# SPDX-License-Identifier: GPL-2.0-or-later from time import time import unittest import sys import os from random import random as rand, shuffle import numpy as np numexpr_available = False def getmemsize(): return 0.0 def getptime(): return time() class Grid: def __init__(self, size=10, dtype=np.single): self.center = np.zeros([size, size], dtype) self.water = None self.sediment = None self.scour = None self.flowrate = None self.sedimentpct = None self.sedimentpct = None self.capacity = None self.avalanced = None self.minx = None self.miny = None self.maxx = None self.maxy = None self.zscale = 1 self.maxrss = 0.0 self.sequence = [0, 1, 2, 3] self.watermax = 1.0 self.flowratemax = 1.0 self.scourmax = 1.0 self.sedmax = 1.0 self.scourmin = 1.0 def init_water_and_sediment(self): if self.water is None: self.water = np.zeros(self.center.shape, dtype=np.single) if self.sediment is None: self.sediment = np.zeros(self.center.shape, dtype=np.single) if self.scour is None: self.scour = np.zeros(self.center.shape, dtype=np.single) if self.flowrate is None: self.flowrate = np.zeros(self.center.shape, dtype=np.single) if self.sedimentpct is None: self.sedimentpct = np.zeros(self.center.shape, dtype=np.single) if self.capacity is None: self.capacity = np.zeros(self.center.shape, dtype=np.single) if self.avalanced is None: self.avalanced = np.zeros(self.center.shape, dtype=np.single) def __str__(self): return ''.join(self.__str_iter__(fmt="%.3f")) def __str_iter__(self, fmt): for row in self.center[::]: values = [] for v in row: values.append(fmt % v) yield ' '.join(values) + '\n' @staticmethod def fromFile(filename): if filename == '-': filename = sys.stdin g = Grid() g.center = np.loadtxt(filename, np.single) return g def toFile(self, filename, fmt="%.3f"): if filename == '-': filename = sys.stdout.fileno() with open(filename, "w") as f: for line in self.__str_iter__(fmt): f.write(line) def raw(self, format="%.3f"): fstr = format + " " + format + " " + format + " " a = self.center / self.zscale minx = 0.0 if self.minx is None else self.minx miny = 0.0 if self.miny is None else self.miny maxx = 1.0 if self.maxx is None else self.maxx maxy = 1.0 if self.maxy is None else self.maxy dx = (maxx - minx) / (a.shape[0] - 1) dy = (maxy - miny) / (a.shape[1] - 1) for row in range(a.shape[0] - 1): row0 = miny + row * dy row1 = row0 + dy for col in range(a.shape[1] - 1): col0 = minx + col * dx col1 = col0 + dx yield (fstr % (row0, col0, a[row][col]) + fstr % (row0, col1, a[row][col + 1]) + fstr % (row1, col0, a[row + 1][col]) + "\n") yield (fstr % (row0, col1, a[row][col + 1]) + fstr % (row1, col0, a[row + 1][col]) + fstr % (row1, col1, a[row + 1][col + 1]) + "\n") def toRaw(self, filename, infomap=None): with open(filename if type(filename) == str else sys.stdout.fileno(), "w") as f: f.writelines(self.raw()) if infomap: with open(os.path.splitext(filename)[0] + ".inf" if type(filename) == str else sys.stdout.fileno(), "w") as f: f.writelines("\n".join("%-15s: %s" % t for t in sorted(infomap.items()))) @staticmethod def fromRaw(filename): """initialize a grid from a Blender .raw file. currently supports just rectangular grids of all triangles """ g = Grid.fromFile(filename) # we assume tris and an axis aligned grid g.center = np.reshape(g.center, (-1, 3)) g._sort() return g def _sort(self, expfact): # keep unique vertices only by creating a set and sort first on x then on y coordinate # using rather slow python sort but couldn't wrap my head around np.lexsort verts = sorted(list({tuple(t) for t in self.center[::]})) x = set(c[0] for c in verts) y = set(c[1] for c in verts) nx = len(x) ny = len(y) self.minx = min(x) self.maxx = max(x) self.miny = min(y) self.maxy = max(y) xscale = (self.maxx - self.minx) / (nx - 1) yscale = (self.maxy - self.miny) / (ny - 1) # note: a purely flat plane cannot be scaled if (yscale != 0.0) and (abs(xscale / yscale) - 1.0 > 1e-3): raise ValueError("Mesh spacing not square %d x %d %.4f x %4.f" % (nx, ny, xscale, yscale)) self.zscale = 1.0 if abs(yscale) > 1e-6: self.zscale = 1.0 / yscale # keep just the z-values and null any offset # we might catch a reshape error that will occur if nx*ny != # of vertices # (if we are not dealing with a heightfield but with a mesh with duplicate # x,y coords, like an axis aligned cube self.center = np.array([c[2] for c in verts], dtype=np.single).reshape(nx, ny) self.center = (self.center - np.amin(self.center)) * self.zscale if self.rainmap is not None: rmscale = np.max(self.center) self.rainmap = expfact + (1 - expfact) * (self.center / rmscale) @staticmethod def fromBlenderMesh(me, vg, expfact): g = Grid() g.center = np.asarray(list(tuple(v.co) for v in me.vertices), dtype=np.single) g.rainmap = None if vg is not None: for v in me.vertices: vg.add([v.index], 0.0, 'ADD') g.rainmap = np.asarray(list((v.co[0], v.co[1], vg.weight(v.index)) for v in me.vertices), dtype=np.single) g._sort(expfact) return g def setrainmap(self, rainmap): self.rainmap = rainmap def _verts(self, surface): a = surface / self.zscale minx = 0.0 if self.minx is None else self.minx miny = 0.0 if self.miny is None else self.miny maxx = 1.0 if self.maxx is None else self.maxx maxy = 1.0 if self.maxy is None else self.maxy dx = (maxx - minx) / (a.shape[0] - 1) dy = (maxy - miny) / (a.shape[1] - 1) for row in range(a.shape[0]): row0 = miny + row * dy for col in range(a.shape[1]): col0 = minx + col * dx yield (row0, col0, a[row][col]) def _faces(self): nrow, ncol = self.center.shape for row in range(nrow - 1): for col in range(ncol - 1): vi = row * ncol + col yield (vi, vi + ncol, vi + 1) yield (vi + 1, vi + ncol, vi + ncol + 1) def toBlenderMesh(self, me): # pass me as argument so that we don't need to import bpy and create a dependency # the docs state that from_pydata takes iterators as arguments but it will # fail with generators because it does len(arg) me.from_pydata(list(self._verts(self.center)), [], list(self._faces())) def toWaterMesh(self, me): # pass me as argument so that we don't need to import bpy and create a dependency # the docs state that from_pydata takes iterators as arguments but it will # fail with generators because it does len(arg) me.from_pydata(list(self._verts(self.water)), [], list(self._faces())) def peak(self, value=1): nx, ny = self.center.shape self.center[int(nx / 2), int(ny / 2)] += value def shelf(self, value=1): nx, ny = self.center.shape self.center[:nx / 2] += value def mesa(self, value=1): nx, ny = self.center.shape self.center[nx / 4:3 * nx / 4, ny / 4:3 * ny / 4] += value def random(self, value=1): self.center += np.random.random_sample(self.center.shape) * value def neighborgrid(self): self.up = np.roll(self.center, -1, 0) self.down = np.roll(self.center, 1, 0) self.left = np.roll(self.center, -1, 1) self.right = np.roll(self.center, 1, 1) def zeroedge(self, quantity=None): c = self.center if quantity is None else quantity c[0, :] = 0 c[-1, :] = 0 c[:, 0] = 0 c[:, -1] = 0 def diffuse(self, Kd, IterDiffuse, numexpr): self.zeroedge() c = self.center[1:-1, 1:-1] up = self.center[:-2, 1:-1] down = self.center[2:, 1:-1] left = self.center[1:-1, :-2] right = self.center[1:-1, 2:] if(numexpr and numexpr_available): self.center[1:-1, 1:-1] = ne.evaluate('c + Kd * (up + down + left + right - 4.0 * c)') else: self.center[1:-1, 1:-1] = c + (Kd / IterDiffuse) * (up + down + left + right - 4.0 * c) self.maxrss = max(getmemsize(), self.maxrss) return self.center def avalanche(self, delta, iterava, prob, numexpr): self.zeroedge() c = self.center[1:-1, 1:-1] up = self.center[:-2, 1:-1] down = self.center[2:, 1:-1] left = self.center[1:-1, :-2] right = self.center[1:-1, 2:] where = np.where if(numexpr and numexpr_available): self.center[1:-1, 1:-1] = ne.evaluate('c + where((up -c) > delta ,(up -c -delta)/2, 0) \ + where((down -c) > delta ,(down -c -delta)/2, 0) \ + where((left -c) > delta ,(left -c -delta)/2, 0) \ + where((right-c) > delta ,(right-c -delta)/2, 0) \ + where((up -c) < -delta,(up -c +delta)/2, 0) \ + where((down -c) < -delta,(down -c +delta)/2, 0) \ + where((left -c) < -delta,(left -c +delta)/2, 0) \ + where((right-c) < -delta,(right-c +delta)/2, 0)') else: sa = ( # incoming where((up - c) > delta, (up - c - delta) / 2, 0) + where((down - c) > delta, (down - c - delta) / 2, 0) + where((left - c) > delta, (left - c - delta) / 2, 0) + where((right - c) > delta, (right - c - delta) / 2, 0) # outgoing + where((up - c) < -delta, (up - c + delta) / 2, 0) + where((down - c) < -delta, (down - c + delta) / 2, 0) + where((left - c) < -delta, (left - c + delta) / 2, 0) + where((right - c) < -delta, (right - c + delta) / 2, 0) ) randarray = np.random.randint(0, 100, sa.shape) * 0.01 sa = where(randarray < prob, sa, 0) self.avalanced[1:-1, 1:-1] = self.avalanced[1:-1, 1:-1] + sa / iterava self.center[1:-1, 1:-1] = c + sa / iterava self.maxrss = max(getmemsize(), self.maxrss) return self.center def rain(self, amount=1, variance=0, userainmap=False): self.water += (1.0 - np.random.random(self.water.shape) * variance) * \ (amount if ((self.rainmap is None) or (not userainmap)) else self.rainmap * amount) def spring(self, amount, px, py, radius): # px, py and radius are all fractions nx, ny = self.center.shape rx = max(int(nx * radius), 1) ry = max(int(ny * radius), 1) px = int(nx * px) py = int(ny * py) self.water[px - rx:px + rx + 1, py - ry:py + ry + 1] += amount def river(self, Kc, Ks, Kdep, Ka, Kev, numexpr): zeros = np.zeros where = np.where min = np.minimum max = np.maximum abs = np.absolute arctan = np.arctan sin = np.sin center = (slice(1, -1, None), slice(1, -1, None)) up = (slice(None, -2, None), slice(1, -1, None)) down = (slice(2, None, None), slice(1, -1, None)) left = (slice(1, -1, None), slice(None, -2, None)) right = (slice(1, -1, None), slice(2, None, None)) water = self.water rock = self.center sediment = self.sediment height = rock + water # !! this gives a runtime warning for division by zero verysmallnumber = 0.0000000001 water += verysmallnumber sc = where(water > verysmallnumber, sediment / water, 0) sdw = zeros(water[center].shape) svdw = zeros(water[center].shape) sds = zeros(water[center].shape) angle = zeros(water[center].shape) for d in (up, down, left, right): if(numexpr and numexpr_available): hdd = height[d] hcc = height[center] dw = ne.evaluate('hdd-hcc') inflow = ne.evaluate('dw > 0') wdd = water[d] wcc = water[center] # nested where() represent min() and max() dw = ne.evaluate('where(inflow, where(wdddw, -wcc, dw))/4.0') sdw = ne.evaluate('sdw + dw') scd = sc[d] scc = sc[center] rockd = rock[d] rockc = rock[center] sds = ne.evaluate('sds + dw * where(inflow, scd, scc)') svdw = ne.evaluate('svdw + abs(dw)') angle = ne.evaluate('angle + arctan(abs(rockd-rockc))') else: dw = (height[d] - height[center]) inflow = dw > 0 dw = where(inflow, min(water[d], dw), max(-water[center], dw)) / 4.0 sdw = sdw + dw sds = sds + dw * where(inflow, sc[d], sc[center]) svdw = svdw + abs(dw) angle = angle + np.arctan(abs(rock[d] - rock[center])) if numexpr and numexpr_available: wcc = water[center] scc = sediment[center] rcc = rock[center] water[center] = ne.evaluate('wcc + sdw') sediment[center] = ne.evaluate('scc + sds') sc = ne.evaluate('where(wcc>0, scc/wcc, 2000*Kc)') fKc = ne.evaluate('Kc*sin(Ka*angle)*svdw') ds = ne.evaluate('where(sc > fKc, -Kd * scc, Ks * svdw)') rock[center] = ne.evaluate('rcc - ds') # there isn't really a bottom to the rock but negative values look ugly rock[center] = ne.evaluate('where(rcc<0,0,rcc)') sediment[center] = ne.evaluate('scc + ds') else: wcc = water[center] scc = sediment[center] rcc = rock[center] water[center] = wcc * (1 - Kev) + sdw sediment[center] = scc + sds sc = where(wcc > 0, scc / wcc, 2 * Kc) fKc = Kc * svdw ds = where(fKc > sc, (fKc - sc) * Ks, (fKc - sc) * Kdep) * wcc self.flowrate[center] = svdw self.scour[center] = ds self.sedimentpct[center] = sc self.capacity[center] = fKc sediment[center] = scc + ds + sds def flow(self, Kc, Ks, Kz, Ka, numexpr): zeros = np.zeros where = np.where min = np.minimum max = np.maximum abs = np.absolute arctan = np.arctan sin = np.sin center = (slice(1, -1, None), slice(1, -1, None)) rock = self.center ds = self.scour[center] rcc = rock[center] rock[center] = rcc - ds * Kz # there isn't really a bottom to the rock but negative values look ugly rock[center] = where(rcc < 0, 0, rcc) def rivergeneration( self, rainamount, rainvariance, userainmap, Kc, Ks, Kdep, Ka, Kev, Kspring, Kspringx, Kspringy, Kspringr, numexpr, ): self.init_water_and_sediment() self.rain(rainamount, rainvariance, userainmap) self.zeroedge(self.water) self.zeroedge(self.sediment) self.river(Kc, Ks, Kdep, Ka, Kev, numexpr) self.watermax = np.max(self.water) def fluvial_erosion( self, rainamount, rainvariance, userainmap, Kc, Ks, Kdep, Ka, Kspring, Kspringx, Kspringy, Kspringr, numexpr, ): self.flow(Kc, Ks, Kdep, Ka, numexpr) self.flowratemax = np.max(self.flowrate) self.scourmax = np.max(self.scour) self.scourmin = np.min(self.scour) self.sedmax = np.max(self.sediment) def analyze(self): self.neighborgrid() # just looking at up and left to avoid needless double calculations slopes = np.concatenate((np.abs(self.left - self.center), np.abs(self.up - self.center))) return '\n'.join(["%-15s: %.3f" % t for t in [ ('height average', np.average(self.center)), ('height median', np.median(self.center)), ('height max', np.max(self.center)), ('height min', np.min(self.center)), ('height std', np.std(self.center)), ('slope average', np.average(slopes)), ('slope median', np.median(slopes)), ('slope max', np.max(slopes)), ('slope min', np.min(slopes)), ('slope std', np.std(slopes)) ]]) class TestGrid(unittest.TestCase): def test_diffuse(self): g = Grid(5) g.peak(1) self.assertEqual(g.center[2, 2], 1.0) g.diffuse(0.1, numexpr=False) for n in [(2, 1), (2, 3), (1, 2), (3, 2)]: self.assertAlmostEqual(g.center[n], 0.1) self.assertAlmostEqual(g.center[2, 2], 0.6) def test_diffuse_numexpr(self): g = Grid(5) g.peak(1) g.diffuse(0.1, numexpr=False) h = Grid(5) h.peak(1) h.diffuse(0.1, numexpr=True) self.assertEqual(list(g.center.flat), list(h.center.flat)) def test_avalanche_numexpr(self): g = Grid(5) g.peak(1) g.avalanche(0.1, numexpr=False) h = Grid(5) h.peak(1) h.avalanche(0.1, numexpr=True) print(g) print(h) np.testing.assert_almost_equal(g.center, h.center) if __name__ == "__main__": import argparse parser = argparse.ArgumentParser(description='Erode a terrain while assuming zero boundary conditions.') parser.add_argument('-I', dest='iterations', type=int, default=1, help='the number of iterations') parser.add_argument('-Kd', dest='Kd', type=float, default=0.01, help='Diffusion constant') parser.add_argument('-Kh', dest='Kh', type=float, default=6, help='Maximum stable cliff height') parser.add_argument('-Kp', dest='Kp', type=float, default=0.1, help='Avalanche probability for unstable cliffs') parser.add_argument('-Kr', dest='Kr', type=float, default=0.1, help='Average amount of rain per iteration') parser.add_argument('-Kspring', dest='Kspring', type=float, default=0.0, help='Average amount of wellwater per iteration') parser.add_argument('-Kspringx', dest='Kspringx', type=float, default=0.5, help='relative x position of spring') parser.add_argument('-Kspringy', dest='Kspringy', type=float, default=0.5, help='relative y position of spring') parser.add_argument('-Kspringr', dest='Kspringr', type=float, default=0.02, help='radius of spring') parser.add_argument('-Kdep', dest='Kdep', type=float, default=0.1, help='Sediment deposition constant') parser.add_argument('-Ks', dest='Ks', type=float, default=0.1, help='Soil softness constant') parser.add_argument('-Kc', dest='Kc', type=float, default=1.0, help='Sediment capacity') parser.add_argument('-Ka', dest='Ka', type=float, default=2.0, help='Slope dependency of erosion') parser.add_argument( '-ri', action='store_true', dest='rawin', default=False, help='use Blender raw format for input') parser.add_argument( '-ro', action='store_true', dest='rawout', default=False, help='use Blender raw format for output') parser.add_argument('-i', action='store_true', dest='useinputfile', default=False, help='use an inputfile (instead of just a synthesized grid)') parser.add_argument( '-t', action='store_true', dest='timingonly', default=False, help='do not write anything to an output file') parser.add_argument('-infile', type=str, default="-", help='input filename') parser.add_argument('-outfile', type=str, default="-", help='output filename') parser.add_argument('-Gn', dest='gridsize', type=int, default=20, help='Gridsize (always square)') parser.add_argument('-Gp', dest='gridpeak', type=float, default=0, help='Add peak with given height') parser.add_argument('-Gs', dest='gridshelf', type=float, default=0, help='Add shelve with given height') parser.add_argument('-Gm', dest='gridmesa', type=float, default=0, help='Add mesa with given height') parser.add_argument('-Gr', dest='gridrandom', type=float, default=0, help='Add random values between 0 and given value') parser.add_argument('-m', dest='threads', type=int, default=1, help='number of threads to use') parser.add_argument('-u', action='store_true', dest='unittest', default=False, help='perform unittests') parser.add_argument('-a', action='store_true', dest='analyze', default=False, help='show some statistics of input and output meshes') parser.add_argument('-d', action='store_true', dest='dump', default=False, help='show sediment and water meshes at end of run') parser.add_argument('-n', action='store_true', dest='usenumexpr', default=False, help='use numexpr optimizations') args = parser.parse_args() print("\nInput arguments:") print("\n".join("%-15s: %s" % t for t in sorted(vars(args).items())), file=sys.stderr) if args.unittest: unittest.main(argv=[sys.argv[0]]) sys.exit(0) if args.useinputfile: if args.rawin: grid = Grid.fromRaw(args.infile) else: grid = Grid.fromFile(args.infile) else: grid = Grid(args.gridsize) if args.gridpeak > 0: grid.peak(args.gridpeak) if args.gridmesa > 0: grid.mesa(args.gridmesa) if args.gridshelf > 0: grid.shelf(args.gridshelf) if args.gridrandom > 0: grid.random(args.gridrandom) if args.analyze: print('\nstatistics of the input grid:\n\n', grid.analyze(), file=sys.stderr, sep='') t = getptime() for g in range(args.iterations): if args.Kd > 0: grid.diffuse(args.Kd, args.usenumexpr) if args.Kh > 0 and args.Kp > rand(): grid.avalanche(args.Kh, args.usenumexpr) if args.Kr > 0 or args.Kspring > 0: grid.fluvial_erosion( args.Kr, args.Kc, args.Ks, args.Kdep, args.Ka, args.Kspring, args.Kspringx, args.Kspringy, args.Kspringr, args.usenumexpr, ) t = getptime() - t print("\nElapsed time: %.1f seconds, max memory %.1f Mb.\n" % (t, grid.maxrss), file=sys.stderr) if args.analyze: print('\nstatistics of the output grid:\n\n', grid.analyze(), file=sys.stderr, sep='') if not args.timingonly: if args.rawout: grid.toRaw(args.outfile, vars(args)) else: grid.toFile(args.outfile) if args.dump: print("sediment\n", np.array_str(grid.sediment, precision=3), file=sys.stderr) print("water\n", np.array_str(grid.water, precision=3), file=sys.stderr) print("sediment concentration\n", np.array_str(grid.sediment / grid.water, precision=3), file=sys.stderr)