--
-- This file contains parts of pgfplotscoordprocessing.code.tex and pgfplotsplothandlers.code.tex .
--
-- It contains
--
-- pgfplots.Axis
-- pgfplots.Coord
-- pgfplots.Plothandler
-- 
-- and some related classes.

local math=math
local pgfplotsmath = pgfplots.pgfplotsmath
local type=type
local tostring=tostring
local error=error
local table=table
local pgfmathparse = pgfplots.pgfluamathparser.pgfmathparse

do
-- all globals will be read from/defined in pgfplots:
local _ENV = pgfplots
-----------------------------------

local pgftonumber =pgfluamathfunctions.tonumber

Coord = newClass()

function Coord:constructor()
    self.x = { nil, nil, nil }
    self.unboundedDir = nil
    self.meta= nil
    self.metatransformed = nil -- assigned during vis phase only
    self.unfiltered = nil
	self.pgfXY = nil -- assigned during visphase only
    return self
end

function Coord:copy(other)
	for i = 1,#other.x do self.x[i] = other.x[i] end
	self.meta = other.meta
	self.metatransformed = other.metatransformed
	self.unfiltered = nil -- not needed
end

function Coord:__tostring()
    local result = '(' .. stringOrDefault(self.x[1], "--") .. 
        ',' .. stringOrDefault(self.x[2], "--") .. 
        ',' .. stringOrDefault(self.x[3], "--") .. 
        ') [' .. stringOrDefault(self.meta, "--") .. ']'
    
    if not self.x[1] and self.unfiltered then
        result = result .. "(was " .. tostring(self.unfiltered) .. ")"
    end
    return result
end

local stringToFunctionMap = pgfluamathfunctions.stringToFunctionMap

-- a reference to a Coord which is returned by math expressions involving 'x', 'y', or 'z'
-- see surveystart()
local pseudoconstant_pt = nil
local function pseudoconstant_x() return pseudoconstant_pt.x[1] end
local function pseudoconstant_y() return pseudoconstant_pt.x[2] end
local function pseudoconstant_z() return pseudoconstant_pt.x[3] end
local function pseudoconstant_rawx() return pgftonumber(pseudoconstant_pt.unfiltered.x[1]) end
local function pseudoconstant_rawy() return pgftonumber(pseudoconstant_pt.unfiltered.x[2]) end
local function pseudoconstant_rawz() return pgftonumber(pseudoconstant_pt.unfiltered.x[3]) end
local function pseudoconstant_meta() return pseudoconstant_pt.meta end

-- @return the old value
local function updatePseudoConstants(pt)
	local old = pseudoconstant_pt
	pseudoconstant_pt = pt
	return old
end

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

LinearMap = newClass()

-- A map such that
-- [inMin,inMax] is mapped linearly to [outMin,outMax]
--
function LinearMap:constructor(inMin, inMax, outMin, outMax)
    if not inMin or not inMax or not outMin or not outMax then error("arguments must not be nil") end
	if inMin == inMax then
		self.map = function (x) return inMin end
	else
		if inMin > inMax then error("linear map received invalid input domain " .. tostring(inMin) .. ":" .. tostring(inMax)) end
		self.offset = outMin - (outMax-outMin)*inMin/(inMax-inMin)
		self.scale = (outMax-outMin)/(inMax-inMin)
	end
end

function LinearMap:map(x)
    return x*self.scale + self.offset
end

PointMetaMap = newClass()

function PointMetaMap:constructor(inMin,inMax, warnForfilterDiscards)
    if not inMin or not inMax or warnForfilterDiscards == nil then error("arguments must not be nil") end
    self._mapper = LinearMap.new(inMin,inMax, 0, 1000)
    self.warnForfilterDiscards = warnForfilterDiscards
end

function PointMetaMap:map(meta)
    if pgfplotsmath.isfinite(meta) then
        local result = self._mapper:map(meta)
        result = math.max(0, result)
        result = math.min(1000, result)
        return result
    else
        if self.warnForfilterDiscards then  
            log("The per point meta data '" .. tostring(meta) .. " (and probably others as well) is unbounded - using the minimum value instead.\n")
            self.warnForfilterDiscards=false
        end
        return 0
    end
end
    
    

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

-- Abstract base class of all plot handlers.
-- It offers basic functionality for the survey phase.
Plothandler = newClass()

-- @param name the plot handler's name (a string)
-- @param axis the parent axis
-- @param pointmetainputhandler an instance of PointMetaHandler or nil if there is none
function Plothandler:constructor(name, axis, pointmetainputhandler)
    if not name or not axis then
        error("arguments must not be nil")
    end
    self.axis = axis
    self.config = PlothandlerConfig.new()
    self.name = name
    self.coordindex = 0
    self.metamin = math.huge
    self.metamax = -math.huge
    self.autocomputeMetaMin = true
    self.autocomputeMetaMax = true
    self.coords = {}
    self.pointmetainputhandler = pointmetainputhandler
    self.pointmetamap = nil -- will be set later
    self.filteredCoordsAway = false
    self.plotHasJumps = false
	-- will be set before the visualization phase starts. At least.
	self.plotIs3d = false
    return self
end

function Plothandler:__tostring()
    return 'plot handler ' .. self.name
end

-- @see \pgfplotsplothandlersurveybeforesetpointmeta
function Plothandler:surveyBeforeSetPointMeta()
end

-- @see \pgfplotsplothandlersurveyaftersetpointmeta
function Plothandler:surveyAfterSetPointMeta()
end

-- PRIVATE
--
-- appends a fully surveyed point
function Plothandler:addSurveyedPoint(pt)
    table.insert(self.coords, pt)
    -- log("addSurveyedPoint(" .. tostring(pt) .. ") ...\n")
end

-- PRIVATE
--
-- assigns the point meta value by means of the PointMetaHandler
function Plothandler:setperpointmeta(pt)
    if pt.meta == nil and self.pointmetainputhandler ~= nil then
        self.pointmetainputhandler:assign(pt)
    end
end

-- PRIVATE
--
-- updates point meta limits
function Plothandler:setperpointmetalimits(pt)
    if pt.meta ~= nil then
        if not type(pt.meta) == 'number' then error("got unparsed input "..tostring(pt)) end
        if self.autocomputeMetaMin then
            self.metamin = math.min(self.metamin, pt.meta )
        end

        if self.autocomputeMetaMax then
            self.metamax = math.max(self.metamax, pt.meta )
        end
    end
end

-- @see \pgfplotsplothandlersurveystart
function Plothandler:surveystart()
	stringToFunctionMap["x"] = pseudoconstant_x
	stringToFunctionMap["y"] = pseudoconstant_y
	stringToFunctionMap["z"] = pseudoconstant_z
	stringToFunctionMap["rawx"] = pseudoconstant_rawx
	stringToFunctionMap["rawy"] = pseudoconstant_rawy
	stringToFunctionMap["rawz"] = pseudoconstant_rawz
	stringToFunctionMap["meta"] = pseudoconstant_meta
end

-- @see \pgfplotsplothandlersurveyend
-- returns executable TeX code to communicate return values.
function Plothandler:surveyend()
    -- empty by default.
	return ""
end

-- @see \pgfplotsplothandlersurveypoint
function Plothandler:surveypoint(pt)
	updatePseudoConstants(nil)

	local updateLimits = self.config.updateLimits
    local current = self.axis:parsecoordinate(pt, self.config.filterExpressionByDir)

	-- this here defines the math functions for x, y, or z.
	-- FIXME: are there any hidden callers which rely on these constants in parsecoordinate!?
	updatePseudoConstants(current)

    if current.x[1] ~= nil then
        current = self.axis:preparecoordinate(current)
		if updateLimits then
			self.axis:updatelimitsforcoordinate(current)
		end
    end
    self.axis:datapointsurveyed(current, self)
    
    self.coordindex = self.coordindex + 1;
end

-- PUBLIC
--
-- @return a string containing all surveyed coordinates in the format which is accepted \pgfplotsaxisdeserializedatapointfrom
function Plothandler:surveyedCoordsToPgfplots(axis)
	return self:getCoordsInTeXFormat(axis, self.coords)
end

-- PUBLIC
--
-- @return a string containing all coordinates in the format which is accepted \pgfplotsaxisdeserializedatapointfrom
-- @param extraSerializer a function which takes an instance of Coord and returns a string. can be nil.
function Plothandler:getCoordsInTeXFormat(axis, coords, extraSerializer)
    if not axis then error("arguments must not be nil") end
    local result = {}
    for i = 1,#coords,1 do
        local pt = coords[i]
        local ptstr = self:serializeCoordToPgfplots(pt)
        local axisPrivate = axis:serializeCoordToPgfplotsPrivate(pt)
		if extraSerializer then
			axisPrivate = extraSerializer(pt) .. "{" .. axisPrivate .. "}"
		end
        local serialized = "{" .. axisPrivate .. ";" .. ptstr .. "}"
        table.insert(result, serialized)
    end
    return table.concat(result)
end

-- PRIVATE 
--
-- does the same as \pgfplotsplothandlerserializepointto
function Plothandler:serializeCoordToPgfplots(pt)
    return 
        toTeXstring(pt.x[1]) .. "," ..
        toTeXstring(pt.x[2]) .. "," ..
        toTeXstring(pt.x[3])
end

function Plothandler:visualizationPhaseInit()
	if self.pointmetainputhandler ~=nil then
		local rangeMin
		local rangeMax
		if self.config.pointmetarel == PointMetaRel.axiswide then
			rangeMin = self.axis.axiswidemetamin
			rangeMax = self.axis.axiswidemetamax
		else
			rangeMin = self.metamin
			rangeMax = self.metamax
		end
		self.pointmetamap = PointMetaMap.new(rangeMin, rangeMax, self.config.warnForfilterDiscards)
	end
end

-- PRECONDITION: visualizationPhaseInit() has been called some time before.
function Plothandler:visualizationTransformMeta(meta)
    if meta == nil then
        log("could not access the 'point meta' (used for example by scatter plots and color maps). Maybe you need to add '\\addplot[point meta=y]' or something like that?\n")
        return 1
    else
        return self.pointmetamap:map(meta)
    end
end

-- Modifies coords inplace.
-- @return nothing.
-- see \pgfplots@apply@zbuffer@sort@coordinates
function Plothandler:sortCoordinatesByViewDepth()
    local coords = self.coords

	local axis = self.axis
	local viewdir = axis.viewdir

	-- Step 1: compute view depth for every coordinate
	local getVertexDepth = axis.getVertexDepth
	for i=1,#coords do
		local vertexDepth = getVertexDepth(axis,coords[i])
		coords[i].vertexDepth = vertexDepth
	end
	
	-- Step 2: sort (inplace)
	local comparator = function(ptA, ptB)
		return ptA.vertexDepth > ptB.vertexDepth
	end
	table.sort(coords, comparator)

	-- Step 3: cleanup: do not leave 'vertexDepth' inside of the array
	for i=1,#coords do
		coords[i].vertexDepth = nil
	end
end

-------------------------------------------------------
-- Generic plot handler: one which has the default survey phase
-- It is actually the same as Plothandler...

GenericPlothandler = newClassExtends(Plothandler)

function GenericPlothandler:constructor(name, axis, pointmetainputhandler)
    Plothandler.constructor(self,name, axis, pointmetainputhandler)
end


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

UnboundedCoords = { discard="d", jump="j" }

PointMetaRel = { axiswide = 0, perplot =1 }


-- contains static configuration entities.
PlothandlerConfig = newClass()

function PlothandlerConfig:constructor()
    self.unboundedCoords = UnboundedCoords.discard
    self.warnForfilterDiscards=true
    self.pointmetarel = PointMetaRel.axiswide
	self.updateLimits = true
	self.filterExpressionByDir = {"", "", ""}
	return self
end

-------------------------------------------------------
-- a PlotVisualizer takes an input Plothandler and visualizes its results.
--
-- "Visualize" can mean
-- * apply the plot handler's default visualization phase
-- * visualize just plot marks at each of the collected coordinates
-- * visualize just error bars at each collected coordinate
-- * ...
-- 

-- this class offers basic visualization support. "Basic" means that it will merely transform and finalize input coordinates.
PlotVisualizer = newClass()
-- @param sourcePlotHandler an instance of Plothandler
function PlotVisualizer:constructor(sourcePlotHandler)
	if not sourcePlotHandler then error("arguments must not be nil") end
	self.axis = sourcePlotHandler.axis
	self.sourcePlotHandler=sourcePlotHandler
	if sourcePlotHandler.plotIs3d then
		self.qpointxyz = self.axis.qpointxyz
	else
		self.qpointxyz = self.axis.qpointxy
	end
end

-- Visualizes the results.
--
-- @return any results. The format of the results is currently a list of Coord, but I am unsure of whether it will stay this way.
--
-- Note that a PlotVisualizer does _not_ modify self.sourcePlotHandler.coords 
function PlotVisualizer:getVisualizationOutput()
	local result = {}
	local coords = self.sourcePlotHandler.coords

	-- standard z buffer choices (not mesh + sort) is currently handled in TeX
	-- as well as other preparations

	-- FIXME : stacked plots?
	-- FIXME : error bars?

	for i = 1,#coords do
		local result_i
		local result_i = Coord.new()
		result_i:copy(coords[i])
		
		if result_i.x[1] ~= nil then
			self:visphasegetpoint(result_i)
		else
			self:notifyJump(result_i)
		end

		result[i] = result_i
	end

	return result
end

-- PROTECTED
-- resembles \pgfplotsplothandlervisualizejump -- or at least that part which can be done in LUA.
-- It does not visualize anything, but it can be used to modify the coordinate 
function PlotVisualizer:notifyJump(pt)
	-- do nothing.
end

function PlotVisualizer:visphasegetpoint(pt)
	pt.untransformed = {}
	for j = 1,#pt.x do
		pt.untransformed[j] = pt.x[j]
	end

	self.axis:visphasetransformcoordinate(pt)

	-- FIXME : prepare data point (only for stacked)

	pt.pgfXY = self.qpointxyz(pt.x)
end



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

-- An abstract base class for a handler of point meta.
-- @see \pgfplotsdeclarepointmetasource
PointMetaHandler = newClass()

-- @param isSymbolic
--    expands to either '1' or '0'
-- 		A numeric source will be processed numerically in float
-- 		arithmetics. Thus, the output of the @assign routine should be
-- 		a macro \pgfplots@current@point@meta in float format.
--
--		The output of a numeric point meta source will result in meta
--		limit updates and the final map to [0,1000] will be
--		initialised automatically.
--
-- 		A symbolic input routine won't be processed.
-- 	Default is '0'
--
-- @param explicitInput
--   expands to either
--   '1' or '0'. In case '1', it expects explicit input from the
--   coordinate input routines. For example, 'plot file' will look for
--   further input after the x,y,z coordinates.
--   Default is '0'
--
function PointMetaHandler:constructor(isSymbolic, explicitInput)
    self.isSymbolic =isSymbolic
    self.explicitInput = explicitInput
    return self
end

-- 	During the survey phase, this macro is expected to assign
-- 	\pgfplots@current@point@meta
--	if it is a numeric input method, it should return a
--	floating point number.
--	It is allowed to return an empty string to say "there is no point
--	meta".
--	PRECONDITION for '@assign':
--		- the coordinate input method has already assigned its
--		'\pgfplots@current@point@meta' (probably as raw input string).
--		- the other input coordinates are already read.
--	POSTCONDITION for '@assign':
--		- \pgfplots@current@point@meta is ready for use:
--		- EITHER a parsed floating point number 
--		- OR an empty string,
--		- OR a symbolic string (if the issymbolic boolean is true)
--	The default implementation is
--	\let\pgfplots@current@point@meta=\pgfutil@empty
--
function PointMetaHandler.assign(pt)
    error("This instance of PointMetaHandler is not implemented")
end


-- A PointMetaHandler which merely acquires values of either x,y, or z.
CoordAssignmentPointMetaHandler = newClassExtends( PointMetaHandler )
function CoordAssignmentPointMetaHandler:constructor(dir)
    PointMetaHandler.constructor(self, false,false)
    if not dir then error "nil argument for 'dir' is unsupported." end
    self.dir=dir 
end

function CoordAssignmentPointMetaHandler:assign(pt)
    if not pt then error("arguments must not be nil") end
    pt.meta = pgftonumber(pt.x[self.dir])
end

XcoordAssignmentPointMetaHandler = CoordAssignmentPointMetaHandler.new(1)
YcoordAssignmentPointMetaHandler = CoordAssignmentPointMetaHandler.new(2)
ZcoordAssignmentPointMetaHandler = CoordAssignmentPointMetaHandler.new(3)

-- A class of PointMetaHandler which takes the 'Coord.meta' as input
ExplicitPointMetaHandler = newClassExtends( PointMetaHandler )
function ExplicitPointMetaHandler:constructor()
    PointMetaHandler.constructor(self, false,true)
end

function ExplicitPointMetaHandler:assign(pt)
    if pt.unfiltered ~= nil and pt.unfiltered.meta ~= nil then
        pt.meta = pgftonumber(pt.unfiltered.meta)
    end
end

-- a point meta handler which evaluates a math expression.
-- ATTENTION: the expression cannot depend on TeX macro values
ExpressionPointMetaHandler = newClassExtends( PointMetaHandler )

-- @param expression an expression. It can rely on functions which are only available in plot context (in plot expression, x and y are typically defined)
function ExpressionPointMetaHandler:constructor(expression)
	PointMetaHandler.constructor(self, false,false)
	self.expression = expression
end

function ExpressionPointMetaHandler:assign(pt)
	pt.meta = pgfmathparse(self.expression)
	if not pt.meta then
		error("point meta=" .. self.expression .. ": expression has been rejected.")
    end
end
	

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

DatascaleTrafo = newClass()

function DatascaleTrafo:constructor(exponent, shift)
	self.exponent=exponent
	self.shift=shift
	self.scale = math.pow(10, exponent)
end

function DatascaleTrafo:map(x)
	return self.scale * x - self.shift
end


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

-- An axis. 
Axis = newClass()

function Axis:constructor()
    self.is3d = false
    self.clipLimits = true
    self.autocomputeAllLimits = true -- FIXME : redundant!?
    self.autocomputeMin = { true, true, true }
    self.autocomputeMax = { true, true, true }
    self.isLinear = { true, true, true }
    self.min = { math.huge, math.huge, math.huge }
    self.max = { -math.huge, -math.huge, -math.huge }
    self.datamin = { math.huge, math.huge, math.huge }
    self.datamax = { -math.huge, -math.huge, -math.huge }
    self.axiswidemetamin = { math.huge, math.huge }
    self.axiswidemetamax = { -math.huge, -math.huge }
    -- will be populated by the TeX code:
    self.plothandlers = {}
	-- needed during visualization phase:
	self.datascaleTrafo={}
	-- needed during visualization phase: a vector of 3 elements, each is a vector of 2 elements.
	-- self.unitvectors[1] is (\pgf@xx,\pgf@xy)
	self.unitvectors={}
	-- needed during visualization phase -- but only for 3d!
	self.viewdir = {}
    return self
end

function Axis:getVertexDepth(pt)
	local vertexDepth = 0
	local vertex = pt.x
	local viewdir = self.viewdir
	if vertex[1] == nil then
		-- an empty coordinate. Get rid of it.
		return 0
	end

	if #vertex ~=3 then
		error("Cannot compute vertex depth of " .. tostring(pt) .. ": expected a 3d point but got " .. tostring(#vertex)) 
	end
	if not viewdir or #viewdir~=3 then error("got unexpected view dir " ..tostring(viewdir) ) end

	for k = 1,3 do
		local component = vertex[k]
		vertexDepth = vertexDepth + component*viewdir[k]
	end

	return vertexDepth
end

function Axis:setunitvectors(unitvectors)
	if not unitvectors or #unitvectors ~= 3 then error("got illegal arguments " .. tostring(unitvectors)) end
	self.unitvectors = unitvectors

	local pgfxx = unitvectors[1][1]
	local pgfxy = unitvectors[1][2]
	local pgfyx = unitvectors[2][1]
	local pgfyy = unitvectors[2][2]
	local pgfzx = unitvectors[3][1]
	local pgfzy = unitvectors[3][2]

	self.qpointxyz = function(xyz)
		local result = {}
		result[1] = xyz[1] * pgfxx + xyz[2] * pgfyx  + xyz[3] * pgfzx
		result[2] = xyz[1] * pgfxy + xyz[2] * pgfyy  + xyz[3] * pgfzy
		return result
	end

	if pgfxy==0 and pgfyx ==0 then
		self.qpointxy = function(xy)
			local result = {}
			result[1] = xy[1] * pgfxx
			result[2] = xy[2] * pgfyy
			return result
		end
	else
		self.qpointxy = function(xyz)
			local result = {}
			result[1] = xyz[1] * pgfxx + xyz[2] * pgfyx
			result[2] = xyz[1] * pgfxy + xyz[2] * pgfyy
			return result
		end
	end
end

-- PRIVATE
--
-- applies user transformations and logs
--
-- @see \pgfplots@prepared@xcoord
function Axis:preparecoord(dir, value)
    -- FIXME : user trafos, logs (switches off LUA backend)
    return value
end

function Axis:filtercoord(dir, ptCoords, filterExpressionByDir)
	if not dir or not ptCoords or not filterExpressionByDir then error("Arguments must not be nil") end
	local result = ptCoords.x[dir]
	if filterExpressionByDir[dir]:len() > 0 then

		for j = 1,#ptCoords.x do
			ptCoords.x[j] = pgftonumber(ptCoords.x[j])
		end
		local old = updatePseudoConstants(ptCoords)

		result = pgfmathparse(filterExpressionByDir[dir])

		updatePseudoConstants(old)
	end
	return result
end

-- PRIVATE
-- @see \pgfplotsaxisserializedatapoint@private
function Axis:serializeCoordToPgfplotsPrivate(pt)
    return toTeXstring(pt.meta)
end


-- PRIVATE
--
function Axis:validatecoord(dir, point)
    if not dir or not point then error("arguments must not be nil") end
    local result = pgftonumber(point.x[dir])
    
    if result == nil then
        result = nil
    elseif result == pgfplotsmath.infty or result == -pgfplotsmath.infty or pgfplotsmath.isnan(result) then
        result = nil
        point.unboundedDir = dir
    end

    point.x[dir] = result
end

-- PRIVATE
--
-- @see \pgfplotsaxisparsecoordinate
function Axis:parsecoordinate(pt, filterExpressionByDir)
    -- replace empty strings by 'nil':
    for i = 1,3 do
        pt.x[i] = stringOrDefault(pt.x[i], nil)
    end
    pt.meta = stringOrDefault(pt.meta)

    if pt.x[3] ~= nil then
        self.is3d = true
    end
    
    local result = Coord.new()
    
    local unfiltered = Coord.new()
    unfiltered.x = {}
    unfiltered.meta = pt.meta
    for i = 1,3 do
        unfiltered.x[i] = pt.x[i]
    end
    result.unfiltered = unfiltered

	-- copy values such that filtercoord can access them in the same order as the TeX impl.
    for i = 1,self:loopMax() do
		result.x[i] = pt.x[i]
	end

    -- FIXME : self:prefilter(pt[i])
    for i = 1,self:loopMax() do
        result.x[i] = self:preparecoord(i, pt.x[i])
        result.x[i] = self:filtercoord(i, result, filterExpressionByDir)
    end
    -- FIXME : result.x = self:xyzfilter(result.x)

    for i = 1,self:loopMax() do
        self:validatecoord(i, result)
    end
    
    local resultIsBounded = true
    for i = 1,self:loopMax() do
        if result.x[i] == nil then
            resultIsBounded = false
        end
    end

    if not resultIsBounded then
        result.x = { nil, nil, nil}
    end

    return result    
end

-- PROTECTED
--
-- @see \pgfplotsaxispreparecoordinate
function Axis:preparecoordinate(pt)
    -- the default "preparation" is to return it as is (no number parsing)
	--
	-- FIXME : data cs! Stacking!
    return pt
end

-- PRIVATE
--
-- returns either 2 if this axis is 2d or 3 otherwise
--
-- FIXME : shouldn't this depend on the current plot handler!?
function Axis:loopMax()
    if self.is3d then return 3 else return 2 end
end

-- PRIVATE:
--
-- updates axis limits for pt
-- @param pt an instance of Coord
function Axis:updatelimitsforcoordinate(pt)
    local isClipped = false
    if self.clipLimits then
        for i = 1,self:loopMax(),1 do
            if not self.autocomputeMin[i] then
                isClipped = isClipped or pt.x[i] < self.min[i]
            end
            if not self.autocomputeMax[i] then
                isClipped = isClipped or pt.x[i] > self.max[i]
            end
        end                
    end
    
    if not isClipped then
        for i = 1,self:loopMax(),1 do
            if self.autocomputeMin[i] then
                self.min[i] = math.min(pt.x[i], self.min[i])
            end
            
            if self.autocomputeMax[i] then
                self.max[i] = math.max(pt.x[i], self.max[i])
            end
        end
    end

    -- Compute data range:
    if self.autocomputeAllLimits then
        -- the data range will be acquired simply from the axis
        -- range, see below!
    else
        for i = 1,self:loopMax(),1 do
            self.datamin[i] = math.min(pt.x[i], self.min[i])
            self.datamax[i] = math.max(pt.x[i], self.max[i])
        end
    end
end

-- PRIVATE
--
-- unfinished, see its fixmes
function Axis:addVisualizationDependencies(pt)
    -- FIXME : 'visualization depends on' 
    -- FIXME : 'execute for finished point'
    return pt
end

-- PROTECTED
--
-- indicates that a data point has been surveyed by the axis and that it can be consumed 
function Axis:datapointsurveyed(pt, plothandler)
    if not pt or not plothandler then error("arguments must not be nil") end
    if pt.x[1] ~= nil then
        plothandler:surveyBeforeSetPointMeta()
        plothandler:setperpointmeta(pt)
        plothandler:setperpointmetalimits(pt)
        plothandler:surveyAfterSetPointMeta()

        -- FIXME : error bars
        -- FIXME: collect first plot as tick

        -- note that that TeX code would also remember the first/last coordinate in a stream.
        -- This is unnecessary here.

        local serialized = self:addVisualizationDependencies(pt)
        plothandler:addSurveyedPoint(serialized)
    else
        -- COORDINATE HAS BEEN FILTERED AWAY
        if plothandler.config.unboundedCoords == UnboundedCoords.discard then
            plothandler.filteredCoordsAway = true
            if plothandler.config.warnForfilterDiscards then
                local reason
                if pt.unboundedDir == nil then
                    reason = "of a coordinate filter."
                else
                    reason = "it is unbounding (in " .. tostring(pt.unboundedDir) .. ")."
                end
                log("NOTE: coordinate " .. tostring(pt) .. " has been dropped because " .. reason .. "\n")
            end
        elseif plothandler.config.unboundedCoords == UnboundedCoords.jump then
            if pt.unboundedDir == nil then
                plothandler.filteredCoordsAway = true
                if plothandler.config.warnForfilterDiscards then
                    local reason = "of a coordinate filter."
                    log("NOTE: coordinate " .. tostring(pt) .. " has been dropped because " .. reason .. "\n")
                end
            else
                plothandler.plotHasJumps = true

                local serialized = self:addVisualizationDependencies(pt)
                plothandler:addSurveyedPoint(serialized)
            end
        end
    end
    
    -- note that the TeX variant would increase the coord index here.
    -- We do it it surveypoint.
end

local function axisLimitToTeXString(name, value)
	if value == math.huge or value == -math.huge then
		return ""
	end
	return "\\gdef" .. name .. "{" .. toTeXstring(value) .. "}"
end

local function toTeXxyzCoord(namePrefix, pt )
	local x = toTeXstring(pt.x[1])
	local y = toTeXstring(pt.x[2])
	local z = toTeXstring(pt.x[3])
	return 
		"\\gdef" .. namePrefix .. "@x{" .. x .. "}" ..
		"\\gdef" .. namePrefix .. "@y{" .. y .. "}" ..
		"\\gdef" .. namePrefix .. "@z{" .. z .. "}";
end

local function findFirstValidCoord(coords)
	for i=1,#coords do
		local pt = coords[i]
		if pt.x[1] ~=nil then
			return pt
		end
	end
	return nil
end

local function findLastValidCoord(coords)
	for i=#coords,1,-1 do
		local pt = coords[i]
		if pt.x[1] ~=nil then
			return pt
		end
	end
	return nil
end

-- PUBLIC
--
-- @return a set of (private) key-value pairs such that the TeX code of pgfplots can
-- access survey results of the provided plot handler
--
-- @param plothandler an instance of Plothandler
function Axis:surveyToPgfplots(plothandler)
	local plothandlerResult = plothandler:surveyend()
    local firstCoord = findFirstValidCoord(plothandler.coords) or Coord.new()
    local lastCoord = findLastValidCoord(plothandler.coords) or Coord.new()

    local result = 
		plothandlerResult .. 
		toTeXxyzCoord("\\pgfplots@currentplot@firstcoord", firstCoord) ..
		toTeXxyzCoord("\\pgfplots@currentplot@lastcoord", lastCoord) ..
        axisLimitToTeXString("\\pgfplots@metamin", plothandler.metamin) ..
        axisLimitToTeXString("\\pgfplots@metamax", plothandler.metamax) ..
		"\\c@pgfplots@coordindex=" .. tostring(plothandler.coordindex) .. " " ..
        axisLimitToTeXString("\\pgfplots@xmin", self.min[1]) ..
        axisLimitToTeXString("\\pgfplots@ymin", self.min[2]) ..
        axisLimitToTeXString("\\pgfplots@xmax", self.max[1]) ..
        axisLimitToTeXString("\\pgfplots@ymax", self.max[2]);
	if self.is3d then
		result = result ..
        axisLimitToTeXString("\\pgfplots@zmin", self.min[3]) ..
        axisLimitToTeXString("\\pgfplots@zmax", self.max[3]) ..
		"\\global\\pgfplots@threedimtrue ";
	end
    if plothandler.plotHasJumps then 
		result = result ..
		"\\def\\pgfplotsaxisplothasjumps{1}"
	else
		result = result ..
		"\\def\\pgfplotsaxisplothasjumps{0}"
	end
    if plothandler.filteredCoordsAway then 
		result = result ..
		"\\def\\pgfplotsaxisfilteredcoordsaway{1}"
	else
		result = result ..
		"\\def\\pgfplotsaxisfilteredcoordsaway{0}"
	end

    return result
end

-- resembles \pgfplotsaxisvisphasetransformcoordinate
function Axis:visphasetransformcoordinate(pt)
	for i = 1,#pt.x do
		pt.x[i] = self.datascaleTrafo[i]:map( pt.x[i] )
	end
end

-- will be set by TeX code (in \begin{axis})
gca = nil


end