mapgen_rivers/heightmap.lua

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-- Transform polygon data into a heightmap
2021-06-03 19:21:45 +02:00
local modpath = mapgen_rivers.modpath
local sea_level = mapgen_rivers.settings.sea_level
local riverbed_slope = mapgen_rivers.settings.riverbed_slope * mapgen_rivers.settings.blocksize
local out_elev = mapgen_rivers.settings.margin_elev
-- Localize for performance
local floor, min, max, sqrt, abs = math.floor, math.min, math.max, math.sqrt, math.abs
local unpk = unpack
-- Geometrical helpers
local function distance_to_segment(x1, y1, x2, y2, x, y)
-- get the distance between point (x,y) and segment (x1,y1)-(x2,y2)
local a = (x1-x2)^2 + (y1-y2)^2 -- square of distance
local b = (x1-x)^2 + (y1-y)^2
local c = (x2-x)^2 + (y2-y)^2
if a + b < c then
-- The closest point of the segment is the extremity 1
return sqrt(b)
elseif a + c < b then
-- The closest point of the segment is the extremity 2
return sqrt(c)
else
-- The closest point is on the segment
return abs(x1 * (y2-y) + x2 * (y-y1) + x * (y1-y2)) / sqrt(a)
end
end
local function transform_quadri(X, Y, x, y)
-- To index points in an irregular quadrilateral, giving x and y between 0 (one edge) and 1 (opposite edge)
-- X, Y 4-vectors giving the coordinates of the 4 vertices
-- x, y position to index.
local x1, x2, x3, x4 = unpk(X)
local y1, y2, y3, y4 = unpk(Y)
-- Compare distance to 2 opposite edges, they give the X coordinate
local d23 = distance_to_segment(x2,y2,x3,y3,x,y)
local d41 = distance_to_segment(x4,y4,x1,y1,x,y)
local xc = d41 / (d23+d41)
-- Same for the 2 other edges, they give the Y coordinate
local d12 = distance_to_segment(x1,y1,x2,y2,x,y)
local d34 = distance_to_segment(x3,y3,x4,y4,x,y)
local yc = d12 / (d12+d34)
return xc, yc
end
-- Linear interpolation
local function interp(v00, v01, v11, v10, xf, zf)
local v0 = v01*xf + v00*(1-xf)
local v1 = v11*xf + v10*(1-xf)
return v1*zf + v0*(1-zf)
end
function mapgen_rivers.make_heightmaps(minp, maxp)
local polygons = mapgen_rivers.make_polygons(minp, maxp)
local incr = maxp.z-minp.z+1
local terrain_height_map = {}
local lake_height_map = {}
local i = 1
for z=minp.z, maxp.z do
for x=minp.x, maxp.x do
local poly = polygons[i]
if poly then
local xf, zf = transform_quadri(poly.x, poly.z, x, z)
local i00, i01, i11, i10 = unpk(poly.i)
-- Load river width on 4 edges and corners
local r_west, r_north, r_east, r_south = unpk(poly.rivers)
local c_NW, c_NE, c_SE, c_SW = unpk(poly.river_corners)
-- Calculate the depth factor for each edge and corner.
-- Depth factor:
-- < 0: outside river
-- = 0: on riverbank
-- > 0: inside river
local depth_factors = {
r_west - xf , -- West edge (1)
r_north - zf , -- North edge (2)
r_east - (1-xf), -- East edge (3)
r_south - (1-zf), -- South edge (4)
c_NW - xf - zf , -- North-West corner (5)
c_NE - (1-xf) - zf , -- North-East corner (6)
c_SE - (1-xf) - (1-zf), -- South-East corner (7)
c_SW - xf - (1-zf), -- South-West corner (8)
}
-- Find the maximal depth factor, which determines to which of the 8 river sections (4 edges + 4 corners) the current point belongs.
-- If imax is still at 0, it means that we are not in a river.
local dpmax = 0
local imax = 0
for i=1, 8 do
if depth_factors[i] > dpmax then
dpmax = depth_factors[i]
imax = i
end
end
-- Transform the coordinates to have xfc and zfc = 0 or 1 in rivers (to avoid rivers having lateral slope and to accomodate the riverbanks smoothly)
local xfc, zfc
-- xfc:
if imax == 0 or imax == 2 or imax == 4 then -- river segment does not constrain X coordinate, so accomodate xf in function of other river sections
local x0 = max(r_west-dpmax, c_NW-zf-dpmax, c_SW-(1-zf)-dpmax, 0) -- new xf will be bounded to 0 by western riverbank
local x1 = 1-max(r_east-dpmax, c_NE-zf-dpmax, c_SE-(1-zf)-dpmax, 0) -- and bounded to 1 by eastern riverbank
if x0 >= x1 then
xfc = 0.5
else
xfc = (xf-x0) / (x1-x0)
end
elseif imax == 1 or imax == 5 or imax == 8 then -- river at the western side of the polygon
xfc = 0
else -- 3, 6, 7 : river at the eastern side of the polygon
xfc = 1
end
-- Same for zfc:
if imax == 0 or imax == 1 or imax == 3 then -- river segment does not constrain Z coordinate, so accomodate zf in function of other river sections
local z0 = max(r_north-dpmax, c_NW-xf-dpmax, c_NE-(1-xf)-dpmax, 0) -- new zf will be bounded to 0 by northern riverbank
local z1 = 1-max(r_south-dpmax, c_SW-xf-dpmax, c_SE-(1-xf)-dpmax, 0) -- and bounded to 1 by southern riverbank
if z0 >= z1 then
zfc = 0.5
else
zfc = (zf-z0) / (z1-z0)
end
elseif imax == 2 or imax == 5 or imax == 6 then -- river at the northern side of the polygon
zfc = 0
else -- 4, 7, 8 : river at the southern side of the polygon
zfc = 1
end
-- Determine elevation by interpolation
local vdem = poly.dem
local terrain_height = floor(0.5+interp(
vdem[1],
vdem[2],
vdem[3],
vdem[4],
xfc, zfc
))
-- Spatial gradient of the interpolation
local slope_x = zfc*(vdem[3]-vdem[4]) + (1-zfc)*(vdem[2]-vdem[1]) < 0
local slope_z = xfc*(vdem[3]-vdem[2]) + (1-xfc)*(vdem[4]-vdem[1]) < 0
local lake_id = 0
if slope_x then
if slope_z then
lake_id = 3
else
lake_id = 2
end
else
if slope_z then
lake_id = 4
else
lake_id = 1
end
end
local lake_height = max(floor(poly.lake[lake_id]), terrain_height)
if imax > 0 and dpmax > 0 then
terrain_height = min(max(lake_height, sea_level) - floor(1+dpmax*riverbed_slope), terrain_height)
end
terrain_height_map[i] = terrain_height
lake_height_map[i] = lake_height
else
terrain_height_map[i] = out_elev
lake_height_map[i] = out_elev
end
i = i + 1
end
end
return terrain_height_map, lake_height_map
end