------------------------------------------------------------------------------
-- procedural.lua: Procedural layout functions
--
-- These generators accept a params object which configures the final
-- function produced. The resultant function will take an x,y coord and
-- return a result typically in the range 0..1. These functions should
-- be considered primitives that can be combined together other functions
-- to produce more complex patterns which can serve as the blueprints
-- for actual layouts.
------------------------------------------------------------------------------

procedural = {}
crawl_require("dlua/layout/procedural_primitives.lua")
crawl_require("dlua/util.lua")
------------------------------------------------------------------------------
-- Aggregate functions
--
-- These factories return a function that aggregates several functions or
-- values together with a mathematical operation. Each one takes a parameter
-- list which can consist of any mixture of functions and numerical values.
-- The returned function performs the aggregate of those functions and values
-- at each x,y coordinate.

-- Add the output of several functions together
function procedural.add(...)
  local vars = { ... }
  return procedural.aggregate(vars,function(t,v) return t+v end)
end

-- Takes the value of the first function,
-- subtracts the values of the rest from it
function procedural.sub(...)
  local vars = { ... }
  return procedural.aggregate(vars,function(t,v) return t-v end)
end

-- Multiplies together several functions or values
function procedural.mul(...)
  local vars = { ... }
  return procedural.aggregate(vars,function(t,v) return t*v end)
end

function procedural.div(...)
  local vars = { ... }
  return procedural.aggregate(vars,function(t,v) return t/v end)
end

-- Creates a function that returns the minimum value of several functions
function procedural.min(...)
  local vars = { ... }
  return procedural.aggregate(vars,function(t,v) return math.min(t,v) end)
end

-- Creates a function that returns the maximum value of several functions
function procedural.max(...)
  local vars = { ... }
  return procedural.aggregate(vars,function(t,v) return math.max(t,v) end)
end

function procedural.aggregate(list,op)

  return function(x,y)
    local val = 0
    local r
    for i,f in ipairs(list) do
      if type(f) == "function" then
        r = f(x,y)
      else
        r = f
      end
      if i==1 then
        val = r
      else
        val = op(val,r)
      end
    end
    return val
  end

end

-- Some non-aggregate function transforms
function procedural.abs(func)
  return function(x,y)
    return math.abs(func(x,y))
  end
end

-- Negate a function
function procedural.neg(func)
  return function(x,y)
    return -func(x,y)
  end
end

function procedural.phase(func,rep,offset)
  return function(x,y)
    local v = func(x,y)
    v = (v * rep + offset) % 1
    return v
  end
end

-- Loops a function along the x axis over a given period
function procedural.loop_x(func,period)
  if period == nil then period = 1 end
  return function(x,y)
    return func(x % period,y)
  end
end

-- Bounces a function along the x axis over a given period
-- The x value increases over 0..period, decreases over
-- period..period*2, and repeats for infinity
function procedural.bounce_x(func,period)
  if period == nil then period = 1 end
  return function(x,y)
    local bounced = x % period * 2
    if bounced > period then bounced = period-bounced end
    return func(bounced,y)
  end
end

-- Loops a function along the y axis over a given period
function procedural.loop_y(func,period)
  if period == nil then period = 1 end
  return function(x,y)
    return func(x,y % period)
  end
end

-- Bounces a function along the y axis over a given period
-- The y value increases over 0..period, decreases over
-- period..period*2, and repeats for infinity
function procedural.bounce_y(func,period)
  if period == nil then period = 1 end
  return function(x,y)
    local bounced = y % period * 2
    if bounced > period then bounced = period-bounced end
    return func(x,bounced)
  end
end

-- A function that returns 1 around the border edge, and fades to 0 over
-- a specified number of padding squares.
function procedural.border(params)
  local x1,y1 = 0,0
  local x2,y2 = dgn.builder_bounds()
  x2 = x2 - 1
  y2 = y2 - 1
  if params.x1 ~= nil then x1 = params.x1 end
  if params.x2 ~= nil then x2 = params.x2 end
  if params.y1 ~= nil then y1 = params.y1 end
  if params.y2 ~= nil then y2 = params.y2 end
  local padding = params.padding == nil and 10 or params.padding
  if params.margin ~= nil then
    x1 = x1 + params.margin
    x2 = x2 - params.margin
    y1 = y1 + params.margin
    y2 = y2 - params.margin
  end
  if params.additive then
    return function(x,y)
      local nearx = math.min(x-x1,x2-x)
      local neary = math.min(y-y1,y2-y)
      return math.min(1, 2 - procedural.minmax_map(nearx, 0, padding + 1)
                           - procedural.minmax_map(neary, 0, padding + 1))
    end
  else
    return function(x,y)
      local near = math.min(x - x1, y - y1, x2 - x, y2 - y)
      return 1 - procedural.minmax_map(near, 0, padding + 1)
    end
  end
end

-- Calculates nearest distance to edge of a box. Returns 0 in the
-- box center, 1 at the box edge.
-- TODO: Border is basically this with a numerical map applied,
-- we can get rid of the border implementation and replace it with that
function procedural.box(params)

  local x1,y1 = 0,0
  local x2,y2 = dgn.builder_bounds()
  x2 = x2 - 1
  y2 = y2 - 1
  if params.x1 ~= nil then x1 = params.x1 end
  if params.x2 ~= nil then x2 = params.x2 end
  if params.y1 ~= nil then y1 = params.y1 end
  if params.y2 ~= nil then y2 = params.y2 end

  -- TODO: Mathematically speaking this is correct but in reality
  -- we might have to adjust this a little for the grid
  local minhalf = math.min((x2-x1)/2,(y2-y1)/2)

  return function(x,y)
    local near = math.min(x-x1,y-y1,x2-x,y2-y)
    return 1 - near/minhalf
  end

end

-- Returns distance from a point, useful for circles and ellipses
-- Unfortunately it's causing a two-way reference between here and primitives
function procedural.distance(params)
  local func = primitive.distance
  if params.radius ~= nil then func = procedural.scale(func,params.radius) end
  if params.origin ~= nil then func = procedural.translate(func,params.origin) end
  return func
end

-- Gives the radial value from a point, i.e. the arctangent of the line
-- from the origin to the point
function procedural.radial(params)

  local xo,yo = 0,0
  if params.origin ~= nil then xo,yo = params.origin.x,params.origin.y end

  return function(x,y)
    local xd,yd = xo-x,yo-y
    local r
    if yd == 0 then r = (xd>0) and 270 or 90
    else
      r = math.atan(xd/yd) / math.pi * 180
      if yd>0 then r = r+180 end
    end
    if params.phase ~= nil then
      r = (r + params.phase*360)
    end
    return (r % 360)/360
  end

end

-- Draws a horizontal or vertical bar at the specified position. The bar has
-- value 1 at the position and tails off to 0 at a distance of width/2 to
-- either side
-- TODO: Implement rotation transforms to eliminate this v/h logic
function procedural.bar(params)

  local horizontal = params.horizontal == nil and true or params.horizontal
  local width = params.width or 1
  local position = params.position or 1
  local positiona,positionb = position,position
  if params.inner ~= nil then
    positiona,positionb = position - params.inner/2, position + params.inner/2
  end
  local start = math.floor(position - width/2)
  local finish = start + width + 1
  if horizontal then
    return function(x,y) return procedural.boundary_map(y,start,positiona,positionb,finish) end
  end
  return function(x,y) return procedural.boundary_map(x,start,positiona,positionb,finish) end

end

-- This is more of a complex than a primitive, should move to some sort of
-- library file if it's going to be used more than once
function procedural.river(params)

  local gxm,gym = dgn.builder_bounds()

  local horizontal = params.horizontal == nil and true or params.horizontal
  local width = params.width or 15
  local position = params.position or math.floor(gym/2)
  local turbulence = params.turbulence == nil and 10 or params.turbulence
  local turbulence_scale = params.turbulence_scale or 1

  local fbase = procedural.bar{horizontal = horizontal, width = width, position = position}
  if not turbulence then return fbase end
  return procedural.distort{ source = fbase, scale = turbulence,
    offsetx = (not horizontal) and procedural.simplex3d{ scale = turbulence_scale } or nil,
    offsety = horizontal and procedural.simplex3d{ scale = turbulence_scale } or nil }

end

-- Provides the full data from a Worley call, should not be directly used
-- e.g.  as a transform
function procedural.worley(params)
  local final_scale_x = params.scale * 0.8
  local final_scale_y = params.scale * 0.8
  local final_scale_z = params.scale * 0.8
  local major_offset_x = crawl.random2(1000000)
  local major_offset_y = crawl.random2(1000000)
  local major_offset_z = crawl.random2(1000000)
  return function(x,y,z)
    if z == nil then z = 0 end
    local d1,d2,id1,id2,pos1x,pos1y,pos1z,pos2x,pos2y,pos2z =
        crawl.worley(x * final_scale_x + major_offset_x,
                     y * final_scale_y + major_offset_y,
                     z * final_scale_z + major_offset_z)
    return {
      d = { d1,d2 },
      id = { id1,id2 },
      pos = { { x = pos1x, y = pos1y, z = pos1z },
              { x = pos2x, y = pos2y, z = pos2z } }
    }
  end
end

-- Returns a function that computes the difference between distance[0] and
-- distance[1] for a given Worley function
function procedural.worley_diff(params)
  local final_scale_x = params.scale * 0.8
  local final_scale_y = params.scale * 0.8
  local final_scale_z = params.scale * 0.8
  local major_offset_x = crawl.random2(1000000)
  local major_offset_y = crawl.random2(1000000)
  local major_offset_z = crawl.random2(1000000)
  return function(x,y,z)
    if z == nil then z = 0 end
    local diff, id =
        crawl.worley_diff(x * final_scale_x + major_offset_x,
                          y * final_scale_y + major_offset_y,
                          z * final_scale_z + major_offset_z)
    return diff, id
  end
end

function procedural.simplex3d(params)
  local final_scale_x = params.scale / 10
  local final_scale_y = params.scale / 10
  local final_scale_z = params.scale / 10

  local major_offset_x = 100 + util.random_range_real(0,1)
  local major_offset_y = 100 + util.random_range_real(0,1)
  local major_offset_z = 100 + util.random_range_real(0,1)
  local unit = (params.unit == nil or params.unit) and true or false
  return function(x,y,z)
    if z == nil then z = 0 end
    local result = crawl.simplex(x * final_scale_x + major_offset_x,
                                 y * final_scale_y + major_offset_y,
                                 z * final_scale_z + major_offset_z)
    if unit then result = result / 2.0 + 0.5 end
    return result
  end
end

function procedural.simplex4d(params)
  local final_scale_x = params.scale / 10
  local final_scale_y = params.scale / 10
  local major_offset_x = crawl.random2(1000000)
  local major_offset_y = crawl.random2(1000000)
  local major_offset_z = crawl.random2(1000000)
  local major_offset_w = crawl.random2(1000000)
  return function(x,y)
    return crawl.simplex(x * final_scale_x + major_offset_x,
                         y * final_scale_y + major_offset_y,
                         major_offset_z, major_offset_w) / 2 + 0.5
  end
end

-- Domain transformations

-- Creates a domain distortion function to offset one function using two others
-- for the x,y offsets
function procedural.distort(params)
  local source = params.source
  local offsetx = params.offsetx or function(x,y) return 0 end
  local offsety = params.offsety or function(x,y) return 0 end
  local scale = params.scale or 1
  return function(x,y)
    return source(x+offsetx(x,y) * scale,y+offsety(x,y) * scale)
  end
end

-- Simple transformations
function procedural.translate(func,xo,yo)
  if xo == nil then xo,yo = 0,0
  elseif type(xo) == "table" then xo,yo = xo.x,xo.y
  elseif yo == nil then yo = xo end

  return function(x,y)
    return func(x-xo,y-yo)
  end
end

function procedural.scale(func,xs,ys)
  if xs == nil then xs,ys = 1,1
  elseif type(xs) == "table" then xs,ys = xs.x,xs.y
  elseif ys == nil then ys = xs end

  return function(x,y)
    return func(x/xs,y/ys)
  end
end

-- Flip in the x-axis
function procedural.flip_x(func)
  return function(x,y)
    return func(-x,y)
  end
end

-- Flip in the y-axis
function procedural.flip_y(func)
  return function(x,y)
    return func(x,-y)
  end
end

-- Mirror about the x axis (i.e. the y vector is negated)
function procedural.mirror_x(func)
  return function(x,y)
    return func(x,math.abs(y))
  end
end

-- Mirror about the y axis (i.e. the x vector is negated)
function procedural.mirror_y(func)
  return function(x,y)
    return func(math.abs(x),y)
  end
end

-- TODO: Rotate, matrix

-- Output mapping to an array of ranges
function procedural.map(func,map,b,c,d)
  if type(map) ~= "table" then
    map = { { nil, map, c }, { map, b, c, d }, { b, nil, d } }
  end
  return function(x,y)
    local v = func(x,y)
    for i,m in ipairs(map) do
      -- Outer limits
      if m[1] == nil then
        if v <= m[2] then return m[3] end
      elseif m[2] == nil then
        if v >= m[1] then return m[3] end
      elseif m[1]<=v and v<=m[2] then
        return m[3] + (v-m[1])/(m[2]-m[1]) * (m[4]-m[3])
      end
    end
    -- If the map hasn't given us a value, don't alter it
    return v
  end

end

-- Utility functions. These don't return a function themselves, just a value.

-- Maps a value onto a 0..1..0 scale. Outside the boundaries it is 0, and
-- when between b2 and b3 it is 1. Between b1 and b2, and b3 and b4, it
-- smoothly scales between 1 and 0.
function procedural.boundary_map(val, b1,b2,b3,b4)
  if val<=b1 or val>=b4 then return 0
  elseif b2<=val and val<=b3 then return 1
  elseif val < b2 then return (val-b1)/(b2-b1)
  else return (b4-val)/(b4-b3) end
end

-- Similar but maps just onto 0..1 on min/max boundaries.
function procedural.minmax_map(val,min,max)
  if val<min then return 0
  elseif val>max then return 1
  else return (val-min)/(max-min) end
end

-- Render functions
function procedural.render_map(e, fval, fresult)

  local gxm,gym = dgn.builder_bounds()
  e.extend_map { width = gxm, height = gym, fill = 'x' }
  for x = 1,gxm-2,1 do
    for y = 1,gym-2,1 do
      local val = fval(x,y)
      local r = fresult(val,x,y)
      if r ~= nil then e.mapgrd[x][y] = r end
    end
  end

end

function procedural.render_map_area(e,x1,y1,x2,y2,fval,brush,space)
  local fbrush
  if type(brush)=="string" then
    fbrush = function(v) return (v <= 1) and brush or space end
  end
  for x = x1,x2,1 do
    for y = y1,y2,1 do
      local val = fval(x-x1,y-y1,x,y)
      local r = fbrush(val,x,y)
      if r ~= nil then e.mapgrd[x][y] = r end
    end
  end
end