Added an offset of 0.5 on terrain elevation

This prevents rounding errors and improves interpolation on nearly flat areas

.gitignore

@@ -1,7 +1,9 @@
 __pycache__/
 dem
 lakes
-links
-rivers
 size
+offset_x
+offset_y
+bounds_x
+bounds_y
 unused/

README.md

@@ -5,6 +5,8 @@ Procedural map generator for Minetest 5.x. Still experimental and basic.
 
 Contains two distinct programs: Python scripts for pre-processing, and Lua scripts to generate the map on Minetest.
 
+![Screenshot](https://user-images.githubusercontent.com/6905002/79073532-7a567f00-7ce7-11ea-9791-8fb453f5175d.png)
+
 # Installation
 This mod should be placed in the `/mods` directory like any other Minetest mod.
 

bounds.py

@@ -0,0 +1,62 @@
+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

geometry.lua

@@ -0,0 +1,45 @@
+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 b = (x1-x)^2 + (y1-y)^2
+	local c = (x2-x)^2 + (y2-y)^2
+	if a + b < c then
+		return math.sqrt(b)
+	elseif a + c < b then
+		return math.sqrt(c)
+	else
+		return math.abs(x1 * (y2-y) + x2 * (y-y1) + x * (y1-y2)) / math.sqrt(a)
+	end
+end
+
+local function transform_quadri(X, Y, x, y)
+	-- X, Y 4-vectors giving the coordinates of the 4 nodes
+	-- x, y position to index.
+	local x1, x2, x3, x4 = unpack(X)
+	local y1, y2, y3, y4 = unpack(Y)
+
+	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)
+
+	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,
+}

init.lua

@@ -1,6 +1,7 @@
 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')
 
 local function copy_if_needed(filename)
 	local wfilename = worldpath..filename
@@ -26,26 +27,45 @@ copy_if_needed('dem')
 local dem = load_map(worldpath..'dem', 2, true)
 copy_if_needed('lakes')
 local lakes = load_map(worldpath..'lakes', 2, true)
-copy_if_needed('links')
-local links = load_map(worldpath..'links', 1, false)
-copy_if_needed('rivers')
-local rivers = load_map(worldpath..'rivers', 4, false)
+copy_if_needed('bounds_x')
+local bounds_x = load_map(worldpath..'bounds_x', 4, false)
+copy_if_needed('bounds_y')
+local bounds_z = load_map(worldpath..'bounds_y', 4, false)
+
+copy_if_needed('offset_x')
+local offset_x = load_map(worldpath..'offset_x', 1, true)
+for k, v in ipairs(offset_x) do
+	offset_x[k] = (v+0.5)/256
+end
+
+copy_if_needed('offset_y')
+local offset_z = load_map(worldpath..'offset_y', 1, true)
+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 interp(v00, v01, v10, v11, xf, zf)
-	v0 = v01*xf + v00*(1-xf)
-	v1 = v11*xf + v10*(1-xf)
+local function get_point_location(x, z)
+	local i = index(x, z)
+	return x+offset_x[i], z+offset_z[i]
+end
+
+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 data = {}
 
-local blocksize = 6
+local blocksize = 12
 local sea_level = 1
 local min_catchment = 25
+local max_catchment = 40000
 
 local storage = minetest.get_mod_storage()
 if storage:contains("blocksize") then
@@ -63,6 +83,25 @@ if storage:contains("min_catchment") then
 else
 	storage:set_float("min_catchment", min_catchment)
 end
+if storage:contains("max_catchment") then
+	max_catchment = storage:get_float("max_catchment")
+else
+	storage:set_float("max_catchment", max_catchment)
+end
+
+-- 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 function generate(minp, maxp, seed)
 	local c_stone = minetest.get_content_id("default:stone")
@@ -77,59 +116,122 @@ local function generate(minp, maxp, seed)
 
 	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)
+
+	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 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}
+		end
+	end
+
+	local i = 1
 	for x = minp.x, maxp.x do
 		for z = minp.z, maxp.z do
-			local xb = x/blocksize
-			local zb = z/blocksize
+			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)
 
-			if xb >= 0 and xb < X-1 and zb >= 0 and zb < Z-1 then
-				local x0 = math.floor(xb)
-				local x1 = x0+1
-				local z0 = math.floor(zb)
-				local z1 = z0+1
+				local is_river = false
+				local r_west, r_north, r_east, r_south = unpack(poly.rivers)
+				if xf >= r_east then
+					is_river = true
+					xf = 1
+				elseif xf <= r_west then
+					is_river = true
+					xf = 0
+				end
+				if zf >= r_south then
+					is_river = true
+					zf = 1
+				elseif zf <= r_north then
+					is_river = true
+					zf = 0
+				end
 
-				local xf = xb - x0
-				local zf = zb - z0
+				if not is_river then
+					xf = (xf-r_west) / (r_east-r_west)
+					zf = (zf-r_north) / (r_south-r_north)
+				end
 
-				local i00 = index(x0,z0)
-				local i01 = index(x1,z0)
-				local i10 = index(x0,z1)
-				local i11 = index(x1,z1)
-
-				local terrain_height = math.floor(interp(
-					dem[i00],
-					dem[i01],
-					dem[i10],
-					dem[i11],
+				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.floor(math.min(
-					lakes[i00],
-					lakes[i01],
-					lakes[i10],
-					lakes[i11]
-				))
+				local lake_height = math.floor(poly.lake)
 
 				local is_lake = lake_height > terrain_height
-
-				local is_river = false
-				if xf == 0 then
-					if links[i00] == 1 and rivers[i00] >= min_catchment then
-						is_river = true
-					elseif links[i10] == 3 and rivers[i10] >= min_catchment then
-						is_river = true
-					end
-				end
-
-				if zf == 0 then
-					if links[i00] == 2 and rivers[i00] >= min_catchment then
-						is_river = true
-					elseif links[i01] == 4 and rivers[i01] >= min_catchment then
-						is_river = true
-					end
-				end
 				
 				local ivm = a:index(x, minp.y-1, z)
 
@@ -164,6 +266,7 @@ local function generate(minp, maxp, seed)
 					end
 				end
 			end
+			i = i + 1
 		end
 	end
 

rivermapper.py

@@ -18,7 +18,7 @@ neighbours_dirs = np.array([
 
 neighbours_pattern = neighbours_dirs > 0
 
-def flow_dirs_lakes(dem, random=0.0625):
+def flow_dirs_lakes(dem, random=0):
     (Y, X) = dem.shape
 
     dem_margin = np.zeros((Y+2, X+2))

terrain_rivers.py

@@ -4,6 +4,7 @@ import numpy as np
 import noise
 from save import save
 from erosion import EvolutionModel
+import bounds
 import os
 import sys
 
@@ -22,7 +23,7 @@ n = np.zeros((mapsize, mapsize))
 #micronoise_depth = 0.05
 
 params = {
-    "octaves" : 8,
+    "octaves" : int(np.log2(mapsize)),
     "persistence" : 0.5,
     "lacunarity" : 2.,
 }
@@ -67,10 +68,18 @@ 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(model.dirs, 'links', dtype='u1')
-save(model.rivers, 'rivers', dtype='>u4')
+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')
 
 with open('size', 'w') as sfile:
     sfile.write('{:d}\n{:d}'.format(mapsize, mapsize))

view_map.py

@@ -0,0 +1,30 @@
+#!/usr/bin/env python3
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+shape = np.loadtxt('size', dtype='u4')
+n = shape[0] * shape[1]
+dem = np.fromfile('dem', dtype='>i2').reshape(shape)
+lakes = np.fromfile('lakes', dtype='>i2').reshape(shape)
+rivers = np.fromfile('rivers', dtype='>u4').reshape(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()