From: Perttu Ahola Date: Fri, 8 Jun 2012 12:50:27 +0000 (+0300) Subject: Move genmap.py and pnoise.py to old/ X-Git-Tag: 0.4.0~39 X-Git-Url: https://git.librecmc.org/?a=commitdiff_plain;h=523a5fd2e5dd03ff73a2df647ae0f209acbf9ab9;p=oweals%2Fminetest.git Move genmap.py and pnoise.py to old/ --- diff --git a/util/genmap.py b/util/genmap.py deleted file mode 100755 index 6b36269d5..000000000 --- a/util/genmap.py +++ /dev/null @@ -1,271 +0,0 @@ -#!/usr/bin/python2 - -# This is an example script that generates some valid map data. - -import struct -import random -import os -import sys -import zlib -import array -from pnoise import pnoise - -# Old directory format: -# world/sectors/XXXXZZZZ/YYYY -# XXXX,YYYY,ZZZZ = coordinates in hexadecimal -# fffe = -2 -# ffff = -1 -# 0000 = 0 -# 0001 = 1 -# -# New directory format: -# world/sectors2/XXX/ZZZ/YYYY -# XXX,YYYY,ZZZ = coordinates in hexadecimal -# fffe = -2 -# ffff = -1 -# 0000 = 0 -# 0001 = 1 -# ffe = -2 -# fff = -1 -# 000 = 0 -# 001 = 1 -# -# For more proper file format documentation, refer to mapformat.txt -# For node type documentation, refer to mapnode.h -# NodeMetadata documentation is not complete, refer to nodemeta.cpp -# - -# Seed for generating terrain -SEED = 0 - -# 0=old, 1=new -SECTOR_DIR_FORMAT = 1 - -mapdir = "../world" - -def to4h(i): - s = ""; - s += '{0:1x}'.format((i>>12) & 0x000f) - s += '{0:1x}'.format((i>>8) & 0x000f) - s += '{0:1x}'.format((i>>4) & 0x000f) - s += '{0:1x}'.format((i>>0) & 0x000f) - return s - -def to3h(i): - s = ""; - s += '{0:1x}'.format((i>>8) & 0x000f) - s += '{0:1x}'.format((i>>4) & 0x000f) - s += '{0:1x}'.format((i>>0) & 0x000f) - return s - -def get_sector_dir(px, pz): - global SECTOR_DIR_FORMAT - if SECTOR_DIR_FORMAT == 0: - return "/sectors/"+to4h(px)+to4h(pz) - elif SECTOR_DIR_FORMAT == 1: - return "/sectors2/"+to3h(px)+"/"+to3h(pz) - else: - assert(0) - -def getrand_air_stone(): - i = random.randrange(0,2) - if i==0: - return 0 - return 254 - -# 3-dimensional vector (position) -class v3: - def __init__(self, x=0, y=0, z=0): - self.X = x - self.Y = y - self.Z = z - -class NodeMeta: - def __init__(self, type_id, data): - self.type_id = type_id - self.data = data - -class StaticObject: - def __init__(self): - self.type_id = 0 - self.data = "" - -def ser_u16(i): - return chr((i>>8)&0xff) + chr((i>>0)&0xff) -def ser_u32(i): - return (chr((i>>24)&0xff) + chr((i>>16)&0xff) - + chr((i>>8)&0xff) + chr((i>>0)&0xff)) - -# A 16x16x16 chunk of map -class MapBlock: - def __init__(self): - self.content = array.array('B') - self.param1 = array.array('B') - self.param2 = array.array('B') - for i in range(16*16*16): - # Initialize to air - self.content.append(254) - # Full light on sunlight, none when no sunlight - self.param1.append(15) - # No additional parameters - self.param2.append(0) - - # key = v3 pos - # value = NodeMeta - self.nodemeta = {} - - # key = v3 pos - # value = StaticObject - self.static_objects = {} - - def set_content(self, v3, b): - self.content[v3.Z*16*16+v3.Y*16+v3.X] = b - def set_param1(self, v3, b): - self.param1[v3.Z*16*16+v3.Y*16+v3.X] = b - def set_param2(self, v3, b): - self.param2[v3.Z*16*16+v3.Y*16+v3.X] = b - - # Get data for serialization. Returns a string. - def serialize_data(self): - s = "" - for i in range(16*16*16): - s += chr(self.content[i]) - for i in range(16*16*16): - s += chr(self.param1[i]) - for i in range(16*16*16): - s += chr(self.param2[i]) - return s - - def serialize_nodemeta(self): - s = "" - s += ser_u16(1) - s += ser_u16(len(self.nodemeta)) - for pos, meta in self.nodemeta.items(): - pos_i = pos.Z*16*16 + pos.Y*16 + pos.X - s += ser_u16(pos_i) - s += ser_u16(meta.type_id) - s += ser_u16(len(meta.data)) - s += meta.data - return s - - def serialize_staticobj(self): - s = "" - s += chr(0) - s += ser_u16(len(self.static_objects)) - for pos, obj in self.static_objects.items(): - pos_i = pos.Z*16*16 + pos.Y*16 + pos.X - s += ser_s32(pos.X*1000) - s += ser_s32(pos.Y*1000) - s += ser_s32(pos.Z*1000) - s += ser_u16(obj.type_id) - s += ser_u16(len(obj.data)) - s += obj.data - return s - -def writeblock(mapdir, px,py,pz, block): - - sectordir = mapdir + get_sector_dir(px, pz); - - try: - os.makedirs(sectordir) - except OSError: - pass - - path = sectordir+"/"+to4h(py) - - print("writing block file "+path) - - f = open(sectordir+"/"+to4h(py), "wb") - - if f == None: - return - - # version - version = 17 - f.write(struct.pack('B', version)) - - # flags - # 0x01=is_undg, 0x02=dn_diff, 0x04=lighting_expired - flags = 0 + 0x02 + 0x04 - f.write(struct.pack('B', flags)) - - # data - c_obj = zlib.compressobj() - c_obj.compress(block.serialize_data()) - f.write(struct.pack('BB', 0x78, 0x9c)) # zlib magic number - f.write(c_obj.flush()) - - # node metadata - c_obj = zlib.compressobj() - c_obj.compress(block.serialize_nodemeta()) - f.write(struct.pack('BB', 0x78, 0x9c)) # zlib magic number - f.write(c_obj.flush()) - - # mapblockobject count - f.write(ser_u16(0)) - - # static objects - f.write(block.serialize_staticobj()) - - # timestamp - f.write(ser_u32(0xffffffff)) - - f.close() - -for z0 in range(-1,3): - for x0 in range(-1,3): - for y0 in range(-1,3): - print("generating block "+str(x0)+","+str(y0)+","+str(z0)) - #v3 blockp = v3(x0,y0,z0) - - # Create a MapBlock - block = MapBlock() - - # Generate stuff in it - for z in range(0,16): - for x in range(0,16): - h = 20.0*pnoise((x0*16+x)/100.,(z0*16+z)/100.,SEED+0) - h += 5.0*pnoise((x0*16+x)/25.,(z0*16+z)/25.,SEED+0) - if pnoise((x0*16+x)/25.,(z0*16+z)/25.,SEED+92412) > 0.05: - h += 10 - #print("r="+str(r)) - # This enables comparison by == - h = int(h) - for y in range(0,16): - p = v3(x,y,z) - b = 254 - y1 = y0*16+y - if y1 <= h-3: - b = 0 #stone - elif y1 <= h and y1 <= 0: - b = 8 #mud - elif y1 == h: - b = 1 #grass - elif y1 < h: - b = 8 #mud - elif y1 <= 1: - b = 9 #water - - # Material content - block.set_content(p, b) - - # Place a sign at the center at surface level. - # Placing a sign means placing the sign node and - # adding node metadata to the mapblock. - if x == 8 and z == 8 and y0*16 <= h-1 and (y0+1)*16-1 > h: - p = v3(8,h+1-y0*16,8) - # 14 = Sign - content_type = 14 - block.set_content(p, content_type) - # This places the sign to the bottom of the cube. - # Working values: 0x01, 0x02, 0x04, 0x08, 0x10, 0x20 - block.set_param2(p, 0x08) - # Then add metadata to hold the text of the sign - s = "Hello at sector ("+str(x0)+","+str(z0)+")" - meta = NodeMeta(content_type, ser_u16(len(s))+s) - block.nodemeta[p] = meta - - # Write it on disk - writeblock(mapdir, x0,y0,z0, block) - -#END diff --git a/util/old/genmap.py b/util/old/genmap.py new file mode 100755 index 000000000..6b36269d5 --- /dev/null +++ b/util/old/genmap.py @@ -0,0 +1,271 @@ +#!/usr/bin/python2 + +# This is an example script that generates some valid map data. + +import struct +import random +import os +import sys +import zlib +import array +from pnoise import pnoise + +# Old directory format: +# world/sectors/XXXXZZZZ/YYYY +# XXXX,YYYY,ZZZZ = coordinates in hexadecimal +# fffe = -2 +# ffff = -1 +# 0000 = 0 +# 0001 = 1 +# +# New directory format: +# world/sectors2/XXX/ZZZ/YYYY +# XXX,YYYY,ZZZ = coordinates in hexadecimal +# fffe = -2 +# ffff = -1 +# 0000 = 0 +# 0001 = 1 +# ffe = -2 +# fff = -1 +# 000 = 0 +# 001 = 1 +# +# For more proper file format documentation, refer to mapformat.txt +# For node type documentation, refer to mapnode.h +# NodeMetadata documentation is not complete, refer to nodemeta.cpp +# + +# Seed for generating terrain +SEED = 0 + +# 0=old, 1=new +SECTOR_DIR_FORMAT = 1 + +mapdir = "../world" + +def to4h(i): + s = ""; + s += '{0:1x}'.format((i>>12) & 0x000f) + s += '{0:1x}'.format((i>>8) & 0x000f) + s += '{0:1x}'.format((i>>4) & 0x000f) + s += '{0:1x}'.format((i>>0) & 0x000f) + return s + +def to3h(i): + s = ""; + s += '{0:1x}'.format((i>>8) & 0x000f) + s += '{0:1x}'.format((i>>4) & 0x000f) + s += '{0:1x}'.format((i>>0) & 0x000f) + return s + +def get_sector_dir(px, pz): + global SECTOR_DIR_FORMAT + if SECTOR_DIR_FORMAT == 0: + return "/sectors/"+to4h(px)+to4h(pz) + elif SECTOR_DIR_FORMAT == 1: + return "/sectors2/"+to3h(px)+"/"+to3h(pz) + else: + assert(0) + +def getrand_air_stone(): + i = random.randrange(0,2) + if i==0: + return 0 + return 254 + +# 3-dimensional vector (position) +class v3: + def __init__(self, x=0, y=0, z=0): + self.X = x + self.Y = y + self.Z = z + +class NodeMeta: + def __init__(self, type_id, data): + self.type_id = type_id + self.data = data + +class StaticObject: + def __init__(self): + self.type_id = 0 + self.data = "" + +def ser_u16(i): + return chr((i>>8)&0xff) + chr((i>>0)&0xff) +def ser_u32(i): + return (chr((i>>24)&0xff) + chr((i>>16)&0xff) + + chr((i>>8)&0xff) + chr((i>>0)&0xff)) + +# A 16x16x16 chunk of map +class MapBlock: + def __init__(self): + self.content = array.array('B') + self.param1 = array.array('B') + self.param2 = array.array('B') + for i in range(16*16*16): + # Initialize to air + self.content.append(254) + # Full light on sunlight, none when no sunlight + self.param1.append(15) + # No additional parameters + self.param2.append(0) + + # key = v3 pos + # value = NodeMeta + self.nodemeta = {} + + # key = v3 pos + # value = StaticObject + self.static_objects = {} + + def set_content(self, v3, b): + self.content[v3.Z*16*16+v3.Y*16+v3.X] = b + def set_param1(self, v3, b): + self.param1[v3.Z*16*16+v3.Y*16+v3.X] = b + def set_param2(self, v3, b): + self.param2[v3.Z*16*16+v3.Y*16+v3.X] = b + + # Get data for serialization. Returns a string. + def serialize_data(self): + s = "" + for i in range(16*16*16): + s += chr(self.content[i]) + for i in range(16*16*16): + s += chr(self.param1[i]) + for i in range(16*16*16): + s += chr(self.param2[i]) + return s + + def serialize_nodemeta(self): + s = "" + s += ser_u16(1) + s += ser_u16(len(self.nodemeta)) + for pos, meta in self.nodemeta.items(): + pos_i = pos.Z*16*16 + pos.Y*16 + pos.X + s += ser_u16(pos_i) + s += ser_u16(meta.type_id) + s += ser_u16(len(meta.data)) + s += meta.data + return s + + def serialize_staticobj(self): + s = "" + s += chr(0) + s += ser_u16(len(self.static_objects)) + for pos, obj in self.static_objects.items(): + pos_i = pos.Z*16*16 + pos.Y*16 + pos.X + s += ser_s32(pos.X*1000) + s += ser_s32(pos.Y*1000) + s += ser_s32(pos.Z*1000) + s += ser_u16(obj.type_id) + s += ser_u16(len(obj.data)) + s += obj.data + return s + +def writeblock(mapdir, px,py,pz, block): + + sectordir = mapdir + get_sector_dir(px, pz); + + try: + os.makedirs(sectordir) + except OSError: + pass + + path = sectordir+"/"+to4h(py) + + print("writing block file "+path) + + f = open(sectordir+"/"+to4h(py), "wb") + + if f == None: + return + + # version + version = 17 + f.write(struct.pack('B', version)) + + # flags + # 0x01=is_undg, 0x02=dn_diff, 0x04=lighting_expired + flags = 0 + 0x02 + 0x04 + f.write(struct.pack('B', flags)) + + # data + c_obj = zlib.compressobj() + c_obj.compress(block.serialize_data()) + f.write(struct.pack('BB', 0x78, 0x9c)) # zlib magic number + f.write(c_obj.flush()) + + # node metadata + c_obj = zlib.compressobj() + c_obj.compress(block.serialize_nodemeta()) + f.write(struct.pack('BB', 0x78, 0x9c)) # zlib magic number + f.write(c_obj.flush()) + + # mapblockobject count + f.write(ser_u16(0)) + + # static objects + f.write(block.serialize_staticobj()) + + # timestamp + f.write(ser_u32(0xffffffff)) + + f.close() + +for z0 in range(-1,3): + for x0 in range(-1,3): + for y0 in range(-1,3): + print("generating block "+str(x0)+","+str(y0)+","+str(z0)) + #v3 blockp = v3(x0,y0,z0) + + # Create a MapBlock + block = MapBlock() + + # Generate stuff in it + for z in range(0,16): + for x in range(0,16): + h = 20.0*pnoise((x0*16+x)/100.,(z0*16+z)/100.,SEED+0) + h += 5.0*pnoise((x0*16+x)/25.,(z0*16+z)/25.,SEED+0) + if pnoise((x0*16+x)/25.,(z0*16+z)/25.,SEED+92412) > 0.05: + h += 10 + #print("r="+str(r)) + # This enables comparison by == + h = int(h) + for y in range(0,16): + p = v3(x,y,z) + b = 254 + y1 = y0*16+y + if y1 <= h-3: + b = 0 #stone + elif y1 <= h and y1 <= 0: + b = 8 #mud + elif y1 == h: + b = 1 #grass + elif y1 < h: + b = 8 #mud + elif y1 <= 1: + b = 9 #water + + # Material content + block.set_content(p, b) + + # Place a sign at the center at surface level. + # Placing a sign means placing the sign node and + # adding node metadata to the mapblock. + if x == 8 and z == 8 and y0*16 <= h-1 and (y0+1)*16-1 > h: + p = v3(8,h+1-y0*16,8) + # 14 = Sign + content_type = 14 + block.set_content(p, content_type) + # This places the sign to the bottom of the cube. + # Working values: 0x01, 0x02, 0x04, 0x08, 0x10, 0x20 + block.set_param2(p, 0x08) + # Then add metadata to hold the text of the sign + s = "Hello at sector ("+str(x0)+","+str(z0)+")" + meta = NodeMeta(content_type, ser_u16(len(s))+s) + block.nodemeta[p] = meta + + # Write it on disk + writeblock(mapdir, x0,y0,z0, block) + +#END diff --git a/util/old/pnoise.py b/util/old/pnoise.py new file mode 100644 index 000000000..fcab5ac15 --- /dev/null +++ b/util/old/pnoise.py @@ -0,0 +1,102 @@ +# +# A python perlin noise implementation, from +# http://www.fundza.com/c4serious/noise/perlin/perlin.html +# +# This is used for testing how to create maps with a python script. +# + +import math +p = ( +151,160,137,91,90,15,131,13,201,95,96,53,194,233,7,225,140,36,103, +30,69,142,8,99,37,240,21,10,23,190,6,148,247,120,234,75,0,26,197, +62,94,252,219,203,117,35,11,32,57,177,33,88,237,149,56,87,174,20, +125,136,171,168,68,175,74,165,71,134,139,48,27,166,77,146,158,231, +83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,102, +143,54,65,25,63,161,1,216,80,73,209,76,132,187,208,89,18,169,200, +196,135,130,116,188,159,86,164,100,109,198,173,186,3,64,52,217,226, +250,124,123,5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16, +58,17,182,189,28,42,223,183,170,213,119,248,152,2,44,154,163,70, +221,153,101,155,167,43,172,9,129,22,39,253,19,98,108,110,79,113, +224,232,178,185,112,104,218,246,97,228,251,34,242,193,238,210,144, +12,191,179,162,241,81,51,145,235,249,14,239,107,49,192,214,31,181, +199,106,157,184,84,204,176,115,121,50,45,127,4,150,254,138,236, +205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180, +151,160,137,91,90,15,131,13,201,95,96,53,194,233,7,225,140,36,103, +30,69,142,8,99,37,240,21,10,23,190,6,148,247,120,234,75,0,26,197, +62,94,252,219,203,117,35,11,32,57,177,33,88,237,149,56,87,174,20, +125,136,171,168,68,175,74,165,71,134,139,48,27,166,77,146,158,231, +83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,102, +143,54,65,25,63,161,1,216,80,73,209,76,132,187,208,89,18,169,200, +196,135,130,116,188,159,86,164,100,109,198,173,186,3,64,52,217,226, +250,124,123,5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16, +58,17,182,189,28,42,223,183,170,213,119,248,152,2,44,154,163,70, +221,153,101,155,167,43,172,9,129,22,39,253,19,98,108,110,79,113, +224,232,178,185,112,104,218,246,97,228,251,34,242,193,238,210,144, +12,191,179,162,241,81,51,145,235,249,14,239,107,49,192,214,31,181, +199,106,157,184,84,204,176,115,121,50,45,127,4,150,254,138,236, +205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180) + +def lerp(t, a, b): + return a + t * (b - a) + +def fade(t): + return t * t * t * (t * (t * 6 - 15) + 10) + +def grad(hash, x, y, z): + h = hash & 15 + if h < 8: + u = x + else: + u = y + if h < 4: + v = y + elif h == 12 or h == 14: + v = x + else: + v = z + if h & 1 != 0: + u = -u + if h & 2 != 0: + v = -v + return u + v + +def pnoise(x, y, z): + global p + X = int(math.floor(x)) & 255 + Y = int(math.floor(y)) & 255 + Z = int(math.floor(z)) & 255 + x -= math.floor(x) + y -= math.floor(y) + z -= math.floor(z) + + u = fade(x) + v = fade(y) + w = fade(z) + + A = p[X] + Y + AA = p[A] + Z + AB = p[A + 1] + Z + B = p[X + 1] + Y + BA = p[B] + Z + BB = p[B + 1] + Z + + pAA = p[AA] + pAB = p[AB] + pBA = p[BA] + pBB = p[BB] + pAA1 = p[AA + 1] + pBA1 = p[BA + 1] + pAB1 = p[AB + 1] + pBB1 = p[BB + 1] + + gradAA = grad(pAA, x, y, z) + gradBA = grad(pBA, x-1, y, z) + gradAB = grad(pAB, x, y-1, z) + gradBB = grad(pBB, x-1, y-1, z) + gradAA1 = grad(pAA1,x, y, z-1) + gradBA1 = grad(pBA1,x-1, y, z-1) + gradAB1 = grad(pAB1,x, y-1, z-1) + gradBB1 = grad(pBB1,x-1, y-1, z-1) + return lerp(w, + lerp(v, lerp(u, gradAA, gradBA), lerp(u, gradAB, gradBB)), + lerp(v, lerp(u, gradAA1,gradBA1),lerp(u, gradAB1,gradBB1))) diff --git a/util/pnoise.py b/util/pnoise.py deleted file mode 100644 index fcab5ac15..000000000 --- a/util/pnoise.py +++ /dev/null @@ -1,102 +0,0 @@ -# -# A python perlin noise implementation, from -# http://www.fundza.com/c4serious/noise/perlin/perlin.html -# -# This is used for testing how to create maps with a python script. -# - -import math -p = ( -151,160,137,91,90,15,131,13,201,95,96,53,194,233,7,225,140,36,103, -30,69,142,8,99,37,240,21,10,23,190,6,148,247,120,234,75,0,26,197, -62,94,252,219,203,117,35,11,32,57,177,33,88,237,149,56,87,174,20, -125,136,171,168,68,175,74,165,71,134,139,48,27,166,77,146,158,231, -83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,102, -143,54,65,25,63,161,1,216,80,73,209,76,132,187,208,89,18,169,200, -196,135,130,116,188,159,86,164,100,109,198,173,186,3,64,52,217,226, -250,124,123,5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16, -58,17,182,189,28,42,223,183,170,213,119,248,152,2,44,154,163,70, -221,153,101,155,167,43,172,9,129,22,39,253,19,98,108,110,79,113, -224,232,178,185,112,104,218,246,97,228,251,34,242,193,238,210,144, -12,191,179,162,241,81,51,145,235,249,14,239,107,49,192,214,31,181, -199,106,157,184,84,204,176,115,121,50,45,127,4,150,254,138,236, -205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180, -151,160,137,91,90,15,131,13,201,95,96,53,194,233,7,225,140,36,103, -30,69,142,8,99,37,240,21,10,23,190,6,148,247,120,234,75,0,26,197, -62,94,252,219,203,117,35,11,32,57,177,33,88,237,149,56,87,174,20, -125,136,171,168,68,175,74,165,71,134,139,48,27,166,77,146,158,231, -83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,102, -143,54,65,25,63,161,1,216,80,73,209,76,132,187,208,89,18,169,200, -196,135,130,116,188,159,86,164,100,109,198,173,186,3,64,52,217,226, -250,124,123,5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16, -58,17,182,189,28,42,223,183,170,213,119,248,152,2,44,154,163,70, -221,153,101,155,167,43,172,9,129,22,39,253,19,98,108,110,79,113, -224,232,178,185,112,104,218,246,97,228,251,34,242,193,238,210,144, -12,191,179,162,241,81,51,145,235,249,14,239,107,49,192,214,31,181, -199,106,157,184,84,204,176,115,121,50,45,127,4,150,254,138,236, -205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180) - -def lerp(t, a, b): - return a + t * (b - a) - -def fade(t): - return t * t * t * (t * (t * 6 - 15) + 10) - -def grad(hash, x, y, z): - h = hash & 15 - if h < 8: - u = x - else: - u = y - if h < 4: - v = y - elif h == 12 or h == 14: - v = x - else: - v = z - if h & 1 != 0: - u = -u - if h & 2 != 0: - v = -v - return u + v - -def pnoise(x, y, z): - global p - X = int(math.floor(x)) & 255 - Y = int(math.floor(y)) & 255 - Z = int(math.floor(z)) & 255 - x -= math.floor(x) - y -= math.floor(y) - z -= math.floor(z) - - u = fade(x) - v = fade(y) - w = fade(z) - - A = p[X] + Y - AA = p[A] + Z - AB = p[A + 1] + Z - B = p[X + 1] + Y - BA = p[B] + Z - BB = p[B + 1] + Z - - pAA = p[AA] - pAB = p[AB] - pBA = p[BA] - pBB = p[BB] - pAA1 = p[AA + 1] - pBA1 = p[BA + 1] - pAB1 = p[AB + 1] - pBB1 = p[BB + 1] - - gradAA = grad(pAA, x, y, z) - gradBA = grad(pBA, x-1, y, z) - gradAB = grad(pAB, x, y-1, z) - gradBB = grad(pBB, x-1, y-1, z) - gradAA1 = grad(pAA1,x, y, z-1) - gradBA1 = grad(pBA1,x-1, y, z-1) - gradAB1 = grad(pAB1,x, y-1, z-1) - gradBB1 = grad(pBB1,x-1, y-1, z-1) - return lerp(w, - lerp(v, lerp(u, gradAA, gradBA), lerp(u, gradAB, gradBB)), - lerp(v, lerp(u, gradAA1,gradBA1),lerp(u, gradAB1,gradBB1)))