Bump version (1.0.2) and add changelog

and remove an unnecessary index calculation

.gitignore

@@ -6,5 +6,7 @@ offset_x
 offset_y
 bounds_x
 bounds_y
+dirs
 rivers
 unused/
+river_data/

CHANGELOG.md

@@ -0,0 +1,18 @@
+CHANGELOG
+=========
+
+## `v1.0.2` (2022-01-10)
+- Use builtin logging system and appropriate loglevels
+- Skip empty chunks, when generating high above ground (~20% speedup)
+- Minor optimizations (turning global variables to local...)
+
+## `v1.0.1` (2021-09-14)
+- Automatically switch to `singlenode` mapgen at init time
+
+## `v1.0` (2021-08-01)
+- Rewritten pregen code (terrainlib) in pure Lua
+- Optimized grid loading
+- Load grid nodes on request by default
+- Changed river width settings
+- Added map size in settings
+- Added logs

LICENSE

@@ -0,0 +1,165 @@
+GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+
+  This version of the GNU Lesser General Public License incorporates
+the terms and conditions of version 3 of the GNU General Public
+License, supplemented by the additional permissions listed below.
+
+  0. Additional Definitions.
+
+  As used herein, "this License" refers to version 3 of the GNU Lesser
+General Public License, and the "GNU GPL" refers to version 3 of the GNU
+General Public License.
+
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+other than an Application or a Combined Work as defined below.
+
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+Library.

README.md

@@ -1,29 +1,41 @@
-mapgen_rivers
-=============
+# Map Generator with Rivers
+`mapgen_rivers v1.0.2` by Gaël de Sailly.
 
-Procedural map generator for Minetest 5.x. Still experimental and basic.
+Semi-procedural map generator for Minetest 5.x. It aims to create realistic and nice-looking landscapes for the game, focused on river networks. It is based on algorithms modelling water flow and river erosion at a broad scale, similar to some used by researchers in Earth Sciences. It is taking some inspiration from [Fastscape](https://github.com/fastscape-lem/fastscape).
 
-Contains two distinct programs: Python scripts for pre-processing, and Lua scripts to generate the map on Minetest.
+Its main particularity compared to conventional Minetest mapgens is that rivers that flow strictly downhill, and combine together to form wider rivers, until they reach the sea. Another notable feature is the possibility of large lakes above sea level.
 
-![Screenshot](https://user-images.githubusercontent.com/6905002/79073532-7a567f00-7ce7-11ea-9791-8fb453f5175d.png)
+![Screenshot](https://content.minetest.net/uploads/fff09f2269.png)
+
+It used to be composed of a Python script doing pre-generation, and a Lua mod reading the pre-generation output and generating the map. The code has been rewritten in full Lua for version 1.0 (July 2021), and is now usable out-of-the-box as any other Minetest mod.
+
+# Author and license
+License: GNU LGPLv3.0
+
+Code: Gaël de Sailly
+
+Flow routing algorithm concept (in `terrainlib/rivermapper.lua`): Cordonnier, G., Bovy, B., & Braun, J. (2019). A versatile, linear complexity algorithm for flow routing in topographies with depressions. Earth Surface Dynamics, 7(2), 549-562.
+
+# Requirements
+Mod dependencies: `default` required, and [`biomegen`](https://github.com/Gael-de-Sailly/biomegen) optional (provides biome system).
 
 # Installation
-This mod should be placed in the `/mods` directory like any other Minetest mod.
-
-The Python part relies on external libraries that you need to install:
-- `numpy`, a widely used library for numerical calculations
-- `noise`, doing Perlin/Simplex noises
-- optionally, `matplotlib` (for map preview)
-
-They are commonly found on `pip` or `conda` Python distributions.
+This mod should be placed in the `mods/` directory of Minetest like any other mod.
 
 # Usage
-## Pre-processing
-Run the script `terrain_rivers.py` via command line. You can optionally append the map size (by default 400). Example for a 1000x1000 map:
-```
-./terrain_rivers.py 1000
-```
-For a default 400x400 map, it should take between 1 and 2 minutes. It will generate 5 files directly in the mod folder, containing the map data (1.4 MB for the default size).
+It is recommended to use it **only in new worlds, with `singlenode` mapgen**. On first start, it runs pre-generation to produce a grid, from which the map will be generated. This usually takes a few seconds, but depending on custom settings this can grow considerably longer.
 
-## Map generation
-Just create a Minetest world with `singlenode` mapgen, enable this mod and start the world. The data files are immediately copied in the world folder so you can re-generate them afterwards, it won't affect the old worlds.
+By default, it only generates a 15k x 15k map, centered around the origin. To obtain a bigger map, you can increase grid size and/or block size in settings, but this can be more ressource-intensive (as the map has to be loaded in full at pre-generation).
+
+## Settings
+Settings can be found in Minetest in the `Settings` tab, `All settings` -> `Mods` -> `mapgen_rivers`.
+
+Most settings are world-specific and a copy is made in `mapgen_rivers.conf` in the world folder, during world first use, which means that further modification of global settings will not alter existing worlds.
+
+## Map preview
+The Python script `view_map.py` can display the full map. You need to have Python 3 installed, as well as the libraries `numpy`, `matplotlib`, and optionally `colorcet`. For `conda` users, an `environment.yml` file is provided.
+
+It can be run from command line by passing the world folder. Example:
+```
+./view_map.py ~/.minetest/worlds/test_mg_rivers
+```

bounds.py

@@ -1,62 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-
-def make_bounds(dirs, rivers):
-    (Y, X) = dirs.shape
-    bounds_h = np.zeros((Y, X-1), dtype='i4')
-    bounds_v = np.zeros((Y-1, X), dtype='i4')
-
-    bounds_v += (rivers * (dirs==1))[:-1,:]
-    bounds_h += (rivers * (dirs==2))[:,:-1]
-    bounds_v -= (rivers * (dirs==3))[1:,:]
-    bounds_h -= (rivers * (dirs==4))[:,1:]
-
-    return bounds_h, bounds_v
-
-def get_fixed(dirs):
-    borders = np.zeros(dirs.shape, dtype='?')
-    borders[-1,:] |= dirs[-1,:]==1
-    borders[:,-1] |= dirs[:,-1]==2
-    borders[0,:] |= dirs[0,:]==3
-    borders[:,0] |= dirs[:,0]==4
-
-    donors = np.zeros(dirs.shape, dtype='?')
-    donors[1:,:] |= dirs[:-1,:]==1
-    donors[:,1:] |= dirs[:,:-1]==2
-    donors[:-1,:] |= dirs[1:,:]==3
-    donors[:,:-1] |= dirs[:,1:]==4
-    return borders | ~donors
-
-def twist(bounds_x, bounds_y, fixed, d=0.1, n=5):
-    moveable = ~fixed
-
-    (Y, X) = fixed.shape
-    offset_x = np.zeros((Y, X))
-    offset_y = np.zeros((Y, X))
-
-    for i in range(n):
-        force_long = np.abs(bounds_x) * (1+np.diff(offset_x, axis=1))
-        force_trans = np.abs(bounds_y) * np.diff(offset_x, axis=0)
-
-        force_x = np.zeros((Y, X))
-        force_x[:,:-1] = force_long
-        force_x[:,1:] -= force_long
-        force_x[:-1,:]+= force_trans
-        force_x[1:,:] -= force_trans
-
-        force_long = np.abs(bounds_y) * (1+np.diff(offset_y, axis=0))
-        force_trans = np.abs(bounds_x) * np.diff(offset_y, axis=1)
-
-        force_y = np.zeros((Y, X))
-        force_y[:-1,:] = force_long
-        force_y[1:,:] -= force_long
-        force_y[:,:-1]+= force_trans
-        force_y[:,1:] -= force_trans
-
-        length = np.hypot(force_x, force_y)
-        length[length==0] = 1
-        coeff = d / length * moveable
-        offset_x += force_x * coeff
-        offset_y += force_y * coeff
-
-    return offset_x, offset_y

compatibility.lua

@@ -0,0 +1,34 @@
+local function fix_min_catchment(settings, is_global)
+	local prefix = is_global and "mapgen_rivers_" or ""
+
+	local min_catchment = settings:get(prefix.."min_catchment")
+	if min_catchment then
+		min_catchment = tonumber(min_catchment)
+		local blocksize = tonumber(settings:get(prefix.."blocksize") or 15)
+		settings:set(prefix.."min_catchment", tonumber(min_catchment) * blocksize*blocksize)
+		local max_catchment = settings:get(prefix.."max_catchment")
+		if max_catchment then
+			max_catchment = tonumber(max_catchment)
+			local wpower = math.log(2*blocksize)/math.log(max_catchment/min_catchment)
+			settings:set(prefix.."river_widening_power", wpower)
+		end
+	end
+end
+
+local function fix_compatibility_minetest(settings)
+	local previous_version = settings:get("mapgen_rivers_version") or "0.0"
+
+	if previous_version == "0.0" then
+		fix_min_catchment(settings, true)
+	end
+end
+
+local function fix_compatibility_mapgen_rivers(settings)
+	local previous_version = settings:get("version") or "0.0"
+
+	if previous_version == "0.0" then
+		fix_min_catchment(settings, false)
+	end
+end
+
+return fix_compatibility_minetest, fix_compatibility_mapgen_rivers

environment.yml

@@ -0,0 +1,10 @@
+name: mapgen_rivers
+
+channels:
+    - conda-forge
+
+dependencies:
+    - python
+    - matplotlib
+    - numpy
+    - colorcet

erosion.py

@@ -1,86 +0,0 @@
-import numpy as np
-import scipy.ndimage as im
-import rivermapper as rm
-
-def advection(dem, dirs, rivers, time, K=1, m=0.5, sea_level=0):
-    dirs = dirs.copy()
-    dirs[0,:] = 0
-    dirs[-1,:] = 0
-    dirs[:,0] = 0
-    dirs[:,-1] = 0
-
-    adv_time = 1 / (K*rivers**m)
-    dem = np.maximum(dem, sea_level)
-    dem_new = np.zeros(dem.shape)
-
-    for y in range(dirs.shape[0]):
-        for x in range(dirs.shape[1]):
-            x0, y0 = x, y
-            x1, y1 = x, y
-            remaining = time
-            while True:
-                flow_dir = dirs[y0,x0]
-                if flow_dir == 0:
-                    remaining = 0
-                    break
-                elif flow_dir == 1:
-                    y1 += 1
-                elif flow_dir == 2:
-                    x1 += 1
-                elif flow_dir == 3:
-                    y1 -= 1
-                elif flow_dir == 4:
-                    x1 -= 1
-
-                if remaining <= adv_time[y0,x0]:
-                    break
-                remaining -= adv_time[y0,x0]
-                x0, y0 = x1, y1
-
-            c = remaining / adv_time[y0,x0]
-            dem_new[y,x] = c*dem[y1,x1] + (1-c)*dem[y0,x0]
-
-    return np.minimum(dem, dem_new)
-
-def diffusion(dem, time, d=1):
-    radius = d * time**.5
-    return im.gaussian_filter(dem, radius, mode='reflect')
-
-class EvolutionModel:
-    def __init__(self, dem, K=1, m=0.5, d=1, sea_level=0, flow=False, flex_radius=100):
-        self.dem = dem
-        #self.bedrock = dem
-        self.K = K
-        self.m = m
-        self.d = d
-        self.sea_level = sea_level
-        self.flex_radius = flex_radius
-        self.define_isostasy()
-        if flow:
-            self.calculate_flow()
-        else:
-            self.lakes = dem
-            self.dirs = np.zeros(dem.shape, dtype='u1')
-            self.rivers = np.zeros(dem.shape, dtype='u4')
-            self.flow_uptodate = False
-
-    def calculate_flow(self):
-        self.dirs, self.lakes, self.rivers = rm.flow(self.dem)
-        self.flow_uptodate = True
-
-    def advection(self, time):
-        dem = advection(self.lakes, self.dirs, self.rivers, time, K=self.K, m=self.m, sea_level=self.sea_level)
-        self.dem = np.minimum(dem, self.dem)
-        self.flow_uptodate = False
-
-    def diffusion(self, time):
-        self.dem = diffusion(self.dem, time, d=self.d)
-        self.flow_uptodate = False
-
-    def define_isostasy(self):
-        self.ref_isostasy = im.gaussian_filter(self.dem, self.flex_radius, mode='reflect')
-
-    def adjust_isostasy(self, rate=1):
-        isostasy = im.gaussian_filter(self.dem, self.flex_radius, mode='reflect')
-        correction = (self.ref_isostasy - isostasy) * rate
-        self.dem = self.dem + correction

geometry.lua

@@ -1,45 +1,40 @@
+local sqrt, abs = math.sqrt, math.abs
+local unpk = unpack
+
 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
+	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
-		return math.sqrt(b)
+		-- The closest point of the segment is the extremity 1
+		return sqrt(b)
 	elseif a + c < b then
-		return math.sqrt(c)
+		-- The closest point of the segment is the extremity 2
+		return sqrt(c)
 	else
-		return math.abs(x1 * (y2-y) + x2 * (y-y1) + x * (y1-y2)) / math.sqrt(a)
+		-- 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)
-	-- X, Y 4-vectors giving the coordinates of the 4 nodes
+	-- 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 = unpack(X)
-	local y1, y2, y3, y4 = unpack(Y)
+	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
 
-local function area(X, Y) -- Signed area of polygon, in function of direction of rotation. Clockwise = positive.
-	local n = #X
-	local sum = X[1]*Y[n] - X[n]*Y[1]
-	for i=2, n do
-		sum = sum + X[i]*Y[i-1] - X[i-1]*Y[i]
-	end
-
-	return sum/2
-end
-
-return {
-	distance_to_segment = distance_to_segment,
-	transform_quadri = transform_quadri,
-	area = area,
-}
+return transform_quadri

heightmap.lua

@@ -0,0 +1,141 @@
+local modpath = mapgen_rivers.modpath
+
+local make_polygons = dofile(modpath .. 'polygons.lua')
+local transform_quadri = dofile(modpath .. 'geometry.lua')
+
+local sea_level = mapgen_rivers.settings.sea_level
+local riverbed_slope = mapgen_rivers.settings.riverbed_slope * mapgen_rivers.settings.blocksize
+
+local MAP_BOTTOM = -31000
+
+-- Localize for performance
+local floor, min, max = math.floor, math.min, math.max
+local unpk = unpack
+
+-- 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
+
+local function heightmaps(minp, maxp)
+
+	local polygons = 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,
+					r_north - zf,
+					xf - r_east,
+					zf - r_south,
+					c_NW-xf-zf,
+					xf-zf-c_NE,
+					xf+zf-c_SE,
+					zf-xf-c_SW,
+				}
+
+				-- Find the maximal depth factor and determine to which river it belongs
+				local depth_factor_max = 0
+				local imax = 0
+				for i=1, 8 do
+					if depth_factors[i] >= depth_factor_max then
+						depth_factor_max = depth_factors[i]
+						imax = i
+					end
+				end
+
+				-- Transform the coordinates to have xf and zf = 0 or 1 in rivers (to avoid rivers having lateral slope and to accomodate the surrounding smoothly)
+				if imax == 0 then
+					local x0 = max(r_west, c_NW-zf, zf-c_SW)
+					local x1 = min(r_east, c_NE+zf, c_SE-zf)
+					local z0 = max(r_north, c_NW-xf, xf-c_NE)
+					local z1 = min(r_south, c_SW+xf, c_SE-xf)
+					xf = (xf-x0) / (x1-x0)
+					zf = (zf-z0) / (z1-z0)
+				elseif imax == 1 then
+					xf = 0
+				elseif imax == 2 then
+					zf = 0
+				elseif imax == 3 then
+					xf = 1
+				elseif imax == 4 then
+					zf = 1
+				elseif imax == 5 then
+					xf, zf = 0, 0
+				elseif imax == 6 then
+					xf, zf = 1, 0
+				elseif imax == 7 then
+					xf, zf = 1, 1
+				elseif imax == 8 then
+					xf, zf = 0, 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],
+					xf, zf
+				))
+
+				-- Spatial gradient of the interpolation
+				local slope_x = zf*(vdem[3]-vdem[4]) + (1-zf)*(vdem[2]-vdem[1]) < 0
+				local slope_z = xf*(vdem[3]-vdem[2]) + (1-xf)*(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 depth_factor_max > 0 then
+					terrain_height = min(max(lake_height, sea_level) - floor(1+depth_factor_max*riverbed_slope), terrain_height)
+				end
+
+				terrain_height_map[i] = terrain_height
+				lake_height_map[i] = lake_height
+			else
+				terrain_height_map[i] = MAP_BOTTOM
+				lake_height_map[i] = MAP_BOTTOM
+			end
+			i = i + 1
+		end
+	end
+
+	return terrain_height_map, lake_height_map
+end
+
+return heightmaps

init.lua

@@ -1,311 +1,275 @@
+mapgen_rivers = {}
+
 local modpath = minetest.get_modpath(minetest.get_current_modname()) .. '/'
-local worldpath = minetest.get_worldpath() .. '/'
-local load_map = dofile(modpath .. 'load.lua')
-local geometry = dofile(modpath .. 'geometry.lua')
+mapgen_rivers.modpath = modpath
+mapgen_rivers.world_data_path = minetest.get_worldpath() .. '/river_data/'
 
-local function copy_if_needed(filename)
-	local wfilename = worldpath..filename
-	local wfile = io.open(wfilename, 'r')
-	if wfile then
-		wfile:close()
-		return
-	end
-	local mfilename = modpath..filename
-	local mfile = io.open(mfilename, 'r')
-	local wfile = io.open(wfilename, 'w')
-	wfile:write(mfile:read("*all"))
-	mfile:close()
-	wfile:close()
+if minetest.get_mapgen_setting("mg_name") ~= "singlenode" then
+	minetest.set_mapgen_setting("mg_name", "singlenode", true)
+	minetest.log("warning", "[mapgen_rivers] Mapgen set to singlenode")
 end
 
-copy_if_needed('size')
-local sfile = io.open(worldpath..'size')
-local X = tonumber(sfile:read('*l'))
-local Z = tonumber(sfile:read('*l'))
+dofile(modpath .. 'settings.lua')
 
-copy_if_needed('dem')
-local dem = load_map(worldpath..'dem', 2, true, X*Z)
-copy_if_needed('lakes')
-local lakes = load_map(worldpath..'lakes', 2, true, X*Z)
-copy_if_needed('bounds_x')
-local bounds_x = load_map(worldpath..'bounds_x', 4, false, (X-1)*Z)
-copy_if_needed('bounds_y')
-local bounds_z = load_map(worldpath..'bounds_y', 4, false, X*(Z-1))
+local sea_level = mapgen_rivers.settings.sea_level
+local elevation_chill = mapgen_rivers.settings.elevation_chill
+local use_distort = mapgen_rivers.settings.distort
+local use_biomes = mapgen_rivers.settings.biomes
+local use_biomegen_mod = use_biomes and minetest.global_exists('biomegen')
+use_biomes = use_biomes and not use_biomegen_mod
 
-copy_if_needed('offset_x')
-local offset_x = load_map(worldpath..'offset_x', 1, true, X*Z)
-for k, v in ipairs(offset_x) do
-	offset_x[k] = (v+0.5)/256
+if use_biomegen_mod then
+	biomegen.set_elevation_chill(elevation_chill)
 end
+dofile(modpath .. 'noises.lua')
 
-copy_if_needed('offset_y')
-local offset_z = load_map(worldpath..'offset_y', 1, true, X*Z)
-for k, v in ipairs(offset_z) do
-	offset_z[k] = (v+0.5)/256
-end
-
-
-local function index(x, z)
-	return z*X+x+1
-end
-
-local function get_point_location(x, z)
-	local i = index(x, z)
-	return x+offset_x[i], z+offset_z[i]
-end
+local heightmaps = dofile(modpath .. 'heightmap.lua')
 
+-- 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
 
+-- Localize for performance
+local floor, min = math.floor, math.min
+
 local data = {}
 
-local blocksize = 12
-local sea_level = 1
-local min_catchment = 25
-local max_catchment = 40000
-local riverbed_slope = 0.4
+local noise_x_obj, noise_z_obj, noise_distort_obj, noise_heat_obj, noise_heat_blend_obj
+local noise_x_map = {}
+local noise_z_map = {}
+local noise_distort_map = {}
+local noise_heat_map = {}
+local noise_heat_blend_map = {}
+local mapsize
+local init = false
 
-local get_settings = dofile(modpath .. 'settings.lua')
-
-blocksize = get_settings('blocksize', 'int', blocksize)
-sea_level = get_settings('sea_level', 'int', sea_level)
-min_catchment = get_settings('min_catchment', 'float', min_catchment)
-max_catchment = get_settings('max_catchment', 'float', max_catchment)
-riverbed_slope = get_settings('riverbed_slope', 'float', riverbed_slope) * blocksize
-
--- Width coefficients: coefficients solving
---   wfactor * min_catchment ^ wpower = 1/(2*blocksize)
---   wfactor * max_catchment ^ wpower = 1
-local wpower = math.log(2*blocksize)/math.log(max_catchment/min_catchment)
-local wfactor = 1 / max_catchment ^ wpower
-local function river_width(flow)
-	flow = math.abs(flow)
-	if flow < min_catchment then
-		return 0
-	end
-
-	return math.min(wfactor * flow ^ wpower, 1)
-end
+local sumtime = 0
+local sumtime2 = 0
+local ngen = 0
 
 local function generate(minp, maxp, seed)
+	minetest.log("info", ("[mapgen_rivers] Generating from %s to %s"):format(minetest.pos_to_string(minp), minetest.pos_to_string(maxp)))
+
+	local chulens = {
+		x = maxp.x-minp.x+1,
+		y = maxp.y-minp.y+1,
+		z = maxp.z-minp.z+1,
+	}
+
+	if not init then
+		mapsize = {
+			x = chulens.x,
+			y = chulens.y+1,
+			z = chulens.z,
+		}
+		if use_distort then
+			noise_x_obj = minetest.get_perlin_map(mapgen_rivers.noise_params.distort_x, mapsize)
+			noise_z_obj = minetest.get_perlin_map(mapgen_rivers.noise_params.distort_z, mapsize)
+			noise_distort_obj = minetest.get_perlin_map(mapgen_rivers.noise_params.distort_amplitude, chulens)
+		end
+		if use_biomes then
+			noise_heat_obj = minetest.get_perlin_map(mapgen_rivers.noise_params.heat, chulens)
+			noise_heat_blend_obj = minetest.get_perlin_map(mapgen_rivers.noise_params.heat_blend, chulens)
+		end
+		init = true
+	end
+
+	local t0 = os.clock()
+	local minp2d = {x=minp.x, y=minp.z}
+	if use_distort then
+		noise_x_obj:get_3d_map_flat(minp, noise_x_map)
+		noise_z_obj:get_3d_map_flat(minp, noise_z_map)
+		noise_distort_obj:get_2d_map_flat(minp2d, noise_distort_map)
+	end
+	if use_biomes then
+		noise_heat_obj:get_2d_map_flat(minp2d, noise_heat_map)
+		noise_heat_blend_obj:get_2d_map_flat(minp2d, noise_heat_blend_map)
+	end
+
+	local terrain_map, lake_map, incr, i_origin
+
+	if use_distort then
+		local xmin, xmax, zmin, zmax = minp.x, maxp.x, minp.z, maxp.z
+		local i = 0
+		local i2d = 0
+		for z=minp.z, maxp.z do
+			for y=minp.y, maxp.y+1 do
+				for x=minp.x, maxp.x do
+					i = i+1
+					i2d = i2d+1
+					local distort = noise_distort_map[i2d]
+					local xv = noise_x_map[i]*distort + x
+					if xv < xmin then xmin = xv end
+					if xv > xmax then xmax = xv end
+					noise_x_map[i] = xv
+					local zv = noise_z_map[i]*distort + z
+					if zv < zmin then zmin = zv end
+					if zv > zmax then zmax = zv end
+					noise_z_map[i] = zv
+				end
+				i2d = i2d-chulens.x
+			end
+		end
+
+		local pminp = {x=floor(xmin), z=floor(zmin)}
+		local pmaxp = {x=floor(xmax)+1, z=floor(zmax)+1}
+		incr = pmaxp.x-pminp.x+1
+		i_origin = 1 - pminp.z*incr - pminp.x
+		terrain_map, lake_map = heightmaps(pminp, pmaxp)
+	else
+		terrain_map, lake_map = heightmaps(minp, maxp)
+	end
+
+	-- Check that there is at least one position that reaches min y
+	if minp.y > sea_level then
+		local y0 = minp.y
+		local is_empty = true
+		for i=1, #terrain_map do
+			if terrain_map[i] >= y0 or lake_map[i] >= y0 then
+				is_empty = false
+				break
+			end
+		end
+
+		-- If not, skip chunk
+		if is_empty then
+			local t = os.clock() - t0
+			ngen = ngen + 1
+			sumtime = sumtime + t
+			sumtime2 = sumtime2 + t*t
+
+			minetest.log("verbose", "[mapgen_rivers] Skipping empty chunk (fully above ground level)")
+			minetest.log("verbose", ("[mapgen_rivers] Done in %5.3f s"):format(t))
+			return
+		end
+	end
+
 	local c_stone = minetest.get_content_id("default:stone")
 	local c_dirt = minetest.get_content_id("default:dirt")
 	local c_lawn = minetest.get_content_id("default:dirt_with_grass")
+	local c_dirtsnow = minetest.get_content_id("default:dirt_with_snow")
+	local c_snow = minetest.get_content_id("default:snowblock")
 	local c_sand = minetest.get_content_id("default:sand")
 	local c_water = minetest.get_content_id("default:water_source")
 	local c_rwater = minetest.get_content_id("default:river_water_source")
+	local c_ice = minetest.get_content_id("default:ice")
 
 	local vm, emin, emax = minetest.get_mapgen_object("voxelmanip")
 	vm:get_data(data)
 
 	local a = VoxelArea:new({MinEdge = emin, MaxEdge = emax})
 	local ystride = a.ystride -- Tip : the ystride of a VoxelArea is the number to add to the array index to get the index of the position above. It's faster because it avoids to completely recalculate the index.
-	local chulens = maxp.z - minp.z + 1
 
-	local polygons = {}
-	local xpmin, xpmax = math.max(math.floor(minp.x/blocksize - 0.5), 0), math.min(math.ceil(maxp.x/blocksize), X-2)
-	local zpmin, zpmax = math.max(math.floor(minp.z/blocksize - 0.5), 0), math.min(math.ceil(maxp.z/blocksize), Z-2)
+	local nid = mapsize.x*(mapsize.y-1) + 1
+	local incrY = -mapsize.x
+	local incrX = 1 - mapsize.y*incrY
+	local incrZ = mapsize.x*mapsize.y - mapsize.x*incrX - mapsize.x*mapsize.y*incrY
 
-	for xp = xpmin, xpmax do
-		for zp=zpmin, zpmax do
-			local iA = index(xp, zp)
-			local iB = index(xp+1, zp)
-			local iC = index(xp+1, zp+1)
-			local iD = index(xp, zp+1)
-			local poly_x = {offset_x[iA]+xp, offset_x[iB]+xp+1, offset_x[iC]+xp+1, offset_x[iD]+xp}
-			local poly_z = {offset_z[iA]+zp, offset_z[iB]+zp, offset_z[iC]+zp+1, offset_z[iD]+zp+1}
-			local polygon = {x=poly_x, z=poly_z, i={iA, iB, iC, iD}}
+	local i2d = 1
 
-			local bounds = {}
-			local xmin = math.max(math.floor(blocksize*math.min(unpack(poly_x)))+1, minp.x)
-			local xmax = math.min(math.floor(blocksize*math.max(unpack(poly_x))), maxp.x)
-			for x=xmin, xmax do
-				bounds[x] = {}
-			end
-
-			local i1 = 4
-			for i2=1, 4 do -- Loop on 4 edges
-				local x1, x2 = poly_x[i1], poly_x[i2]
-				local lxmin = math.floor(blocksize*math.min(x1, x2))+1
-				local lxmax = math.floor(blocksize*math.max(x1, x2))
-				if lxmin <= lxmax then
-					local z1, z2 = poly_z[i1], poly_z[i2]
-					local a = (z1-z2) / (x1-x2)
-					local b = blocksize*(z1 - a*x1)
-					for x=math.max(lxmin, minp.x), math.min(lxmax, maxp.x) do
-						table.insert(bounds[x], a*x+b)
-					end
-				end
-				i1 = i2
-			end
-			for x=xmin, xmax do
-				local xlist = bounds[x]
-				table.sort(xlist)
-				local c = math.floor(#xlist/2)
-				for l=1, c do
-					local zmin = math.max(math.floor(xlist[l*2-1])+1, minp.z)
-					local zmax = math.min(math.floor(xlist[l*2]), maxp.z)
-					local i = (x-minp.x) * chulens + (zmin-minp.z) + 1
-					for z=zmin, zmax do
-						polygons[i] = polygon
-						i = i + 1
-					end
-				end
-			end
-
-			polygon.dem = {dem[iA], dem[iB], dem[iC], dem[iD]}
-			polygon.lake = math.min(lakes[iA], lakes[iB], lakes[iC], lakes[iD])
-
-			local river_west = river_width(bounds_z[iA])
-			local river_north = river_width(bounds_x[iA-zp])
-			local river_east = 1-river_width(bounds_z[iB])
-			local river_south = 1-river_width(bounds_x[iD-zp-1])
-			if river_west > river_east then
-				local mean = (river_west + river_east) / 2
-				river_west = mean
-				river_east = mean
-			end
-			if river_north > river_south then
-				local mean = (river_north + river_south) / 2
-				river_north = mean
-				river_south = mean
-			end
-			polygon.rivers = {river_west, river_north, river_east, river_south}
-
-			local around = {0,0,0,0,0,0,0,0}
-			if zp > 0 then
-				around[1] = river_width(bounds_z[iA-X])
-				around[2] = river_width(bounds_z[iB-X])
-			end
-			if xp < X-2 then
-				around[3] = river_width(bounds_x[iB-zp])
-				around[4] = river_width(bounds_x[iC-zp-1])
-			end
-			if zp < Z-2 then
-				around[5] = river_width(bounds_z[iC])
-				around[6] = river_width(bounds_z[iD])
-			end
-			if xp > 0 then
-				around[7] = river_width(bounds_x[iD-zp-2])
-				around[8] = river_width(bounds_x[iA-zp-1])
-			end
-			polygon.river_corners = {math.max(around[8], around[1]), math.max(around[2], around[3]), math.max(around[4], around[5]), math.max(around[6], around[7])}
-		end
-	end
-
-	local i = 1
-	for x = minp.x, maxp.x do
 	for z = minp.z, maxp.z do
-			local poly = polygons[i]
-			if poly then
-				local xf, zf = geometry.transform_quadri(poly.x, poly.z, x/blocksize, z/blocksize)
-				local i00, i01, i11, i10 = unpack(poly.i)
-
-				local is_river = false
-				local depth_factor = 0
-				local r_west, r_north, r_east, r_south = unpack(poly.rivers)
-				if xf >= r_east then
-					is_river = true
-					depth_factor = xf-r_east
-					xf = 1
-				elseif xf <= r_west then
-					is_river = true
-					depth_factor = r_west-xf
-					xf = 0
+		for x = minp.x, maxp.x do
+			local ivm = a:index(x, maxp.y+1, z)
+			local ground_above = false
+			local temperature
+			if use_biomes then
+				temperature = noise_heat_map[i2d]+noise_heat_blend_map[i2d]
 			end
-				if zf >= r_south then
-					is_river = true
-					depth_factor = zf-r_south
-					zf = 1
-				elseif zf <= r_north then
-					is_river = true
-					depth_factor = r_north-zf
-					zf = 0
+			local terrain, lake
+			if not use_distort then
+				terrain = terrain_map[i2d]
+				lake = lake_map[i2d]
 			end
 
-				if not is_river then
-					local c_NW, c_NE, c_SE, c_SW = unpack(poly.river_corners)
-					if xf+zf <= c_NW then
-						is_river = true
-						depth_factor = c_NW-xf-zf
-						xf, zf = 0, 0
-					elseif 1-xf+zf <= c_NE then
-						is_river = true
-						depth_factor = c_NE-1+xf-zf
-						xf, zf = 1, 0
-					elseif 2-xf-zf <= c_SE then
-						is_river = true
-						depth_factor = c_SE-2+xf+zf
-						xf, zf = 1, 1
-					elseif xf+1-zf <= c_SW then
-						is_river = true
-						depth_factor = c_SW-xf-1+zf
-						xf, zf = 0, 1
-					end
+			for y = maxp.y+1, minp.y, -1 do
+				if use_distort then
+					local xn = noise_x_map[nid]
+					local zn = noise_z_map[nid]
+					local x0 = floor(xn)
+					local z0 = floor(zn)
+
+					local i0 = i_origin + z0*incr + x0
+					local i1 = i0+1
+					local i2 = i1+incr
+					local i3 = i2-1
+
+					terrain = interp(terrain_map[i0], terrain_map[i1], terrain_map[i2], terrain_map[i3], xn-x0, zn-z0)
+					lake = min(lake_map[i0], lake_map[i1], lake_map[i2], lake_map[i3])
 				end
 
-				if not is_river then
-					xf = (xf-r_west) / (r_east-r_west)
-					zf = (zf-r_north) / (r_south-r_north)
-				end
+				if y <= maxp.y then
 
-				local vdem = poly.dem
-				local terrain_height = math.floor(0.5+interp(
-					vdem[1],
-					vdem[2],
-					vdem[3],
-					vdem[4],
-					xf, zf
-				))
-
-				local lake_height = math.max(math.floor(poly.lake), terrain_height)
-				if is_river then
-					terrain_height = math.min(math.max(lake_height, sea_level) - math.floor(1+depth_factor*riverbed_slope), terrain_height)
-				end
-				local is_lake = lake_height > terrain_height
-				local ivm = a:index(x, minp.y-1, z)
-				if terrain_height >= minp.y then
-					for y=minp.y, math.min(maxp.y, terrain_height) do
-						if y == terrain_height then
-							if is_lake or y <= sea_level then
+					local is_lake = lake > terrain
+					if y <= terrain then
+						if not use_biomes or y <= terrain-1 or ground_above then
+							data[ivm] = c_stone
+						elseif is_lake or y < sea_level then
 							data[ivm] = c_sand
 						else
+							local temperature_y = temperature - y*elevation_chill
+							if temperature_y >= 15 then
 								data[ivm] = c_lawn
-							end
+							elseif temperature_y >= 0 then
+								data[ivm] = c_dirtsnow
 							else
-							data[ivm] = c_stone
-						end
-						ivm = ivm + ystride
+								data[ivm] = c_snow
 							end
 						end
-
-				if lake_height > sea_level then
-					if is_lake and lake_height > minp.y then
-						for y=math.max(minp.y, terrain_height+1), math.min(maxp.y, lake_height) do
+					elseif y <= lake and lake > sea_level then
+						if not use_biomes or temperature - y*elevation_chill >= 0 then
 							data[ivm] = c_rwater
-							ivm = ivm + ystride
-						end
-					end
 						else
-					for y=math.max(minp.y, terrain_height+1), math.min(maxp.y, sea_level) do
+							data[ivm] = c_ice
+						end
+					elseif y <= sea_level then
 						data[ivm] = c_water
-						ivm = ivm + ystride
-					end
-				end
-			end
-			i = i + 1
 					end
 				end
 
+				ground_above = y <= terrain
+
+				ivm = ivm - ystride
+				if use_distort then
+					nid = nid + incrY
+				end
+			end
+
+			if use_distort then
+				nid = nid + incrX
+			end
+			i2d = i2d + 1
+		end
+
+		if use_distort then
+			nid = nid + incrZ
+		end
+	end
+
+	if use_biomegen_mod then
+		biomegen.generate_all(data, a, vm, minp, maxp, seed)
+	else
 		vm:set_data(data)
 		minetest.generate_ores(vm, minp, maxp)
+	end
+
 	vm:set_lighting({day = 0, night = 0})
 	vm:calc_lighting()
 	vm:update_liquids()
 	vm:write_to_map()
+
+	local t = os.clock()-t0
+	ngen = ngen + 1
+	sumtime = sumtime + t
+	sumtime2 = sumtime2 + t*t
+	minetest.log("verbose", ("[mapgen_rivers] Done in %5.3f s"):format(t))
 end
 
 minetest.register_on_generated(generate)
+minetest.register_on_shutdown(function()
+	local avg = sumtime / ngen
+	local std = math.sqrt(sumtime2/ngen - avg*avg)
+	minetest.log("action", ("[mapgen_rivers] Mapgen statistics:\n- Mapgen calls: %4d\n- Mean time: %5.3f s\n- Standard deviation: %5.3f s"):format(ngen, avg, std))
+end)

load.lua

@@ -1,5 +1,11 @@
-local function load_map(filename, bytes, signed, size)
-	local file = io.open(filename, 'r')
+local worldpath = mapgen_rivers.world_data_path
+
+local floor = math.floor
+local sbyte, schar = string.byte, string.char
+local unpk = unpack
+
+function mapgen_rivers.load_map(filename, bytes, signed, size, converter)
+	local file = io.open(worldpath .. filename, 'rb')
 	local data = file:read('*all')
 	if #data < bytes*size then
 		data = minetest.decompress(data)
@@ -8,22 +14,85 @@ local function load_map(filename, bytes, signed, size)
 	local map = {}
 
 	for i=1, size do
-		local i0, i1 = (i-1)*bytes+1, i*bytes
+		local i0 = (i-1)*bytes+1
 		local elements = {data:byte(i0, i1)}
-		local n = elements[1]
+		local n = sbyte(data, i0)
 		if signed and n >= 128 then
 			n = n - 256
 		end
 
-		for j=2, bytes do
-			n = n*256 + elements[j]
+		for j=1, bytes-1 do
+			n = n*256 + sbyte(data, i0+j)
 		end
 
 		map[i] = n
 	end
 	file:close()
 
+	if converter then
+		for i=1, size do
+			map[i] = converter(map[i])
+		end
+	end
+
 	return map
 end
 
-return load_map
+local loader_mt = {
+	__index = function(loader, i)
+		local file = loader.file
+		local bytes = loader.bytes
+		file:seek('set', (i-1)*bytes)
+		local strnum = file:read(bytes)
+
+		local n = sbyte(strnum, 1)
+		if loader.signed and n >= 128 then
+			n = n - 256
+		end
+
+		for j=2, bytes do
+			n = n*256 + sbyte(strnum, j)
+		end
+
+		if loader.conv then
+			n = loader.conv(n)
+		end
+		loader[i] = n
+		return n
+	end,
+}
+
+function mapgen_rivers.interactive_loader(filename, bytes, signed, size, converter)
+	local file = io.open(worldpath .. filename, 'rb')
+	if file then
+		minetest.register_on_shutdown(function()
+			file:close()
+		end)
+		converter = converter or false
+		return setmetatable({file=file, bytes=bytes, signed=signed, size=size, conv=converter}, loader_mt)
+	end
+end
+
+function mapgen_rivers.write_map(filename, data, bytes)
+	local size = #data
+	local file = io.open(worldpath .. filename, 'wb')
+
+	local bytelist = {}
+	for j=1, bytes do
+		bytelist[j] = 0
+	end
+
+	for i=1, size do
+		local n = floor(data[i])
+		data[i] = n
+		for j=bytes, 2, -1 do
+			bytelist[j] = n % 256
+			n = floor(n / 256)
+		end
+		bytelist[1] = n % 256
+
+		file:write(schar(unpk(bytelist)))
+	end
+
+	file:close()
+end

mod.conf

@@ -0,0 +1,4 @@
+name = mapgen_rivers
+title = Map generator with realistic rivers
+depends = default
+optional_depends = biomegen

noises.lua

@@ -0,0 +1,80 @@
+local def_setting = mapgen_rivers.define_setting
+
+mapgen_rivers.noise_params = {
+	base = def_setting('np_base', 'noise', {
+		offset = 0,
+		scale = 300,
+		seed = 2469,
+		octaves = 8,
+		spread = {x=2048, y=2048, z=2048},
+		persist = 0.6,
+		lacunarity = 2,
+		flags = "eased",
+	}),
+
+	distort_x = def_setting('np_distort_x', 'noise', {
+		offset = 0,
+		scale = 1,
+		seed = -4574,
+		spread = {x=64, y=32, z=64},
+		octaves = 3,
+		persistence = 0.75,
+		lacunarity = 2,
+	}),
+
+	distort_z = def_setting('np_distort_z', 'noise', {
+		offset = 0,
+		scale = 1,
+		seed = -7940,
+		spread = {x=64, y=32, z=64},
+		octaves = 3,
+		persistence = 0.75,
+		lacunarity = 2,
+	}),
+
+	distort_amplitude = def_setting('np_distort_amplitude', 'noise', {
+		offset = 0,
+		scale = 10,
+		seed = 676,
+		spread = {x=1024, y=1024, z=1024},
+		octaves = 5,
+		persistence = 0.5,
+		lacunarity = 2,
+		flags = "absvalue",
+	}),
+
+	heat = minetest.get_mapgen_setting_noiseparams('mg_biome_np_heat'),
+	heat_blend = minetest.get_mapgen_setting_noiseparams('mg_biome_np_heat_blend'),
+}
+
+-- Convert to number because Minetest API is not able to do it cleanly...
+for name, np in pairs(mapgen_rivers.noise_params) do
+	for field, value in pairs(np) do
+		if field ~= 'flags' and type(value) == 'string' then
+			np[field] = tonumber(value) or value
+		elseif field == 'spread' then
+			for dir, v in pairs(value) do
+				value[dir] = tonumber(v) or v
+			end
+		end
+	end
+end
+
+local heat = mapgen_rivers.noise_params.heat
+local base = mapgen_rivers.noise_params.base
+local settings = mapgen_rivers.settings
+heat.offset = heat.offset + settings.sea_level * settings.elevation_chill
+base.spread.x = base.spread.x / settings.blocksize
+base.spread.y = base.spread.y / settings.blocksize
+base.spread.z = base.spread.z / settings.blocksize
+
+for name, np in pairs(mapgen_rivers.noise_params) do
+	local lac = np.lacunarity or 2
+	if lac > 1 then
+		local omax = math.floor(math.log(math.min(np.spread.x, np.spread.y, np.spread.z)) / math.log(lac))+1
+		if np.octaves > omax then
+			minetest.log("warning", "[mapgen_rivers] Noise " .. name .. ": 'octaves' reduced to " .. omax)
+			np.octaves = omax
+		end
+	end
+end

polygons.lua

@@ -0,0 +1,256 @@
+local modpath = mapgen_rivers.modpath
+local mod_data_path = modpath .. 'river_data/'
+if not io.open(mod_data_path .. 'size', 'r') then
+	mod_data_path = modpath .. 'demo_data/'
+end
+
+local world_data_path = mapgen_rivers.world_data_path
+minetest.mkdir(world_data_path)
+
+dofile(modpath .. 'load.lua')
+
+mapgen_rivers.grid = {}
+
+local X = mapgen_rivers.settings.grid_x_size
+local Z = mapgen_rivers.settings.grid_z_size
+
+local function offset_converter(o)
+	return (o + 0.5) * (1/256)
+end
+
+local load_all = mapgen_rivers.settings.load_all
+
+-- Try to read file 'size'
+local sfile = io.open(world_data_path..'size', 'r')
+local first_mapgen = true
+if sfile then
+	X, Z = tonumber(sfile:read('*l')), tonumber(sfile:read('*l'))
+	sfile:close()
+	first_mapgen = false
+end
+
+if first_mapgen then
+	-- Generate a map!!
+	local pregenerate = dofile(mapgen_rivers.modpath .. '/pregenerate.lua')
+	minetest.register_on_mods_loaded(function()
+		minetest.log("action", '[mapgen_rivers] Generating grid, this may take a while...')
+		pregenerate(load_all)
+
+		if load_all then
+			local offset_x = mapgen_rivers.grid.offset_x
+			local offset_y = mapgen_rivers.grid.offset_y
+			for i=1, X*Z do
+				offset_x[i] = offset_converter(offset_x[i])
+				offset_y[i] = offset_converter(offset_y[i])
+			end
+		end
+	end)
+end
+
+-- if data not already loaded
+if not (first_mapgen and load_all) then
+	local load_map
+	if load_all then
+		load_map = mapgen_rivers.load_map
+	else
+		load_map = mapgen_rivers.interactive_loader
+	end
+
+	minetest.register_on_mods_loaded(function()
+		if load_all then
+			minetest.log("action", '[mapgen_rivers] Loading full grid')
+		else
+			minetest.log("action", '[mapgen_rivers] Loading grid as interactive loaders')
+		end
+		local grid = mapgen_rivers.grid
+
+		grid.dem = load_map('dem', 2, true, X*Z)
+		grid.lakes = load_map('lakes', 2, true, X*Z)
+		grid.dirs = load_map('dirs', 1, false, X*Z)
+		grid.rivers = load_map('rivers', 4, false, X*Z)
+
+		grid.offset_x = load_map('offset_x', 1, true, X*Z, offset_converter)
+		grid.offset_y = load_map('offset_y', 1, true, X*Z, offset_converter)
+	end)
+end
+
+mapgen_rivers.grid.size = {x=X, y=Z}
+
+local function index(x, z)
+	return z*X+x+1
+end
+
+local blocksize = mapgen_rivers.settings.blocksize
+local min_catchment = mapgen_rivers.settings.min_catchment
+local max_catchment = mapgen_rivers.settings.max_catchment
+
+local map_offset = {x=0, z=0}
+if mapgen_rivers.settings.center then
+	map_offset.x = blocksize*X/2
+	map_offset.z = blocksize*Z/2
+end
+
+-- Localize for performance
+local floor, ceil, min, max, abs = math.floor, math.ceil, math.min, math.max, math.abs
+
+local min_catchment = mapgen_rivers.settings.min_catchment / (blocksize*blocksize)
+local wpower = mapgen_rivers.settings.river_widening_power
+local wfactor = 1/(2*blocksize * min_catchment^wpower)
+local function river_width(flow)
+	flow = abs(flow)
+	if flow < min_catchment then
+		return 0
+	end
+
+	return min(wfactor * flow ^ wpower, 1)
+end
+
+local noise_heat -- Need a large-scale noise here so no heat blend
+local elevation_chill = mapgen_rivers.settings.elevation_chill
+local function get_temperature(x, y, z)
+	local pos = {x=x, y=z}
+	return noise_heat:get2d(pos) - y*elevation_chill
+end
+
+local glaciers = mapgen_rivers.settings.glaciers
+local glacier_factor = mapgen_rivers.settings.glacier_factor
+
+local init = false
+
+-- On map generation, determine into which polygon every point (in 2D) will fall.
+-- Also store polygon-specific data
+local function make_polygons(minp, maxp)
+
+	local grid = mapgen_rivers.grid
+	local dem = grid.dem
+	local lakes = grid.lakes
+	local dirs = grid.dirs
+	local rivers = grid.rivers
+
+	local offset_x = grid.offset_x
+	local offset_z = grid.offset_y
+
+	if not init then
+		if glaciers then
+			noise_heat = minetest.get_perlin(mapgen_rivers.noise_params.heat)
+		end
+		init = true
+	end
+
+	local chulens = maxp.x - minp.x + 1
+
+	local polygons = {}
+	-- Determine the minimum and maximum coordinates of the polygons that could be on the chunk, knowing that they have an average size of 'blocksize' and a maximal offset of 0.5 blocksize.
+	local xpmin, xpmax = max(floor((minp.x+map_offset.x)/blocksize - 0.5), 0), min(ceil((maxp.x+map_offset.x)/blocksize + 0.5), X-2)
+	local zpmin, zpmax = max(floor((minp.z+map_offset.z)/blocksize - 0.5), 0), min(ceil((maxp.z+map_offset.z)/blocksize + 0.5), Z-2)
+
+	-- Iterate over the polygons
+	for xp = xpmin, xpmax do
+		for zp=zpmin, zpmax do
+			local iA = index(xp, zp)
+			local iB = index(xp+1, zp)
+			local iC = index(xp+1, zp+1)
+			local iD = index(xp, zp+1)
+			-- Extract the vertices of the polygon
+			local poly_x = {
+				(offset_x[iA]+xp)   * blocksize - map_offset.x,
+				(offset_x[iB]+xp+1) * blocksize - map_offset.x,
+				(offset_x[iC]+xp+1) * blocksize - map_offset.x,
+				(offset_x[iD]+xp)   * blocksize - map_offset.x,
+			}
+			local poly_z = {
+				(offset_z[iA]+zp)   * blocksize - map_offset.z,
+				(offset_z[iB]+zp)   * blocksize - map_offset.z,
+				(offset_z[iC]+zp+1) * blocksize - map_offset.z,
+				(offset_z[iD]+zp+1) * blocksize - map_offset.z,
+			}
+			local polygon = {x=poly_x, z=poly_z, i={iA, iB, iC, iD}}
+
+			local bounds = {} -- Will be a list of the intercepts of polygon edges for every Z position (scanline algorithm)
+			-- Calculate the min and max Z positions 
+			local zmin = max(floor(min(unpack(poly_z)))+1, minp.z)
+			local zmax = min(floor(max(unpack(poly_z))), maxp.z)
+			-- And initialize the arrays
+			for z=zmin, zmax do
+				bounds[z] = {}
+			end
+
+			local i1 = 4
+			for i2=1, 4 do -- Loop on 4 edges
+				local z1, z2 = poly_z[i1], poly_z[i2]
+				-- Calculate the integer Z positions over which this edge spans
+				local lzmin = floor(min(z1, z2))+1
+				local lzmax = floor(max(z1, z2))
+				if lzmin <= lzmax then -- If there is at least one position in it
+					local x1, x2 = poly_x[i1], poly_x[i2]
+					-- Calculate coefficient of the equation defining the edge: X=aZ+b
+					local a = (x1-x2) / (z1-z2)
+					local b = (x1 - a*z1)
+					for z=max(lzmin, minp.z), min(lzmax, maxp.z) do
+						-- For every Z position involved, add the intercepted X position in the table
+						table.insert(bounds[z], a*z+b)
+					end
+				end
+				i1 = i2
+			end
+			for z=zmin, zmax do
+				-- Now sort the bounds list
+				local zlist = bounds[z]
+				table.sort(zlist)
+				local c = floor(#zlist/2)
+				for l=1, c do
+					-- Take pairs of X coordinates: all positions between them belong to the polygon.
+					local xmin = max(floor(zlist[l*2-1])+1, minp.x)
+					local xmax = min(floor(zlist[l*2]), maxp.x)
+					local i = (z-minp.z) * chulens + (xmin-minp.x) + 1
+					for x=xmin, xmax do
+						-- Fill the map at these places
+						polygons[i] = polygon
+						i = i + 1
+					end
+				end
+			end
+
+			local poly_dem = {dem[iA], dem[iB], dem[iC], dem[iD]}
+			polygon.dem = poly_dem
+			polygon.lake = {lakes[iA], lakes[iB], lakes[iC], lakes[iD]}
+
+			-- Now, rivers.
+			-- Load river flux values for the 4 corners
+			local riverA = river_width(rivers[iA])
+			local riverB = river_width(rivers[iB])
+			local riverC = river_width(rivers[iC])
+			local riverD = river_width(rivers[iD])
+			if glaciers then -- Widen the river
+				if get_temperature(poly_x[1], poly_dem[1], poly_z[1]) < 0 then
+					riverA = min(riverA*glacier_factor, 1)
+				end
+				if get_temperature(poly_x[2], poly_dem[2], poly_z[2]) < 0 then
+					riverB = min(riverB*glacier_factor, 1)
+				end
+				if get_temperature(poly_x[3], poly_dem[3], poly_z[3]) < 0 then
+					riverC = min(riverC*glacier_factor, 1)
+				end
+				if get_temperature(poly_x[4], poly_dem[4], poly_z[4]) < 0 then
+					riverD = min(riverD*glacier_factor, 1)
+				end
+			end
+
+			polygon.river_corners = {riverA, 1-riverB, 2-riverC, 1-riverD}
+
+			-- Flow directions
+			local dirA, dirB, dirC, dirD = dirs[iA], dirs[iB], dirs[iC], dirs[iD]
+			-- Determine the river flux on the edges, by testing dirs values
+			local river_west = (dirA==1 and riverA or 0) + (dirD==3 and riverD or 0)
+			local river_north = (dirA==2 and riverA or 0) + (dirB==4 and riverB or 0)
+			local river_east = 1 - (dirB==1 and riverB or 0) - (dirC==3 and riverC or 0)
+			local river_south = 1 - (dirD==2 and riverD or 0) - (dirC==4 and riverC or 0)
+
+			polygon.rivers = {river_west, river_north, river_east, river_south}
+		end
+	end
+
+	return polygons
+end
+
+return make_polygons

pregenerate.lua

@@ -0,0 +1,81 @@
+local EvolutionModel = dofile(mapgen_rivers.modpath .. '/terrainlib_lua/erosion.lua')
+local twist = dofile(mapgen_rivers.modpath .. '/terrainlib_lua/twist.lua')
+
+local blocksize = mapgen_rivers.settings.blocksize
+local tectonic_speed = mapgen_rivers.settings.tectonic_speed
+
+local np_base = table.copy(mapgen_rivers.noise_params.base)
+
+local evol_params = mapgen_rivers.settings.evol_params
+
+local time = mapgen_rivers.settings.evol_time
+local time_step = mapgen_rivers.settings.evol_time_step
+local niter = math.ceil(time/time_step)
+time_step = time / niter
+
+local function pregenerate(keep_loaded)
+	local grid = mapgen_rivers.grid
+	local size = grid.size
+
+	local seed = tonumber(minetest.get_mapgen_setting("seed"))
+	np_base.seed = (np_base.seed or 0) + seed
+
+	local nobj_base = PerlinNoiseMap(np_base, {x=size.x, y=1, z=size.y})
+
+	local dem = nobj_base:get_3d_map_flat({x=0, y=0, z=0})
+	dem.X = size.x
+	dem.Y = size.y
+
+	local model = EvolutionModel(evol_params)
+	model.dem = dem
+	local ref_dem = model:define_isostasy(dem)
+
+	local tectonic_step = tectonic_speed * time_step
+	collectgarbage()
+	for i=1, niter do
+		minetest.log("info", "[mapgen_rivers] Iteration " .. i .. " of " .. niter)
+
+		model:diffuse(time_step)
+		model:flow()
+		model:erode(time_step)
+		if i < niter then
+			if tectonic_step ~= 0 then
+				nobj_base:get_3d_map_flat({x=0, y=tectonic_step*i, z=0}, ref_dem)
+			end
+			model:isostasy()
+		end
+
+		collectgarbage()
+	end
+	model:flow()
+
+	local mfloor = math.floor
+	local mmin, mmax = math.min, math.max
+	local offset_x, offset_y = twist(model.dirs, model.rivers, 5)
+	for i=1, size.x*size.y do
+		offset_x[i] = mmin(mmax(offset_x[i]*256, -128), 127)
+		offset_y[i] = mmin(mmax(offset_y[i]*256, -128), 127)
+	end
+
+	mapgen_rivers.write_map('dem', model.dem, 2)
+	mapgen_rivers.write_map('lakes', model.lakes, 2)
+	mapgen_rivers.write_map('dirs', model.dirs, 1)
+	mapgen_rivers.write_map('rivers', model.rivers, 4)
+	mapgen_rivers.write_map('offset_x', offset_x, 1)
+	mapgen_rivers.write_map('offset_y', offset_y, 1)
+	local sfile = io.open(mapgen_rivers.world_data_path .. 'size', "w")
+	sfile:write(size.x..'\n'..size.y)
+	sfile:close()
+
+	if keep_loaded then
+		grid.dem = model.dem
+		grid.lakes = model.lakes
+		grid.dirs = model.dirs
+		grid.rivers = model.rivers
+		grid.offset_x = offset_x
+		grid.offset_y = offset_y
+	end
+	collectgarbage()
+end
+
+return pregenerate

readconfig.py

@@ -0,0 +1,42 @@
+def read_conf_file(filename):
+    f = open(filename, 'r')
+    return read_conf(f)
+
+def read_conf(f, end_tag=None):
+    conf = {}
+    while True:
+        line = f.readline()
+        if len(line) == 0:
+            return conf
+        line = line.strip()
+        if line == end_tag:
+            return conf
+        if len(line) == 0 or line[0] == '#':
+            continue
+
+        eqpos = line.find('=')
+        if eqpos < 0:
+            continue
+            
+        name, value = line[:eqpos].rstrip(), line[eqpos+1:].lstrip()
+        if value == '{':
+            # Group
+            conf[name] = read_conf(f, end_tag='}')
+
+        elif value == '"""':
+            # Multiline
+            conf[value] = read_multiline(f)
+
+        else:
+            conf[name] = value
+
+def read_multiline(f):
+    mline = ''
+    while True:
+        line = f.readline()
+        if len(line) == 0:
+            return mline
+        line = line.strip()
+        if line == '"""':
+            return mline
+        mline += line + '\n'

rivermapper.py

@@ -1,100 +0,0 @@
-import numpy as np
-import heapq
-import sys
-
-# Conventions:
-# 1 = South (+Y)
-# 2 = East  (+X)
-# 3 = North (-Y)
-# 4 = West  (-X)
-
-sys.setrecursionlimit(65536)
-
-neighbours_dirs = np.array([
-    [0,1,0],
-    [2,0,4],
-    [0,3,0],
-], dtype='u1')
-
-neighbours_pattern = neighbours_dirs > 0
-
-def flow_dirs_lakes(dem, random=0):
-    (Y, X) = dem.shape
-
-    dem_margin = np.zeros((Y+2, X+2))
-    dem_margin[1:-1,1:-1] = dem
-    if random > 0:
-        dem_margin += np.random.random(dem_margin.shape) * random
-
-    # Initialize: list map borders
-    borders = []
-
-    for x in range(1,X+1):
-        dem_north = dem_margin[1,x]
-        borders.append((dem_north, dem_north, 1, x))
-        dem_south = dem_margin[Y,x]
-        borders.append((dem_south, dem_south, Y, x))
-
-    for y in range(2,Y):
-        dem_west = dem_margin[y,1]
-        borders.append((dem_west, dem_west, y, 1))
-        dem_east = dem_margin[y,X]
-        borders.append((dem_east, dem_east, y, X))
-
-    heapq.heapify(borders)
-
-    dirs = np.zeros((Y+2, X+2), dtype='u1')
-    dirs[-2:,:] = 1
-    dirs[:,-2:] = 2
-    dirs[ :2,:] = 3
-    dirs[:, :2] = 4
-
-    lakes = np.zeros((Y, X))
-
-    def add_point(y, x, altmax):
-        alt = dem_margin[y, x]
-        heapq.heappush(borders, (alt, altmax, y, x))
-
-    while len(borders) > 0:
-        (alt, altmax, y, x) = heapq.heappop(borders)
-        neighbours = dirs[y-1:y+2, x-1:x+2]
-        empty_neighbours = (neighbours == 0) * neighbours_pattern
-        neighbours += empty_neighbours * neighbours_dirs
-
-        lake = max(alt, altmax)
-        lakes[y-1,x-1] = lake
-
-        coords = np.transpose(empty_neighbours.nonzero())
-        for (dy,dx) in coords-1:
-            add_point(y+dy, x+dx, lake)
-
-    return dirs[1:-1,1:-1], lakes
-
-def accumulate(dirs, dem=None):
-    (Y, X) = dirs.shape
-    dirs_margin = np.zeros((Y+2,X+2))-1
-    dirs_margin[1:-1,1:-1] = dirs
-    quantity = np.zeros((Y, X), dtype='i4')
-
-    def calculate_quantity(y, x):
-        if quantity[y,x] > 0:
-            return quantity[y,x]
-        q = 1
-        neighbours = dirs_margin[y:y+3, x:x+3]
-        donors = neighbours == neighbours_dirs
-
-        coords = np.transpose(donors.nonzero())
-        for (dy,dx) in coords-1:
-            q += calculate_quantity(y+dy, x+dx)
-        quantity[y, x] = q
-        return q
-
-    for x in range(X):
-        for y in range(Y):
-            calculate_quantity(y, x)
-
-    return quantity
-
-def flow(dem):
-    dirs, lakes = flow_dirs_lakes(dem)
-    return dirs, lakes, accumulate(dirs, dem)

save.py

@@ -1,13 +0,0 @@
-import numpy as np
-import zlib
-
-def save(data, fname, dtype=None):
-    if dtype is not None:
-        data = data.astype(dtype)
-
-    bin_data = data.tobytes()
-    bin_data_comp = zlib.compress(bin_data, 9)
-    if len(bin_data_comp) < len(bin_data):
-        bin_data = bin_data_comp
-    with open(fname, 'wb') as f:
-        f.write(bin_data)

settings.lua

@@ -1,41 +1,95 @@
-local storage = minetest.get_mod_storage()
-local settings = minetest.settings
+local mtsettings = minetest.settings
+local mgrsettings = Settings(minetest.get_worldpath() .. '/mapgen_rivers.conf')
 
-local function get_settings(key, dtype, default)
-	if storage:contains(key) then
-		if dtype == "string" then
-			return storage:get_string(key)
-		elseif dtype == "int" then
-			return storage:get_int(key)
-		elseif dtype == "float" then
-			return storage:get_float(key)
+mapgen_rivers.version = "1.0.2"
+
+local previous_version_mt = mtsettings:get("mapgen_rivers_version") or "0.0"
+local previous_version_mgr = mgrsettings:get("version") or "0.0"
+
+if mapgen_rivers.version ~= previous_version_mt or mapgen_rivers.version ~= previous_version_mgr then
+	local compat_mt, compat_mgr = dofile(minetest.get_modpath(minetest.get_current_modname()) .. "/compatibility.lua")
+	if mapgen_rivers.version ~= previous_version_mt then
+		compat_mt(mtsettings)
+	end
+	if mapgen_rivers.version ~= previous_version_mgr then
+		compat_mgr(mgrsettings)
 	end
 end
 
-	local conf_val = settings:get('mapgen_rivers_' .. key)
-	if conf_val then
-		if dtype == "int" then
-			conf_val = tonumber(conf_val)
-			storage:set_int(key, conf_val)
-		elseif dtype == "float" then
-			conf_val = tonumber(conf_val)
-			storage:set_float(key, conf_val)
-		elseif dtype == "string" then
-			storage:set_string(key, conf_val)
-		end
+mtsettings:set("mapgen_rivers_version", mapgen_rivers.version)
+mgrsettings:set("version", mapgen_rivers.version)
 
-		return conf_val
+function mapgen_rivers.define_setting(name, dtype, default)
+	if dtype == "number" or dtype == "string" then
+		local v = mgrsettings:get(name)
+		if v == nil then
+			v = mtsettings:get('mapgen_rivers_' .. name)
+			if v == nil then
+				v = default
+			end
+			mgrsettings:set(name, v)
+		end
+		if dtype == "number" then
+			return tonumber(v)
 		else
-		if dtype == "int" then
-			storage:set_int(key, default)
-		elseif dtype == "float" then
-			storage:set_float(key, default)
-		elseif dtype == "string" then
-			storage:set_string(key, default)
+			return v
 		end
-
-		return default
+	elseif dtype == "bool" then
+		local v = mgrsettings:get_bool(name)
+		if v == nil then
+			v = mtsettings:get_bool('mapgen_rivers_' .. name)
+			if v == nil then
+				v = default
+			end
+			mgrsettings:set_bool(name, v)
+		end
+		return v
+	elseif dtype == "noise" then
+		local v = mgrsettings:get_np_group(name)
+		if v == nil then
+			v = mtsettings:get_np_group('mapgen_rivers_' .. name)
+			if v == nil then
+				v = default
+			end
+			mgrsettings:set_np_group(name, v)
+		end
+		return v
 	end
 end
 
-return get_settings
+local def_setting = mapgen_rivers.define_setting
+
+mapgen_rivers.settings = {
+	center = def_setting('center', 'bool', true),
+	blocksize = def_setting('blocksize', 'number', 15),
+	sea_level = tonumber(minetest.get_mapgen_setting('water_level')),
+	min_catchment = def_setting('min_catchment', 'number', 3600),
+	river_widening_power = def_setting('river_widening_power', 'number', 0.5),
+	riverbed_slope = def_setting('riverbed_slope', 'number', 0.4),
+	distort = def_setting('distort', 'bool', true),
+	biomes = def_setting('biomes', 'bool', true),
+	glaciers = def_setting('glaciers', 'bool', false),
+	glacier_factor = def_setting('glacier_factor', 'number', 8),
+	elevation_chill = def_setting('elevation_chill', 'number', 0.25),
+
+	grid_x_size = def_setting('grid_x_size', 'number', 1000),
+	grid_z_size = def_setting('grid_z_size', 'number', 1000),
+	evol_params = {
+		K = def_setting('river_erosion_coef', 'number', 0.5),
+		m = def_setting('river_erosion_power', 'number', 0.4),
+		d = def_setting('diffusive_erosion', 'number', 0.5),
+		compensation_radius = def_setting('compensation_radius', 'number', 50),
+	},
+	tectonic_speed = def_setting('tectonic_speed', 'number', 70),
+	evol_time = def_setting('evol_time', 'number', 10),
+	evol_time_step = def_setting('evol_time_step', 'number', 1),
+
+	load_all = mtsettings:get_bool('mapgen_rivers_load_all')
+}
+
+local function write_settings()
+	mgrsettings:write()
+end
+
+minetest.register_on_mods_loaded(write_settings)
+minetest.register_on_shutdown(write_settings)

settingtypes.txt

@@ -0,0 +1,117 @@
+# File containing all settings for 'mapgen_rivers' mod.
+
+#    Whether the map should be centered at x=0, z=0.
+mapgen_rivers_center (Center map) bool true
+
+#    Represents horizontal map scale. Every cell of the grid will be upscaled to
+#    a square of this size.
+#    For example if the grid size is 1000x1000 and block size is 12,
+#    the actual size of the map will be 12000.
+mapgen_rivers_blocksize (Block size) float 15.0 2.0 100.0
+
+#    X size of the grid being generated
+#    Actual size of the map is grid_x_size * blocksize
+mapgen_rivers_grid_x_size (Grid X size) int 1000 50 5000
+
+#    Z size of the grid being generated
+#    Actual size of the map is grid_z_size * blocksize
+mapgen_rivers_grid_z_size (Grid Z size) int 1000 50 5000
+
+#    Minimal catchment area for a river to be drawn, in square nodes
+#    Lower value means bigger river density
+mapgen_rivers_min_catchment (Minimal catchment area) float 3600.0 100.0 1000000.0
+
+#    Coefficient describing how rivers widen when merging.
+#    Riwer width is a power law W = a*D^p. D is river flow and p is this parameter.
+#    Higher value means that a river will grow more when receiving a tributary.
+#    Note that a river can never exceed 2*blocksize.
+mapgen_rivers_river_widening_power (River widening power) float 0.5 0.0 1.0
+
+#    Lateral slope of the riverbed.
+#    Higher value means deeper rivers.
+mapgen_rivers_riverbed_slope (Riverbed slope) float 0.4 0.0 2.0
+
+#    Enable horizontal distorsion (shearing) of landscape, to break the regularity
+#    of grid cells and allow overhangs.
+#    Distorsion uses two 3D noises and thus is intensive in terms of computing time.
+mapgen_rivers_distort (Distorsion) bool true
+
+#    Enable biome generation.
+#    If 'biomegen' mod is installed, 'mapgen_rivers' will generate biomes from the
+#    native biome system. If 'biomegen' is not present, will generate only grass and
+#    snow.
+mapgen_rivers_biomes (Biomes) bool true
+
+#    Whether to enable glaciers.
+#    Glaciers are widened river sections, covered by ice, that are generated in
+#    very cold areas.
+mapgen_rivers_glaciers (Glaciers) bool false
+
+#    River channels are widened by this factor if they are a glacier.
+mapgen_rivers_glacier_widening_factor (Glacier widening factor) float 8.0 1.0 20.0
+
+#    Temperature value decreases by this quantity for every node, vertically.
+#    This results in mountains being more covered by snow.
+mapgen_rivers_elevation_chill (Elevation chill) float 0.25 0.0 5.0
+
+#    If enabled, loads all grid data in memory at init time.
+#    If disabled, data will be loaded on request and cached in memory.
+#    It's recommended to disable it for very large maps (> 2000 grid nodes or so)
+mapgen_rivers_load_all (Load all data in memory) bool false
+
+[Landscape evolution parameters]
+
+#    Modelled landscape evolution time, in arbitrary units
+mapgen_rivers_evol_time (Landscape evolution time) float 10.0 0.0 100.0
+
+#    Model time steps in arbitrary units
+#    Smaller values will result in more time steps to be necessary to
+#    complete the simulation, taking more time.
+mapgen_rivers_evol_time_step (Landscape evolution time step) float 1.0 0.0 50.0
+
+#    To adjust river erosion proportionnally.
+#    This type of erosion acts by deepening the valleys.
+mapgen_rivers_river_erosion_coef (River erosion coefficient) float 0.5 0.0 10.0
+
+#    Represents how much river erosion depends on river flow (catchment area).
+#    Catchment area is elevated to this power.
+#    Extreme cases: 0.0 -> All rivers have the same erosive capabilities
+#    1.0 -> Erosion is proportional to river flow
+#    Reasonable values are generally between 0.4 and 0.7.
+#
+#    This parameter is extremely sensitive, and changes may require to adjust
+#    'river_erosion_coef' as well.
+mapgen_rivers_river_erosion_power (River erosion power) float 0.4 0.0 1.0
+
+#    Intensity of diffusive erosion.
+#    Smoothes peaks and valleys, and tends to prevent sharp cliffs from forming.
+mapgen_rivers_diffusive_erosion (Diffusive erosion) float 0.5 0.0 10.0
+
+#    Radius of compensation for isostatic/tectonic processes
+#    Tectonic uplift forces will have a diffuse effect over this radius
+mapgen_rivers_compensation_radius (Tectonic compensation radius) float 50 1.0 1000.0
+
+#    Speed of evolution of tectonic conditions between steps
+#    Higher values means tectonics will be very different from one step to the other,
+#    resulting in geologically unstable and more varied landforms (plateau, gorge, lake...)
+mapgen_rivers_tectonic_speed (Tectonic speed) float 70 0 10000
+
+[Noises]
+
+#    Y level of terrain at a very large scale. Only used during pre-generation.
+#    X and Z axes correspond to map's X and Z directions, and Y axis is time.
+#    Successive XZ slices of this noise represent successive tectonic states.
+mapgen_rivers_np_base (Terrain base noise) noise_params_3d 0, 300, (2048, 2048, 2048), 2469, 8, 0.6, 2.0, eased
+
+#    This noise will shear the terrain on the X axis,
+#    to break the regularity of the river grid.
+mapgen_rivers_np_distort_x (X-axis distorsion noise) noise_params_3d 0, 1, (64, 32, 64), -4574, 3, 0.75, 2.0
+
+#    This noise will shear the terrain on the Z axis,
+#    to break the regularity of the river grid.
+mapgen_rivers_np_distort_z (Z-axis distorsion noise) noise_params_3d 0, 1, (64, 32, 64), -7940, 3, 0.75, 2.0
+
+#    Amplitude of the distorsion.
+#    Too small values may leave the grid pattern apparent,
+#    and too high values could make the terrain insanely twisted.
+mapgen_rivers_np_distort_amplitude (Distorsion amplitude noise) noise_params_2d 0, 10, (1024, 1024, 1024), 676, 5, 0.5, 2.0, absvalue

terrain_rivers.py

@@ -1,118 +0,0 @@
-#!/usr/bin/env python3
-
-import numpy as np
-import noise
-from save import save
-from erosion import EvolutionModel
-import bounds
-import os
-import sys
-
-# Always place in this script's parent directory
-os.chdir(os.path.dirname(sys.argv[0]))
-argc = len(sys.argv)
-
-if argc > 1:
-	mapsize = int(sys.argv[1])
-else:
-	mapsize = 400
-
-scale = mapsize / 2
-n = np.zeros((mapsize, mapsize))
-
-#micronoise_depth = 0.05
-
-params = {
-    "octaves" : int(np.log2(mapsize)),
-    "persistence" : 0.5,
-    "lacunarity" : 2.,
-}
-
-xbase = np.random.randint(65536)
-ybase = np.random.randint(65536)
-
-for x in range(mapsize):
-    for y in range(mapsize):
-        n[x,y] = noise.snoise2(x/scale + xbase, y/scale + ybase, **params)
-
-#micronoise = np.random.rand(mapsize, mapsize)
-#nn = np.exp(n*2) + micronoise*micronoise_depth
-nn = n*mapsize/5 + mapsize/20
-
-print('Initializing model')
-model = EvolutionModel(nn, K=1, m=0.35, d=1, sea_level=0)
-
-print('Flow calculation 1')
-model.calculate_flow()
-
-print('Advection 1')
-model.advection(2)
-
-print('Isostatic equilibration 1')
-model.adjust_isostasy()
-
-print('Flow calculation 2')
-model.calculate_flow()
-
-print('Diffusion')
-model.diffusion(4)
-
-print('Advection 2')
-model.advection(2)
-
-print('Isostatic equilibration 2')
-model.adjust_isostasy()
-
-print('Flow calculation 3')
-model.calculate_flow()
-
-print('Done')
-
-bx, by = bounds.make_bounds(model.dirs, model.rivers)
-ox, oy = bounds.twist(bx, by, bounds.get_fixed(model.dirs))
-
-offset_x = np.clip(np.floor(ox * 256), -128, 127)
-offset_y = np.clip(np.floor(oy * 256), -128, 127)
-
-save(model.dem, 'dem', dtype='>i2')
-save(model.lakes, 'lakes', dtype='>i2')
-save(np.abs(bx), 'bounds_x', dtype='>i4')
-save(np.abs(by), 'bounds_y', dtype='>i4')
-save(offset_x, 'offset_x', dtype='i1')
-save(offset_y, 'offset_y', dtype='i1')
-
-save(model.rivers, 'rivers', dtype='>u4')
-
-with open('size', 'w') as sfile:
-    sfile.write('{:d}\n{:d}'.format(mapsize, mapsize))
-
-try:
-    import matplotlib.pyplot as plt
-
-    plt.subplot(2,2,1)
-    plt.pcolormesh(nn, cmap='viridis')
-    plt.gca().set_aspect('equal', 'box')
-    #plt.colorbar(orientation='horizontal')
-    plt.title('Raw elevation')
-
-    plt.subplot(2,2,2)
-    plt.pcolormesh(model.lakes, cmap='viridis')
-    plt.gca().set_aspect('equal', 'box')
-    #plt.colorbar(orientation='horizontal')
-    plt.title('Lake surface elevation')
-
-    plt.subplot(2,2,3)
-    plt.pcolormesh(model.dem, cmap='viridis')
-    plt.gca().set_aspect('equal', 'box')
-    #plt.colorbar(orientation='horizontal')
-    plt.title('Elevation after advection')
-
-    plt.subplot(2,2,4)
-    plt.pcolormesh(model.rivers, vmin=0, vmax=mapsize**2/25, cmap='Blues')
-    plt.gca().set_aspect('equal', 'box')
-    #plt.colorbar(orientation='horizontal')
-    plt.title('Rivers discharge')
-
-    plt.show()
-except:
-    pass

terrainlib_lua/erosion.lua

@@ -0,0 +1,244 @@
+-- erosion.lua
+
+-- This is the main file of terrainlib_lua. It registers the EvolutionModel object and some of the 
+
+local function erode(model, time)
+	-- Apply river erosion on the model
+	-- Erosion model is based on the simplified version of the stream-power law Ey = K×A^m×S
+	-- where Ey is the vertical erosion speed, A catchment area of the river, S slope along the river, m and K local constants.
+	-- It is equivalent to considering a horizontal erosion wave travelling at Ex = K×A^m, and this latter approach allows much greather time steps so it is used here.
+	-- For each point, instead of moving upstream and see what point the erosion wave would reach, we move downstream and see from which point the erosion wave would reach the given point, then we can set the elevation.
+	local mmin, mmax = math.min, math.max
+	local dem = model.dem
+	local dirs = model.dirs
+	local lakes = model.lakes
+	local rivers = model.rivers
+	local sea_level = model.params.sea_level
+	local K = model.params.K
+	local m = model.params.m
+	local X, Y = dem.X, dem.Y
+	local scalars = type(K) == "number" and type(m) == "number"
+
+	local erosion_time
+	if model.params.variable_erosion then
+		erosion_time = {}
+	else
+		erosion_time = model.erosion_time or {}
+	end
+
+	if scalars then
+		for i=1, X*Y do
+			local etime = 1 / (K*rivers[i]^m) -- Inverse of erosion speed (Ex); time needed for the erosion wave to move through the river section.
+			erosion_time[i] = etime
+			lakes[i] = mmax(lakes[i], dem[i], sea_level) -- Use lake/sea surface if higher than ground level, because rivers can not erode below.
+		end
+	else
+		for i=1, X*Y do
+			local etime = 1 / (K[i]*rivers[i]^m[i])
+			erosion_time[i] = etime
+			lakes[i] = mmax(lakes[i], dem[i], sea_level)
+		end
+	end
+
+	for i=1, X*Y do
+		local iw = i
+		local remaining = time
+		local new_elev
+		while true do
+			-- Explore downstream until we find the point 'iw' from which the erosion wave will reach 'i'
+			local inext = iw
+			local d = dirs[iw]
+
+			-- Follow the river downstream (move 'iw')
+			if d == 0 then -- If no flow direction, we reach the border of the map: set elevation to the latest node's elev and abort.
+				new_elev = lakes[iw]
+				break
+			elseif d == 1 then
+				inext = iw+X
+			elseif d == 2 then
+				inext = iw+1
+			elseif d == 3 then
+				inext = iw-X
+			elseif d == 4 then
+				inext = iw-1
+			end
+
+			local etime = erosion_time[iw]
+			if remaining <= etime then -- We have found the node from which the erosion wave will take 'time' to arrive to 'i'.
+				local c = remaining / etime
+				new_elev = (1-c) * lakes[iw] + c * lakes[inext] -- Interpolate linearly between the two nodes
+				break
+			end
+
+			remaining = remaining - etime -- If we still don't reach the target time, decrement time and move to next point.
+			iw = inext
+		end
+
+		dem[i] = mmin(dem[i], new_elev)
+	end
+end
+
+local function diffuse(model, time)
+	-- Apply diffusion using finite differences methods
+	-- Adapted for small radiuses
+	local mmax = math.max
+	local dem = model.dem
+	local X, Y = dem.X, dem.Y
+	local d = model.params.d
+	-- 'd' is equal to 4 times the diffusion coefficient
+	local dmax = d
+	if type(d) == "table" then
+		dmax = -math.huge
+		for i=1, X*Y do
+			dmax = mmax(dmax, d[i])
+		end
+	end
+
+	local diff = dmax * time
+	-- diff should never exceed 1 per iteration.
+	-- If needed, we will divide the process in enough iterations so that 'ddiff' is below 1.
+	local niter = math.floor(diff) + 1
+	local ddiff = diff / niter
+
+	local temp = {}
+	for n=1, niter do
+		local i = 1
+		for y=1, Y do
+			local iN = (y==1) and 0 or -X
+			local iS = (y==Y) and 0 or X
+			for x=1, X do
+				local iW = (x==1) and 0 or -1
+				local iE = (x==X) and 0 or 1
+				-- Laplacian Δdem × 1/4
+				temp[i] = (dem[i+iN]+dem[i+iE]+dem[i+iS]+dem[i+iW])*0.25 - dem[i]
+				i = i + 1
+			end
+		end
+
+		for i=1, X*Y do
+			dem[i] = dem[i] + temp[i]*ddiff
+		end
+	end
+end
+
+local modpath = ""
+if minetest then
+	if minetest.global_exists('mapgen_rivers') then
+		modpath = mapgen_rivers.modpath .. "terrainlib_lua/"
+	else
+		modpath = minetest.get_modpath(minetest.get_current_modname()) .. "terrainlib_lua/"
+	end
+end
+
+local rivermapper = dofile(modpath .. "rivermapper.lua")
+local gaussian = dofile(modpath .. "gaussian.lua")
+
+local function flow(model)
+	model.dirs, model.lakes = rivermapper.flow_routing(model.dem, model.dirs, model.lakes, 'semirandom')
+	model.rivers = rivermapper.accumulate(model.dirs, model.rivers)
+end
+
+local function uplift(model, time)
+	-- Raises the terrain according to uplift rate (model.params.uplift)
+	local dem = model.dem
+	local X, Y = dem.X, dem.Y
+	local uplift_rate = model.params.uplift
+	if type(uplift_rate) == "number" then
+		local uplift_total = uplift_rate * time
+		for i=1, X*Y do
+			dem[i] = dem[i] + uplift_total
+		end
+	else
+		for i=1, X*Y do
+			dem[i] = dem[i] + uplift_rate[i]*time
+		end
+	end
+end
+
+local function noise(model, time)
+	-- Adds noise to the terrain according to noise depth (model.params.noise)
+	local random = math.random
+	local dem = model.dem
+	local noise_depth = model.params.noise * 2 * time
+	local X, Y = dem.X, dem.Y
+	for i=1, X*Y do
+		dem[i] = dem[i] + (random()-0.5) * noise_depth
+	end
+end
+
+-- Isostasy
+-- This is the geological phenomenon that makes the lithosphere "float" over the underlying layers.
+-- One of the key implications is that when a very large mass is removed from the ground, the lithosphere reacts by moving upward. This compensation only occurs at large scale (as the lithosphere is not flexible enough for small scale adjustments) so the implementation is using a very large-window Gaussian blur of the elevation array.
+
+-- This implementation is quite simplistic, it does not do a mass balance of the lithosphere as this would introduce too many parameters. Instead, it defines a reference equilibrium elevation, and the ground will react toward this elevation (at the scale of the gaussian window).
+-- A change in reference isostasy during the run can also be used to simulate tectonic forcing, like making a new mountain range appear.
+local function define_isostasy(model, ref, link)
+	ref = ref or model.dem
+	if link then
+		model.isostasy_ref = ref
+		return
+	end
+
+	local X, Y = ref.X, ref.Y
+	local ref2 = model.isostasy_ref or {X=X, Y=Y}
+	model.isostasy_ref = ref2
+	for i=1, X*Y do
+		ref2[i] = ref[i]
+	end
+
+	return ref2
+end
+
+-- Apply isostasy
+local function isostasy(model)
+	local dem = model.dem
+	local X, Y = dem.X, dem.Y
+	local temp = {X=X, Y=Y}
+	local ref = model.isostasy_ref
+	for i=1, X*Y do
+		temp[i] = ref[i] - dem[i] -- Compute the difference between the ground level and the target level
+	end
+
+	-- Blur the difference map using Gaussian blur
+	gaussian.gaussian_blur_approx(temp, model.params.compensation_radius, 4)
+	for i=1, X*Y do
+		dem[i] = dem[i] + temp[i] -- Apply the difference
+	end
+end
+
+local evol_model_mt = {
+	erode = erode,
+	diffuse = diffuse,
+	flow = flow,
+	uplift = uplift,
+	noise = noise,
+	isostasy = isostasy,
+	define_isostasy = define_isostasy,
+}
+
+evol_model_mt.__index = evol_model_mt
+
+local defaults = {
+	K = 1,
+	m = 0.5,
+	d = 1,
+	variable_erosion = false,
+	sea_level = 0,
+	uplift = 10,
+	noise = 0.001,
+	compensation_radius = 50,
+}
+
+local function EvolutionModel(params)
+	params = params or {}
+	local o = {params = params}
+	for k, v in pairs(defaults) do
+		if params[k] == nil then
+			params[k] = v
+		end
+	end
+	o.dem = params.dem
+	return setmetatable(o, evol_model_mt)
+end
+
+return EvolutionModel

terrainlib_lua/gaussian.lua

@@ -0,0 +1,88 @@
+-- gaussian.lua
+
+local function get_box_size(sigma, n)
+	local v = sigma^2 / n
+	local r_ideal = ((12*v + 1) ^ 0.5 - 1) / 2
+	local r_down = math.floor(r_ideal)
+	local r_up = math.ceil(r_ideal)
+	local v_down = ((2*r_down+1)^2 - 1) / 12
+	local v_up = ((2*r_up+1)^2 - 1) / 12
+	local m_ideal = (v - v_down) / (v_up - v_down) * n
+	local m = math.floor(m_ideal+0.5)
+
+	local sizes = {}
+	for i=1, n do
+		sizes[i] = i<=m and 2*r_up+1 or 2*r_down+1
+	end
+
+	return sizes
+end
+
+local function box_blur_1d(map, size, first, incr, len, map2)
+	local n = math.ceil(size/2)
+	first = first or 1
+	incr = incr or 1
+	len = len or math.floor((#map-first)/incr)+1
+	local last = first + (len-1)*incr
+
+	local nth = first+(n-1)*incr
+	local sum = 0
+	for i=first, nth, incr do
+		if i == first then
+			sum = sum + map[i]
+		else
+			sum = sum + 2*map[i]
+		end
+	end
+
+	local i_left = nth
+	local incr_left = -incr
+	local i_right = nth
+	local incr_right = incr
+
+	map2 = map2 or {}
+	for i=first, last, incr do
+		map2[i] = sum / size
+		i_right = i_right + incr_right
+		sum = sum - map[i_left] + map[i_right]
+		i_left = i_left + incr_left
+
+		if i_left == first then
+			incr_left = incr
+		end
+		if i_right == last then
+			incr_right = -incr
+		end
+	end
+
+	return map2
+end
+
+local function box_blur_2d(map1, size, map2)
+	local X, Y = map1.X, map1.Y
+	map2 = map2 or {}
+	for y=1, Y do
+		box_blur_1d(map1, size, (y-1)*X+1, 1, X, map2)
+	end
+	for x=1, X do
+		box_blur_1d(map2, size, x, X, Y, map1)
+	end
+
+	return map1
+end
+
+local function gaussian_blur_approx(map, sigma, n, map2)
+	map2 = map2 or {}
+	local sizes = get_box_size(sigma, n)
+	for i=1, n do
+		box_blur_2d(map, sizes[i], map2)
+	end
+	return map
+end
+
+return {
+	get_box_size = get_box_size,
+	box_blur_1d = box_blur_1d,
+	box_blur_2d = box_blur_2d,
+	gaussian_blur_approx = gaussian_blur_approx,
+}

terrainlib_lua/rivermapper.lua

@@ -0,0 +1,442 @@
+-- rivermapper.lua
+
+-- This file provide functions to construct the river tree from an elevation model.
+-- Based on a research paper:
+--
+--     Cordonnier, G., Bovy, B., and Braun, J.:
+--     A versatile, linear complexity algorithm for flow routing in topographies with depressions,
+--     Earth Surf. Dynam., 7, 549–562, https://doi.org/10.5194/esurf-7-549-2019, 2019.
+--
+-- Big thanks to them for releasing this paper under a free license ! :)
+
+-- The algorithm here makes use of most of the paper's concepts, including the Planar Borůvka algorithm.
+-- Only flow_local and accumulate_flow are custom algorithms.
+
+
+local function flow_local_semirandom(plist)
+	-- Determines how water should flow at 1 node scale.
+	-- The straightforward approach would be "Water will flow to the lowest of the 4 neighbours", but here water flows to one of the lower neighbours, chosen randomly, but probability depends on height difference.
+	-- This makes rivers better follow the curvature of the topography at large scale, and be less biased by pure N/E/S/W directions.
+	-- 'plist': array of downward height differences (0 if upward)
+	local sum = 0
+	for i=1, #plist do
+		sum = sum + plist[i] -- Sum of probabilities
+	end
+
+	if sum == 0 then
+		return 0
+	end
+	local r = math.random() * sum
+	for i=1, #plist do
+		local p = plist[i]
+		if r < p then
+			return i
+		end
+		r = r - p
+	end
+	return 0
+end
+
+-- Maybe implement more flow methods in the future?
+local flow_methods = {
+	semirandom = flow_local_semirandom,
+}
+
+-- Applies all steps of the flow routing, to calculate flow direction for every node, and lake surface elevation.
+-- It's quite a hard piece of code, but we will go step by step and explain what's going on, so stay with me and... let's goooooooo!
+local function flow_routing(dem, dirs, lakes, method) -- 'dirs' and 'lakes' are optional tables to reuse for memory optimization, they may contain any data.
+	method = method or 'semirandom'
+	local flow_local = flow_methods[method] or flow_local_semirandom
+
+	dirs = dirs or {}
+	lakes = lakes or {}
+
+	-- Localize for performance
+	local tremove = table.remove
+	local mmax = math.max
+
+	local X, Y = dem.X, dem.Y
+	dirs.X = X
+	dirs.Y = Y
+	lakes.X = X
+	lakes.Y = Y
+	local i = 1
+	local dirs2 = {}
+	for i=1, X*Y do
+		dirs2[i] = 0
+	end
+
+	----------------------------------------
+	-- STEP 1: Find local flow directions --
+	----------------------------------------
+	-- Use the local flow function and fill the flow direction tables
+	local singular = {}
+	for y=1, Y do
+		for x=1, X do
+			local zi = dem[i]
+			local plist = { -- Get the height difference of the 4 neighbours (and 0 if uphill)
+				y<Y and mmax(zi-dem[i+X], 0) or 0, -- Southward
+				x<X and mmax(zi-dem[i+1], 0) or 0, -- Eastward
+				y>1 and mmax(zi-dem[i-X], 0) or 0, -- Northward
+				x>1 and mmax(zi-dem[i-1], 0) or 0, -- Westward
+			}
+
+			local d = flow_local(plist)
+			-- 'dirs': Direction toward which water flow
+			-- 'dirs2': Directions from which water comes
+			dirs[i] = d
+			if d == 0 then -- If water can't flow from this node, add it to the list of singular nodes that will be resolved later
+				singular[#singular+1] = i
+			elseif d == 1 then
+				dirs2[i+X] = dirs2[i+X] + 1
+			elseif d == 2 then
+				dirs2[i+1] = dirs2[i+1] + 2
+			elseif d == 3 then
+				dirs2[i-X] = dirs2[i-X] + 4
+			elseif d == 4 then
+				dirs2[i-1] = dirs2[i-1] + 8
+			end
+			i = i + 1
+		end
+	end
+
+	--------------------------------------
+	-- STEP 2: Compute basins and links --
+	--------------------------------------
+	-- Now water can flow until it reaches a singular node (which is in most cases the bottom of a depression)
+	-- We will calculate the drainage basin of every singular node (all the nodes from which the water will flow in this singular node, directly or indirectly), make an adjacency list of basins, and find the lowest pass between each pair of adjacent basins (they are potential lake outlets)
+	local nbasins = #singular
+	local basin_id = {}
+	local links = {}
+	local basin_links
+
+	-- Function to analyse a link between two nodes
+	local function add_link(i1, i2, b1, isY)
+		-- i1, i2: coordinates of two nodes
+		-- b1: basin that contains i1
+		-- isY: whether the link is in Y direction
+		local b2
+		-- Note that basin number #0 represents the outside of the map; or if the coordinate is inside the map, means that the basin number is uninitialized.
+		if i2 == 0 then -- If outside the map
+			b2 = 0
+		else
+			b2 = basin_id[i2]
+			if b2 == 0 then -- If basin of i2 is not already computed, skip
+				return
+			end
+		end
+		if b2 ~= b1 then -- If these two nodes don't belong to the same basin, we have found a link between two adjacent basins
+			local elev = i2 == 0 and dem[i1] or mmax(dem[i1], dem[i2]) -- Elevation of the highest of the two sides of the link (or only i1 if b2 is map outside)
+			local l2 = basin_links[b2]
+			if not l2 then
+				l2 = {}
+				basin_links[b2] = l2
+			end
+			if not l2.elev or l2.elev > elev then -- If this link is lower than the lowest registered link between these two basins, register it as the new lowest pass
+				l2.elev = elev
+				l2.i = mmax(i1,i2)
+				l2.is_y = isY
+				l2[1] = b2
+				l2[2] = b1
+			end
+		end
+	end
+
+	for i=1, X*Y do
+		basin_id[i] = 0
+	end
+
+	for ib=1, nbasins do
+		-- Here we will recursively search upstream from the singular node to determine its drainage basin
+		local queue = {singular[ib]} -- Start with the singular node, then this queue will be filled with water donors neighbours
+		basin_links = {}
+		links[#links+1] = basin_links
+		while #queue > 0 do
+			local i = tremove(queue)
+			basin_id[i] = ib
+			local d = dirs2[i] -- Get the directions water is coming from
+
+			-- Iterate through the 4 directions
+			if d >= 8 then -- River coming from the East
+				d = d - 8
+				queue[#queue+1] = i+1
+			-- If no river is coming from the East, we might be at the limit of two basins, thus we need to test adjacency.
+			elseif i%X > 0 then
+				add_link(i, i+1, ib, false)
+			else -- If the eastern neighbour is outside the map
+				add_link(i, 0, ib, false)
+			end
+
+			if d >= 4 then -- River coming from the South
+				d = d - 4
+				queue[#queue+1] = i+X
+			elseif i <= X*(Y-1) then
+				add_link(i, i+X, ib, true)
+			else
+				add_link(i, 0, ib, true)
+			end
+
+			if d >= 2 then -- River coming from the West
+				d = d - 2
+				queue[#queue+1] = i-1
+			elseif i%X ~= 1 then
+				add_link(i, i-1, ib, false)
+			else
+				add_link(i, 0, ib, false)
+			end
+
+			if d >= 1 then -- River coming from the North
+				queue[#queue+1] = i-X
+			elseif i > X then
+				add_link(i, i-X, ib, true)
+			else
+				add_link(i, 0, ib, true)
+			end
+		end
+	end
+	dirs2 = nil
+
+	links[0] = {}
+	local nlinks = {}
+	for i=0, nbasins do
+		nlinks[i] = 0
+	end
+
+	-- Iterate through pairs of adjacent basins, and make the links reciprocal
+	for ib1=1, #links do
+		for ib2, link in pairs(links[ib1]) do
+			if ib2 < ib1 then
+				links[ib2][ib1] = link
+				nlinks[ib1] = nlinks[ib1] + 1
+				nlinks[ib2] = nlinks[ib2] + 1
+			end
+		end
+	end
+
+	-----------------------------------------------------
+	-- STEP 3: Compute minimal spanning tree of basins --
+	-----------------------------------------------------
+	-- We've got an adjacency list of basins with the elevation of their links.
+	-- We will build a minimal spanning tree of the basins (where costs are the elevation of the links). As demonstrated by Cordonnier et al., this finds the outlets of the basins, where water would naturally flow. This does not tell in which direction water is flowing, however.
+	-- We will use a version of Borůvka's algorithm, with Mareš' optimizations to approach linear complexity (see paper).
+	-- The concept of Borůvka's algorithm is to take elements and merge them with their lowest neighbour, until all elements are merged.
+	-- Mareš' optimizations mainly consist in skipping elements that have over 8 links, until extra links are removed when other elements are merged.
+	-- Note that for this step we are only working on basins, not grid nodes.
+	local lowlevel = {}
+	for i, n in pairs(nlinks) do
+		if n <= 8 then
+			lowlevel[i] = links[i]
+		end
+	end
+
+	local basin_graph = {}
+	for n=1, nbasins do
+		-- Iterate in lowlevel but its contents may change during the loop
+		-- 'next' called with only one argument always returns an element if table is not empty
+		local b1, lnk1 = next(lowlevel)
+		lowlevel[b1] = nil
+
+		local b2
+		local lowest = math.huge
+		local lnk1 = links[b1]
+		local i = 0
+		-- Look for lowest link
+		for bn, bdata in pairs(lnk1) do
+			i = i + 1
+			if bdata.elev < lowest then
+				lowest = bdata.elev
+				b2 = bn
+			end
+		end
+
+		-- Add link to the graph, in both directions
+		local bound = lnk1[b2]
+		local bb1, bb2 = bound[1], bound[2]
+		if not basin_graph[bb1] then
+			basin_graph[bb1] = {}
+		end
+		if not basin_graph[bb2] then
+			basin_graph[bb2] = {}
+		end
+		basin_graph[bb1][bb2] = bound
+		basin_graph[bb2][bb1] = bound
+
+		-- Merge basin b1 into b2
+		local lnk2 = links[b2]
+		-- First, remove the link between b1 and b2
+		lnk1[b2] = nil
+		lnk2[b1] = nil
+		nlinks[b2] = nlinks[b2] - 1
+		-- When the number of links is changing, we need to check whether the basin can be added to / removed from 'lowlevel'
+		if nlinks[b2] == 8 then
+			lowlevel[b2] = lnk2
+		end
+		-- Look for basin 1's neighbours, and add them to basin 2 if they have a lower pass
+		for bn, bdata in pairs(lnk1) do
+			local lnkn = links[bn]
+			lnkn[b1] = nil
+
+			if lnkn[b2] then -- If bassin bn is also linked to b2
+				nlinks[bn] = nlinks[bn] - 1 -- Then bassin bn is losing a link because it keeps only one link toward b1/b2 after the merge
+				if nlinks[bn] == 8 then
+					lowlevel[bn] = lnkn
+				end
+			else -- If bn was linked to b1 but not to b2
+				nlinks[b2] = nlinks[b2] + 1 -- Then b2 is gaining a link to bn because of the merge
+				if nlinks[b2] == 9 then
+					lowlevel[b2] = nil
+				end
+			end
+
+			if not lnkn[b2] or lnkn[b2].elev > bdata.elev then -- If the link b1-bn will become the new lowest link between b2 and bn, redirect the link to b2
+				lnkn[b2] = bdata
+				lnk2[bn] = bdata
+			end
+		end
+	end
+
+	--------------------------------------------------------------
+	-- STEP 4: Orient basin graph, and grid nodes inside basins --
+	--------------------------------------------------------------
+	-- We will finally solve those freaking singular nodes.
+	-- To orient the basin graph, we will consider that the ultimate basin water should flow into is the map outside (basin #0). We will start from it and recursively walk upstream to the neighbouring basins, using only links that are in the minimal spanning tree. This gives the flow direction of the links, and thus, the outlet of every basin.
+	-- This will also give lake elevation, which is the highest link encountered between map outside and the given basin on the spanning tree.
+	-- And within each basin, we need to modify flow directions to connect the singular node to the outlet.
+	local queue = {[0] = -math.huge}
+	local basin_lake = {}
+	for n=1, nbasins do
+		basin_lake[n] = 0
+	end
+	local reverse = {3, 4, 1, 2, [0]=0}
+	for n=1, nbasins do
+		local b1, elev1 = next(queue) -- Pop from queue
+		queue[b1] = nil
+		basin_lake[b1] = elev1
+		-- Iterate through b1's neighbours (according to the spanning tree)
+		for b2, bound in pairs(basin_graph[b1]) do
+			-- Make b2 flow into b1
+			local i = bound.i -- Get the coordinate of the link (which is the basin's outlet)
+			local dir = bound.is_y and 3 or 4 -- And get the direction (S/E/N/W)
+			if basin_id[i] ~= b2 then
+				dir = dir - 2
+				-- Coordinate 'i' refers to the side of the link with the highest X/Y position. In case it is in the wrong basin, take the other side by decrementing by one row/column.
+				if bound.is_y then
+					i = i - X
+				else
+					i = i - 1
+				end
+			elseif b1 == 0 then
+				dir = 0
+			end
+
+			-- Use the flow directions computed in STEP 2 to find the route from the outlet position to the singular node, and reverse this route to make the singular node flow into the outlet
+			-- This can make the river flow uphill, which may seem unnatural, but it can only happen below a lake (because outlet elevation defines lake surface elevation)
+			repeat
+				-- Assign i's direction to 'dir', and get i's former direction
+				dir, dirs[i] = dirs[i], dir
+				-- Move i by following its former flow direction (downstream)
+				if dir == 1 then
+					i = i + X
+				elseif dir == 2 then
+					i = i + 1
+				elseif dir == 3 then
+					i = i - X
+				elseif dir == 4 then
+					i = i - 1
+				end
+				-- Reverse the flow direction for the next node, which will flow into i
+				dir = reverse[dir]
+			until dir == 0 -- Stop when reaching the singular node
+
+			-- Add basin b2 into the queue, and keep the highest link elevation, that will define the elevation of the lake in b2
+			queue[b2] = mmax(elev1, bound.elev)
+			-- Remove b1 from b2's neighbours to avoid coming back to b1
+			basin_graph[b2][b1] = nil
+		end
+		basin_graph[b1] = nil
+	end
+
+	-- Every node will be assigned the lake elevation of the basin it belongs to.
+	-- If lake elevation is lower than ground elevation, it simply means that there is no lake here.
+	for i=1, X*Y do
+		lakes[i] = basin_lake[basin_id[i]]
+	end
+
+	-- That's it!
+	return dirs, lakes
+end
+
+
+local function accumulate(dirs, waterq)
+	-- Calculates the river flow by determining the surface of the catchment area for every node
+	-- This means: how many nodes will give their water to that given node, directly or indirectly?
+	-- This is obtained by following rivers downstream and summing up the flow of every tributary, starting with a value of 1 at the sources.
+	-- This will give non-zero values for every node but only large values will be considered to be rivers.
+	waterq = waterq or {}
+	local X, Y = dirs.X, dirs.Y
+
+	local ndonors = {}
+	local waterq = {X=X, Y=Y}
+	for i=1, X*Y do
+		ndonors[i] = 0
+		waterq[i] = 1
+	end
+
+	-- Calculate the number of direct donors
+	for i1=1, X*Y do
+		local i2
+		local dir = dirs[i1]
+		if dir == 1 then
+			i2 = i1+X
+		elseif dir == 2 then
+			i2 = i1+1
+		elseif dir == 3 then
+			i2 = i1-X
+		elseif dir == 4 then
+			i2 = i1-1
+		end
+		if i2 then
+			ndonors[i2] = ndonors[i2] + 1
+		end
+	end
+
+	for i1=1, X*Y do
+		-- Find sources (nodes that have no donor)
+		if ndonors[i1] == 0 then
+			local i2 = i1
+			local dir = dirs[i2]
+			local w = waterq[i2]
+			-- Follow the water flow downstream: move 'i2' to the next node according to its flow direction
+			while dir > 0 do
+				if dir == 1 then
+					i2 = i2 + X
+				elseif dir == 2 then
+					i2 = i2 + 1
+				elseif dir == 3 then
+					i2 = i2 - X
+				elseif dir == 4 then
+					i2 = i2 - 1
+				end
+				-- Increment the water quantity of i2
+				w = w + waterq[i2]
+				waterq[i2] = w
+
+				-- Stop on an unresolved confluence (node with >1 donors) and decrease the number of remaining donors
+				-- When the ndonors of a confluence has decreased to 1, it means that its water quantity has already been incremented by its tributaries, so it can be resolved like a standard river section. However, do not decrease ndonors to zero to avoid considering it as a source.
+				if ndonors[i2] > 1 then
+					ndonors[i2] = ndonors[i2] - 1
+					break
+				end
+				dir = dirs[i2]
+			end
+		end
+	end
+
+	return waterq
+end
+
+return {
+	flow_routing = flow_routing,
+	accumulate = accumulate,
+	flow_methods = flow_methods,
+}

terrainlib_lua/twist.lua

@@ -0,0 +1,102 @@
+-- twist.lua
+
+local function get_bounds(dirs, rivers)
+	local X, Y = dirs.X, dirs.Y
+	local bounds_x = {X=X, Y=Y}
+	local bounds_y = {X=X, Y=Y}
+	for i=1, X*Y do
+		bounds_x[i] = 0
+		bounds_y[i] = 0
+	end
+
+	for i=1, X*Y do
+		local dir = dirs[i]
+		local river = rivers[i]
+		if dir == 1 then -- South (+Y)
+			bounds_y[i] = river
+		elseif dir == 2 then -- East (+X)
+			bounds_x[i] = river
+		elseif dir == 3 then -- North (-Y)
+			bounds_y[i-X] = river
+		elseif dir == 4 then -- West (-X)
+			bounds_x[i-1] = river
+		end
+	end
+
+	return bounds_x, bounds_y
+end
+
+local function twist(dirs, rivers, n)
+	n = n or 5
+	local X, Y = dirs.X, dirs.Y
+	local bounds_x, bounds_y = get_bounds(dirs, rivers)
+	local dn = 0.5 / n
+
+	local offset_x = {X=X, Y=Y}
+	local offset_y = {X=X, Y=Y}
+	local offset_x_alt = {X=X, Y=Y}
+	local offset_y_alt = {X=X, Y=Y}
+	for i=1, X*Y do
+		offset_x[i] = 0
+		offset_y[i] = 0
+	end
+
+	for nn=1, n do
+		local i = 1
+		for y=1, Y do
+			for x=1, X do
+				local ox, oy = offset_x[i], offset_y[i]
+				if dirs[i] ~= 0 and rivers[i] > 1 then
+					local sum_fx = 0
+					local sum_fy = 0
+					local sum_w = 0
+					local b
+					if x < X then
+						b = bounds_x[i]
+						sum_fx = sum_fx + b*(offset_x[i+1]+1)
+						sum_fy = sum_fy + b*offset_y[i+1]
+						sum_w = sum_w + b
+					end
+					if y < Y then
+						b = bounds_y[i]
+						sum_fx = sum_fx + b*offset_x[i+X]
+						sum_fy = sum_fy + b*(offset_y[i+X]+1)
+						sum_w = sum_w + b
+					end
+					if x > 1 then
+						b = bounds_x[i-1]
+						sum_fx = sum_fx + b*(offset_x[i-1]-1)
+						sum_fy = sum_fy + b*offset_y[i-1]
+						sum_w = sum_w + b
+					end
+					if y > 1 then
+						b = bounds_y[i-X]
+						sum_fx = sum_fx + b*offset_x[i-X]
+						sum_fy = sum_fy + b*(offset_y[i-X]-1)
+						sum_w = sum_w + b
+					end
+					local fx, fy = sum_fx/sum_w - ox, sum_fy/sum_w - oy
+					local fd = (fx*fx+fy*fy) ^ 0.5
+					if fd > dn then
+						local c = dn/fd
+						fx, fy = fx*c, fy*c
+					end
+
+					offset_x_alt[i] = ox+fx
+					offset_y_alt[i] = oy+fy
+				else
+					offset_x_alt[i] = ox
+					offset_y_alt[i] = oy
+				end
+
+				i = i + 1
+			end
+		end
+		offset_x, offset_x_alt = offset_x_alt, offset_x
+		offset_y, offset_y_alt = offset_y_alt, offset_y
+	end
+
+	return offset_x, offset_y
+end
+
+return twist

view.py

@@ -0,0 +1,102 @@
+#!/usr/bin/env python3
+
+import numpy as np
+import sys, traceback
+
+has_matplotlib = True
+try:
+    import matplotlib.colors as mcl
+    import matplotlib.pyplot as plt
+    try:
+        import colorcet as cc
+        cmap1 = cc.cm.CET_L11
+        cmap2 = cc.cm.CET_L12
+    except ImportError: # No module colorcet
+        import matplotlib.cm as cm
+        cmap1 = cm.summer
+        cmap2 = cm.Blues
+except ImportError: # No module matplotlib
+    has_matplotlib = False
+
+if has_matplotlib:
+    def view_map(dem, lakes, scale=1, center=False, sea_level=0.0, title=None):
+        lakes_sea = np.maximum(lakes, sea_level)
+        water = np.maximum(lakes_sea - dem, 0)
+        max_elev = dem.max()
+        max_depth = water.max()
+
+        ls = mcl.LightSource(azdeg=315, altdeg=45)
+        norm_ground = plt.Normalize(vmin=sea_level, vmax=max_elev)
+        norm_sea = plt.Normalize(vmin=0, vmax=max_depth)
+        rgb = ls.shade(dem, cmap=cmap1, vert_exag=1/scale, blend_mode='soft', norm=norm_ground)
+
+        (X, Y) = dem.shape
+        if center:
+            extent = (-(Y+1)*scale/2, (Y-1)*scale/2, -(X+1)*scale/2, (X-1)*scale/2)
+        else:
+            extent = (-0.5*scale, (Y-0.5)*scale, -0.5*scale, (X-0.5)*scale)
+        plt.imshow(np.flipud(rgb), extent=extent, interpolation='antialiased')
+        alpha = (water > 0).astype('u1')
+        plt.imshow(np.flipud(water), alpha=np.flipud(alpha), cmap=cmap2, extent=extent, vmin=0, vmax=max_depth, interpolation='antialiased')
+
+        sm1 = plt.cm.ScalarMappable(cmap=cmap1, norm=norm_ground)
+        plt.colorbar(sm1).set_label('Elevation')
+
+        sm2 = plt.cm.ScalarMappable(cmap=cmap2, norm=norm_sea)
+        plt.colorbar(sm2).set_label('Water depth')
+
+        plt.xlabel('X')
+        plt.ylabel('Z')
+
+        if title is not None:
+            plt.title(title, fontweight='bold')
+
+    def update(*args, t=0.01, **kwargs):
+        try:
+            plt.clf()
+            view_map(*args, **kwargs)
+            plt.pause(t)
+        except:
+            traceback.print_exception(*sys.exc_info())
+
+    def plot(*args, **kwargs):
+        try:
+            plt.clf()
+            view_map(*args, **kwargs)
+            plt.pause(0.01)
+            plt.show()
+        except Exception as e:
+            traceback.print_exception(*sys.exc_info())
+
+else:
+    def update(*args, **kwargs):
+        pass
+    def plot(*args, **kwargs):
+        pass
+
+def stats(dem, lakes, scale=1):
+    surface = dem.size
+
+    continent = np.maximum(dem, lakes) >= 0
+    continent_surface = continent.sum()
+
+    lake = continent & (lakes>dem)
+    lake_surface = lake.sum()
+
+    print('---   General    ---')
+    print('Grid size:    {:5d}x{:5d}'.format(dem.shape[0], dem.shape[1]))
+    if scale > 1:
+        print('Map size:     {:5d}x{:5d}'.format(int(dem.shape[0]*scale), int(dem.shape[1]*scale)))
+    print()
+    print('---   Surfaces   ---')
+    print('Continents:        {:6.2%}'.format(continent_surface/surface))
+    print('-> Ground:         {:6.2%}'.format((continent_surface-lake_surface)/surface))
+    print('-> Lakes:          {:6.2%}'.format(lake_surface/surface))
+    print('Oceans:            {:6.2%}'.format(1-continent_surface/surface))
+    print()
+    print('---  Elevations  ---')
+    print('Mean elevation:      {:4.0f}'.format(dem.mean()))
+    print('Mean ocean depth:    {:4.0f}'.format((dem*~continent).sum()/(surface-continent_surface)))
+    print('Mean continent elev: {:4.0f}'.format((dem*continent).sum()/continent_surface))
+    print('Lowest elevation:    {:4.0f}'.format(dem.min()))
+    print('Highest elevation:   {:4.0f}'.format(dem.max()))

view_map.py

@@ -2,7 +2,23 @@
 
 import numpy as np
 import zlib
-import matplotlib.pyplot as plt
+import sys
+import os
+
+from view import stats, plot
+from readconfig import read_conf_file
+
+os.chdir(sys.argv[1])
+conf = read_conf_file('mapgen_rivers.conf')
+if 'center' in conf:
+    center = conf['center'] == 'true'
+else:
+    center = True
+
+if 'blocksize' in conf:
+    blocksize = float(conf['blocksize'])
+else:
+    blocksize = 15.0
 
 def load_map(name, dtype, shape):
     dtype = np.dtype(dtype)
@@ -12,28 +28,10 @@ def load_map(name, dtype, shape):
             data = zlib.decompress(data)
         return np.frombuffer(data, dtype=dtype).reshape(shape)
 
-shape = np.loadtxt('size', dtype='u4')
-n = shape[0] * shape[1]
-dem = load_map('dem', '>i2', shape)
-lakes = load_map('lakes', '>i2', shape)
-rivers = load_map('rivers', '>u4', shape)
+shape = np.loadtxt('river_data/size', dtype='u4')
+shape = (shape[1], shape[0])
+dem = load_map('river_data/dem', '>i2', shape)
+lakes = load_map('river_data/lakes', '>i2', shape)
 
-plt.subplot(1,3,1)
-plt.pcolormesh(dem, cmap='viridis')
-plt.gca().set_aspect('equal', 'box')
-#plt.colorbar(orientation='horizontal')
-plt.title('Raw elevation')
-
-plt.subplot(1,3,2)
-plt.pcolormesh(lakes, cmap='viridis')
-plt.gca().set_aspect('equal', 'box')
-#plt.colorbar(orientation='horizontal')
-plt.title('Lake surface elevation')
-
-plt.subplot(1,3,3)
-plt.pcolormesh(np.log(rivers), vmin=0, vmax=np.log(n/25), cmap='Blues')
-plt.gca().set_aspect('equal', 'box')
-#plt.colorbar(orientation='horizontal')
-plt.title('Rivers discharge')
-
-plt.show()
+stats(dem, lakes, scale=blocksize)
+plot(dem, lakes, scale=blocksize, center=center)