length
	local e1_to_y = e1.to.y + extensionLength * e1.dy / e1.length
	local e2_from_x = e2.from.x - extensionLength * e2.dx / e2.length
	local e2_from_y = e2.from.y - extensionLength * e2.dy / e2.length
	-- see if they intersect now
	local is = getIntersection( e1.from.x, e1.from.y, e1_to_x, e1_to_y, e2_from_x, e2_from_y, e2.to.x, e2.to.y )
	return is
end

function getIntersection(A1x, A1y, A2x, A2y, B1x, B1y, B2x, B2y)
	local s1_x, s1_y, s2_x, s2_y ;
	s1_x = A2x - A1x;
	s1_y = A2y - A1y;
	s2_x = B2x - B1x;
	s2_y = B2y - B1y;

	local s, t;
	s = (-s1_y * (A1x - B1x) + s1_x * (A1y - B1y)) / (-s2_x * s1_y + s1_x * s2_y);
	t = ( s2_x * (A1y - B1y) - s2_y * (A1x - B1x)) / (-s2_x * s1_y + s1_x * s2_y);

	if (s >= 0 and s <= 1 and t >= 0 and t <= 1) then
		--Collision detected
		local x = A1x + (t * s1_x);
		local y = A1y + (t * s1_y);
		return { x = x, y = y };
	end;

	--No collision
	return nil;
end;

function createRectangularPolygon( x, y, dx, dy, step )
	local rect = {}
	for ix = x, x + dx, step do
		table.insert( rect, { x = ix, y = y })
	end
	for iy = y + step, y + dy, step do
		table.insert( rect, { x = x + dx, y = iy })
	end
	for ix = x + dx - step, x, -step do
		table.insert( rect, { x = ix, y = y + dy })
	end
	for iy = y + dy - step, y, -step do
		table.insert( rect, { x = x, y = iy })
	end
	return rect
end

-- TODO: put this into Polyline

function translatePoints( points, dx, dy )
	local result = Polygon:new()
	for i, point in points:iterator() do
		local newPoint = shallowCopy( point )
		newPoint.x = points[ i ].x + dx
		newPoint.y = points[ i ].y + dy
		table.insert( result, newPoint )
	end
	return result
end

-- TODO: put this into Polyline

function rotatePoints( points, angle )
	local result = Polygon:new()
	local sin = math.sin( angle )
	local cos = math.cos( angle )
	for i, point in points:iterator() do
		local newPoint = shallowCopy( point )
		newPoint.x = points[ i ].x * cos - points[ i ].y  * sin
		newPoint.y = points[ i ].x * sin + points[ i ].y  * cos
		table.insert( result, newPoint )
	end
	result.boundingBox = result:getBoundingBox()
	return result
end

--- Reverse elements of an array
function reverse( t )
	local result = {}
	for i = #t, 1, -1 do
		table.insert( result, t[ i ])
	end
	return result
end

function reverseAngle( angle )
	local r = angle + math.pi
	if r > math.pi * 2 then
		r = r - math.pi * 2
	end
	return r
end

function getInwardDirection( isClockwise, angle )
	if not angle then
		angle = math.pi / 2
	end
	if isClockwise then
		return -1 * angle
	else
		return angle
	end
end

function getOutwardDirection( isClockwise, angle )
	return - getInwardDirection( isClockwise, angle )
end

-- shallow copy for preserving point attributes through 
-- transformations
function shallowCopy( point )
	local result = {}
	for k, v in pairs( point ) do
		result[ k ] = v
	end
	return result
end

-- this is from courseplay/helper.lua, should be removed once integrated with courseplay
function deepCopy(tab, recursive)
	-- note that if 'recursive' is not 'true', only tab is copied.
	-- if tab contains tables itself again, these tables are not copied
	-- but referenced again (the reference is copied).
	local result = {};
	for k,v in pairs(tab) do
		if recursive and type(v) == 'table' then
			result[k] = deepCopy(v, recursive);
		else
			result[k] = v;
		end;
	end;
	return result;
end;

function getPointInTheMiddle( a, b )
	return a.x + (( b.x - a.x ) / 2 ),
	a.y + (( b.y - a.y ) / 2 )
end

function getPointBetween( a, b, dFromA )
	local dx, dy = b.x - a.x, b.y - a.y
	local ratio = dFromA / math.sqrt( dx * dx + dy * dy )
	return a.x + (( b.x - a.x ) * ratio ),
	a.y + (( b.y - a.y ) * ratio )
end


function printTable( t )
	if not t then print('nil') return end
	for key, value in pairs( t ) do
		print( key, value )
	end
end

--- Less than operator with limited precision
-- to tolerate floating point precision errors
function lt( a, b )
	-- for courseplay, we are calculating in meters, so
	-- we are fine with one millimeter precision
	local epsilon = 0.001
	return a < ( b - epsilon )
end

--- Classes (these should all be in their own files but require does not 
-- work in the Giants engine so all files must be explicetly loaded with source()
-- and every single file added to courseplay.lua)

-- for 5.1 and 5.2 compatibility
local unpack = unpack or table.unpack
-------------------------------------------------------------------------------

-------------------------------------------------------------------------------

---@class Polyline
Polyline = {}
Polyline.__index = Polyline

--- Polyline constructor.
-- Integer indices are the vertices of the polygon
function Polyline:new( vertices )
	local newPolyline
	if vertices then
		newPolyline = { unpack( vertices ) }
	else
		newPolyline = {}
	end
	return setmetatable( newPolyline, self )
end

--- Create an empty clone of myself
function Polyline:cloneEmpty()
	local newPolyline = {}
	return setmetatable( newPolyline, getmetatable(self))
end


function Polyline:copy( other )
	local newPolyline = {}
	for i, p in other:iterator() do
		newPolyline[ i ] = shallowCopy( p )
	end
	return setmetatable( newPolyline, self )
end

function Polyline:__tostring()
	local result = ''
	for i, p in self:iterator() do
		result = result .. string.format('% 4d %s\n', i, pointToString(p))
	end
	return result
end

function Polyline:getIndex(index)
	return math.max(0, math.min(index, #self))
end

--- Iterator that won't return nil for i < 1 and i > size
function Polyline:iterator( from, to, step )
	local s = step or 1
	local i, n
	if s > 0 then
		i = from and math.max( from, 1 ) or 1
		n = to and math.min( to, #self ) or #self
	else
		i = from and math.min( from, #self ) or #self
		n = to and math.max( to, 1 ) or 1
	end
	local lastOne = false
	return function()
		if ( not lastOne and #self > 0 ) then
			if s > 0 then
				lastOne = i >= n
			else
				lastOne = i <= n
			end
			local key, value = i, self[ i ]
			i = i + s
			return key, value
		end
	end
end

function Polyline:add(p)
	table.insert(self, p)
end

---@param delta number threshold for comparison, any difference less than delta is ignored
function Polyline:getClosestPointIndex(p, delta)
	delta = delta or 0
	local minDistance = math.huge
	local ix
	for i, vertex in self:iterator() do
		local d = getDistanceBetweenPoints(vertex, p)
		if d < minDistance and minDistance - d >= delta then
			minDistance = d
			ix = i
		end
	end
	return ix, minDistance
end

function Polyline:getIteratorParamsFromEndClosestToPoint(point)
	local dFromStart = getDistanceBetweenPoints(point, self[1])
	local dFromEnd = getDistanceBetweenPoints(point, self[#self])
	local startIx = dFromStart <= dFromEnd and 1 or #self
	local endIx = dFromStart > dFromEnd and 1 or #self
	local step = dFromStart <= dFromEnd and 1 or -1
	return startIx, endIx, step
end

--- Iterate starting at the end closest to point
function Polyline:iteratorFromEndClosestToPoint(point)
	local startIx, endIx, step = self:getIteratorParamsFromEndClosestToPoint(point)
	return self:iterator(startIx, endIx, step)
end

--- Iterator to iterate over the edges of a polyline/polygon.
-- will return #self - 1 edges for a polyline, #self edges for the
-- polygon as it wraps around then.
function Polyline:edgeIterator()
	local i = 1
	return function()
		if ( i <= #self and self[i].nextEdge and #self > 1 ) then
			local key,value, from = i, self[i].nextEdge, self[i]
			i = i + 1
			return key, value, from
		else
			return nil, nil, nil
		end
	end
end

function Polyline:calculateData()
	local directionStats = {}
	local dAngle = 0
	local area = 0
	local circumference = 0
	local shortestEdgeLength = 1000
	local dx, dy, angle, length
	for i, point in self:iterator() do
		point.prevEdge, point.nextEdge = nil, nil
		local pp, cp, np = self[ i - 1 ], self[ i ], self[ i + 1 ]
		if pp then
			-- vector from the previous to this point
			dx = cp.x - pp.x
			dy = cp.y - pp.y
			angle, length = toPolar( dx, dy )
			self[ i ].prevEdge = { from=pp , to=cp, angle=angle, length=length, dx=dx, dy=dy }
			if length < shortestEdgeLength then shortestEdgeLength = length end
			-- detect clockwise/counterclockwise direction
			if pp.prevEdge and cp.prevEdge then
				if pp.prevEdge.angle and cp.prevEdge.angle then
					dAngle = dAngle + getDeltaAngle( cp.prevEdge.angle, pp.prevEdge.angle )
				end
			end
		end
		if np then
			-- vector from this to the next point
			dx = np.x - cp.x
			dy = np.y - cp.y
			angle, length = toPolar( dx, dy )
			self[ i ].nextEdge = { from = cp, to = np, angle=angle, length=length, dx=dx, dy=dy }
			if length < shortestEdgeLength then shortestEdgeLength = length end
			addToDirectionStats( directionStats, angle, length )
			area = area + ( cp.x * np.y - cp.y * np.x )
			circumference = circumference + length
		end
		if pp and np then
			-- vector from the previous to the next point
			dx = np.x - pp.x
			dy = np.y - pp.y
			angle, length = toPolar( dx, dy )
			self[ i ].tangent = { angle=angle, length=length, dx=dx, dy=dy }
			self[ i ].deltaAngle = getDeltaAngle( self[ i ].nextEdge.angle, self[ i ].prevEdge.angle )
			self[ i ].radius = math.abs( self[ i ].nextEdge.length / ( 2 * math.asin( self[ i ].deltaAngle / 2 )))
		end
	end
	self.directionStats = directionStats
	self.bestDirection = getBestDirection( directionStats )
	self.isClockwise = dAngle > 0
	self.area = self.isClockwise and - area / 2 or area / 2
	self.circumference = circumference
	self.shortestEdgeLength = shortestEdgeLength
	self.boundingBox = self:getBoundingBox()
end

function Polyline:getBoundingBox()
	local minX, maxX, minY, maxY = math.huge, -math.huge, math.huge, -math.huge
	for i, point in self:iterator() do
		if ( point.x < minX ) then minX = point.x end
		if ( point.y < minY ) then minY = point.y end
		if ( point.x > maxX ) then maxX = point.x end
		if ( point.y > maxY ) then maxY = point.y end
	end
	return { minX=minX, maxX=maxX, minY=minY, maxY=maxY }
end

--- Get center of bounding box
function Polyline:getCenter()
	local bb = self:getBoundingBox()
	return ( bb.maxX + bb.minX ) / 2, ( bb.maxY + bb.minY ) / 2
end

function Polyline:hasTurnWaypoint( iterator )
	for _, p in ( iterator or self:iterator()) do
		if p.turnStart or p.turnEnd then
			return true
		end
	end
	return false
end

--- Replace the points in the line between to indices with
-- an arc with radius r
function Polyline:replacePointsWithArc( fromIx, toIx, r )
	local arc = findArcBetweenEdges( self[ fromIx ].prevEdge, self[ toIx ].nextEdge, r )
	if not arc then return toIx end
	-- remove old vertices
	self:removeElementsBetween( self:getIndex(fromIx + 1), toIx )
	local targetIx = self:getIndex(fromIx + 1)
	-- add the arc instead
	for i, p in ipairs( arc ) do
		table.insert( self, targetIx, p )
		targetIx = self:getIndex(targetIx + 1)
	end
	self:calculateData()
	-- continue with the next vertex after the curve,
	-- TODO: will this work at the end of the line?
	return self:getIndex(targetIx + 1)
end

--- Return the section of self starting at the vertex closest to point a and ending at the vertex closest to b
---@param delta number when searching for the polyline points closest to a and b, use delta as a threshold
--- this is to solve the issue when working on overlapping headlands (where the connection track overlaps with
--- the first part of the headland) in a multitool situation, where the headland is calculated as an offset course
--- and the overlapping part will not have the exact same coordinates (like the vanilla generated course would have).
--- In this case it is possible that one of startIx or endIx are on the overlap, the other on the non-overlap part,
--- resulting in a section going through the first point.
--- Alternatively, we could write getClosestPointIndex() so that it detects overlaps and stops the loop after a full
--- circle, but it is part of Polyline that should not know about overlaps...
function Polyline:getSectionBetweenPoints(a, b, delta)
	local startIx = self:getClosestPointIndex(a, delta)
	local endIx = self:getClosestPointIndex(b, delta)
	local section = Polyline:new()
	local i = 1
	for _, p in self:iteratorClosestDistance(startIx, endIx) do
		table.insert(section, p)
		i = i + 1
	end
	return section
end

-- spline functions: smooth, tuck and refine
-- http://stackoverflow.com/questions/29612584/creating-cubic-and-or-quadratic-bezier-curves-to-fit-a-path

-- insert a point in the middle of each edge.
function Polyline:refine( iterator, minSmoothAngle, maxSmoothAngle )
	local pointsToInsert = {}
	-- iterate through the existing table but do not insert the 
	-- new points, only remember the index where they would end up
	-- (as we do not want to modify the table while iterating)
	local ix = -1
	for i, _ in iterator do
		-- initialize ix to the first value of i
		if ix < 0 then ix = i end
		if self[ i + 1 ] and self[ i ].deltaAngle then
			if math.abs( self[ i ].deltaAngle ) > minSmoothAngle and
				math.abs( self[ i ].deltaAngle ) < maxSmoothAngle then
				-- insert points only when there is really a curve here
				-- also, preserve all attributes of the point
				local newPoint = shallowCopy( self[ i ])
				newPoint.x, newPoint.y =  getPointInTheMiddle( self[ i ], self[ i + 1 ])
				newPoint.text = 'refined'
				newPoint.smoothed = true
				ix = ix + 1
				table.insert( pointsToInsert, { ix = ix, point = newPoint })
			end
		end
		self[ i ].smoothed = true
		ix = ix + 1;
	end
	for _, p in ipairs( pointsToInsert ) do
		table.insert( self, p.ix, p.point )
	end
	self:calculateData()
end

-- move the current point a bit towards the previous and next. 
function Polyline:tuck( iterator, s, minSmoothAngle, maxSmoothAngle )
	for i, _ in iterator do
		local pp, cp, np = self[ i - 1 ], self[ i ], self[ i + 1 ]
		-- tuck points only when there is really a curve here
		-- but if this is a line, don't touch the ends
		if pp and np and
			math.abs( self[ i ].deltaAngle ) > minSmoothAngle and
			math.abs( self[ i ].deltaAngle ) < maxSmoothAngle then
			-- mid point between the previous and next
			local midPNx, midPNy = getPointInTheMiddle( pp, np )
			-- vector from current point to mid point
			local mx, my = midPNx - cp.x, midPNy - cp.y
			-- move current point towards (or away from) the midpoint by the factor s
			self[ i ].x = cp.x + mx * s
			self[ i ].y = cp.y + my * s
		end
	end
	self:calculateData()
end

function Polyline:smooth( minSmoothAngle, maxSmoothAngle, order, from, to )
	if ( order <= 0  ) then
		return
	else
		local origSize = #self
		self:refine( self:iterator( from, to ), minSmoothAngle, maxSmoothAngle )
		-- if refine added waypoints we need to extend the range
		if to then to = to + #self - origSize end
		self:tuck( self:iterator( from, to ), 0.5, minSmoothAngle, maxSmoothAngle )
		self:tuck( self:iterator( from, to ), -0.15, minSmoothAngle, maxSmoothAngle )
		return self:smooth( minSmoothAngle, maxSmoothAngle, order - 1, from, to )
	end
end

--- In place translation
function Polyline:translate( dx, dy )
	for i, point in self:iterator() do
		point.x = point.x + dx
		point.y = point.y + dy
	end
	self:calculateData()
end

--- In place rotation
function Polyline:rotate( angle )
	local sin = math.sin( angle )
	local cos = math.cos( angle )
	for _, point in self:iterator() do
		point.x, point.y = point.x * cos - point.y  * sin, point.x * sin + point.y  * cos
	end
	self:calculateData()
end


function Polyline:space( angleThreshold, d )
	local i = 2
	while i < #self do
		local cp, pp = self[ i ], self[ i - 1 ]
		-- don't remove points around curves and direction changes
		local isCurve = math.abs( getDeltaAngle( cp.nextEdge.angle, pp.nextEdge.angle )) > angleThreshold
		local isDirectionChange = cp.rev or cp.reverse or pp.rev or pp.reverse
		if getDistanceBetweenPoints( cp, pp ) > d or isCurve or isDirectionChange then
			i = i + 1
		else
			table.remove( self, i )
		end
	end
	self:calculateData()
end

-- Yet another cleanup function to remove sudden and short direction changes
-- resulting from lousy calculations.
function Polyline:removeGlitches()
	local i = 2
	while i < #self do
		local cp, pp = self[ i ], self[ i - 1 ]
		local dA = math.abs( getDeltaAngle( pp.nextEdge.angle, pp.prevEdge.angle ))+
			math.abs( getDeltaAngle( cp.prevEdge.angle, cp.nextEdge.angle ))
		-- the direction changes a lot over two points, this is a glitch
		if dA > math.rad(270) then
			table.remove( self, i )
		else
			i = i + 1
		end
	end
	self:calculateData()
end

-- Remove neighbor with the same coordinates
function Polyline:removeOverlaps()
	local i = 2
	while i <= #self do
		local cp, pp = self[ i ], self[ i - 1 ]
		if cp.x == pp.x and cp.y == pp.y then
			table.remove( self, i )
		else
			i = i + 1
		end
	end
	self:calculateData()
end

--- Remove vertices between (and including) two indexes
--
function Polyline:removeElementsBetween( fromIx, toIx )
	local startIx = fromIx
	-- if interval rolls over, start removing vertices at the end
	if fromIx > toIx then
		local endIx = #self
		for ix = fromIx, endIx do
			table.remove( self, fromIx )
		end
		startIx = 1
	end
	for ix = startIx, toIx do
		table.remove( self, startIx )
	end
end

--- Replace vertices between (and including) two indexes
--- @param replacement Polyline
function Polyline:replaceElementsBetween(fromIx, toIx, replacement)
	self:removeElementsBetween(fromIx, toIx)
	for i, p in replacement:iterator() do
		table.insert(self, fromIx + i - 1, shallowCopy(p))
	end
	self:calculateData()
end

-- open line, no wrap around
function Polyline:canWrapAround()
	return false
end

-- Does the line defined by p1 and p2 intersect the polygon?
-- If yes, return two indices. The line intersects the polygon between
-- these two indices
function Polyline:getIntersectionWithLine(p1, p2)
	-- loop through the polygon and check each vector from
	-- the current point to the next
	for i, cp in self:iterator() do
		local np = self[ i + 1 ]
		if np then
			local interSectionPoint = getIntersection( cp.x, cp.y, np.x, np.y, p1.x, p1.y, p2.x, p2.y )
			if interSectionPoint then
				-- the line between p1 and p2 intersects the vector from cp to np
				return i, self:getIndex( i + 1 ), interSectionPoint
			end
		end
	end
	return nil, nil, nil
end

--- Append line to polyline. If they intersect, cut both at the intersection
-- if they don't, extend self's end and/or line's start until they intersect
-- line's start is the end closest to self's end.
-- if trimOnly is true, do not append line, only trim/extend self.
---@return index of the intersection point
function Polyline:appendLine(line, extensionLength, trimOnly, isRetry)
	local lineToAppend = Polyline:new()
	for i, p in line:iteratorFromEndClosestToPoint(self[#self]) do
		table.insert(lineToAppend, shallowCopy(p))
	end
	-- lineToAppend now has the points to append in the correct order
	-- see if it intersects us
	local from, to, is, at, isIx
	for i, p in self:iterator(#self, math.max(2, #self - 10), -1) do
		from, to, is = lineToAppend:getIntersectionWithLine(self[i], self[i - 1])
		at = i
		if is then break end
	end
	if is then
		-- we intersect lineToAppend between lineToAppend[from] and lineToAppend[to].
		for i = #self, at, -1 do
			-- remove points of self beyond the intersection
			table.remove(self, i)
		end
		-- add the intersection point
		table.insert(self, is)
		isIx = #self
		for i = 1, from do
			-- remove points of lineToAppend before the intersection
			table.remove(lineToAppend, 1)
		end
	else
		if isRetry then
			-- this is a recursion call because they did not intersect, we extended them but still
			-- don't intersect. So just return.
			CourseGenerator.debug('Could not append lines, they do not intersect even after extended')
			return
		end
		-- bummer, they do not intersect. So extend them both a bit and retry.
		lineToAppend:calculateData()
		local p = addPolarVectorToPoint(lineToAppend[1], lineToAppend[1].nextEdge.angle, -extensionLength)
		table.insert(lineToAppend, 1, p)
		self:calculateData()
		p = addPolarVectorToPoint(self[#self], self[#self].prevEdge.angle, extensionLength)
		table.insert(self, p)
		return self:appendLine(lineToAppend, extensionLength, trimOnly, true)
	end
	-- now append line
	if not trimOnly then
		for _, p in lineToAppend:iterator() do
			table.insert(self, p)
		end
	end
	return isIx
end

--- Trim section of polyline between its end and intersection with otherLine
---@param otherLine Polyline
---@param d number
function Polyline:trimEnd(otherLine, insertIntersectionPoint)
	local i = #self
	local from, to, is
	while i > 1 do
		from, to, is = otherLine:getIntersectionWithLine(self[i], self[i - 1])
		if is then
			for j = #self, i - 1, -1 do
				table.remove(self)
			end
			if insertIntersectionPoint then
				table.insert(self, is)
			end
			return
		end
		i = i - 1
	end
end

--- Shorten polyline by d
---@param d number
---@param cutOnly boolean Do not add a point at d, just remove everything in d distance
function Polyline:shortenEnd(d, cutOnly)
	local dCut = d
	local from = #self
	for i = from, 2, -1 do
		dCut = dCut - self[i - 1].nextEdge.length
		-- check for something else than zero to make sure the new point does not overlap with the last we did not cut
		if dCut < -0.1 then
			local p = addPolarVectorToPoint(self[i - 1], self[i - 1].nextEdge.angle, - dCut)
			table.remove(self)
			if not cutOnly then
				table.insert(self, p)
			end
			self:calculateData()
			return true
		end
		table.remove(self)
	end
end

--- Shorten polyline by d from start
---@param d number
function Polyline:shortenStart(d)
	local dCut = d
	local to = #self
	for i = 2, to do
		dCut = dCut - self[1].nextEdge.length
		-- check for something else than zero to make sure the new point does not overlap with the last we did not cut
		if dCut < -0.1 then
			local p = addPolarVectorToPoint(self[2], self[2].prevEdge.angle, dCut)
			table.remove(self, 1)
			table.insert(self, 1, p)
			self:calculateData()
			return true
		end
		table.remove(self, 1)
	end
end




----------------------------------------------------------------------------------
---@class Polygon : Polyline
Polygon = {}
-- base class is the polyline
setmetatable( Polygon, { __index = Polyline })
-- TODO: is this really the right way to inherit metamethods?
Polygon.__tostring = Polyline.__tostring

Polygon.__index = function( t, k )
	if not rawget( t, k ) and type( k ) == "number" then
		-- roll over integer indexes
		return rawget( t, t:getIndex( k ))
	else
		return Polygon[ k ]
	end
end

-- closed line, we can wrap around the ends
function Polygon:canWrapAround()
	return true
end

--- Always return a valid index to allow iterating over
-- the beginning or end of a closed polygon.
function Polygon:getIndex( index )
	index = index % #self
	if index == 0 then
		return #self
	else
		return index
	end
end

--- Iterate through elements of a polygon starting
-- between any from and to indexes with the given step.
-- This will do a full circle, that is, roll over from 
-- #polygon to 1 or 1 to #polygon if step < 0
function Polygon:iterator( from, to, step )
	local i = from and self:getIndex(from) or 1
	local n = to and self:getIndex(to) or #self
	local s = step or 1
	local lastOne = false
	return function()
		if ( not lastOne and #self > 0 ) then
			lastOne = ( i == n )
			local key, value = i, rawget( self, i )
			i = self:getIndex( i + s )
			return key, value
		end
	end
end

--- Remove vertices between (and including) two indexes
--
function Polygon:removeElementsBetween( fromIx, toIx )
	local lastIx
	if toIx < fromIx then
		-- overflow case, going around the end of the table
		lastIx = #self + toIx
	else
		lastIx = toIx
	end
	for ix = fromIx, lastIx do
		table.remove( self, self:getIndex( fromIx ))
	end
end

--- Iterate from startIx to endIx in the direction with the 
-- minimum number of steps
function Polygon:iteratorClosestDistance(startIx, endIx)
	local dPlus, dMinus
	if endIx >= startIx then
		dPlus = endIx - startIx
		dMinus = startIx + #self - endIx
	else
		dPlus = endIx + #self - startIx
		dMinus = startIx - endIx
	end
	local step = dPlus < dMinus and 1 or -1
	return self:iterator(startIx, endIx, step)
end

function Polygon:getSmallestRadiusWithinDistance(ix, dForward, dBackward, forwardStep)
	local i, dElapsed, minRadius = ix, 0, math.huge
	while dElapsed < dBackward do
		dElapsed = dElapsed + self[i].prevEdge.length
		minRadius = self[i].radius < minRadius and self[i].radius or minRadius
		i = i - forwardStep
	end
	i, dElapsed = ix, 0
	while dElapsed < dForward do
		dElapsed = dElapsed + self[i].nextEdge.length
		minRadius = self[i].radius < minRadius and self[i].radius or minRadius
		i = i + forwardStep
	end
	return minRadius
end