Alright, so I'd like to start by announcing that I have created a minds account and can be found at https://www.minds.com/TheWrongHands, I have no idea what I'm going to do with this account, but it's now there for what ever I feel like doing with it. Now for this post I would like to talk about the mechanism I intend to use to place cities in my procedurally generated worlds, but we need to work our way up to that by starting with resource distribution.
In Minecraft the resource distribution is in such a way that that you have a little bit of everything everywhere. By that I mean that if you dig down anywhere your likely to easily find every resource you might need but in small pockets. This is perfect for a game that is primarily about construction and exploration as that anywhere you go you can easily find any resource that you might need to get started, but need to do a bit of exploring to amass the amount of resources needed for large scale construction. On the other hand for an RPG, this isn't so great. For the early game I want to force the player to run around and have to interact with NPC's in order to get the resources they need, while in the late game make the player figure out how to build where they need to instead of giving them the freedom to just build anywhere or in anyway they wish. To achieve this I want to put mine-able resources into large deposits that are big enough that if your can lay claim to one, you won't be needing any more of that particular resource for awhile and infrequent enough that if you just randomly dig down, your unlikely to find anything of value. This will give a reason to build mining villages strategically and incentivize trade between the the player and NPC as well as between NPCs. So with that in mind, village, towns, and cities can't just be placed any where and expect to receive a benefit, which leads us into the topic I was to talk about, AI city placement.
Alright, so the best way to get an AI to do what you want it to assign numbers to things, in this case places. Now while you could calculate things on a per-block level, that kind of resolution is unnecessary, so I'm going to use a chunk unit of measurement that's actual size is unspecified because it's not very important.
In the image above you can see I have made a 16x16 grid and placed a badly drawn village in one of the squares. There is also a yellow circle that represents the distance one can reasonably walk in a day. The optimal place to build another village is somewhere on that yellow line, the reason being that halfway between that line and the village is the furthest away someone who lives at that village can travel and expect to be home before sundown and thus is the furthest away they would be willing to go to farm or gather resources. So villages placed that far apart can optimally use the land without risk of overlap. This also gives travelers a fortified location in which to sleep at night, which benefits trade and the flow of resources. Now, there might be a resource or some other reason to not build perfectly on this line, so a little bit closer or somewhat farther might be acceptable. So now lets apply numbers to this so that an AI can understand it.
Ok, so I have gone though and applied a value to every square based on it's distance from the village and gave that yellow line a value of 300. Now because none of the squares are perfectly on that yellow line, none of them got exactly 300, instead the square with the highest value got 295 and is highlighted in red. I have also given any square too close to the village a negative number so that the AI will never build another village there. So now lets look at a resource.
Ok, so this image just shows the kind of effect I think a resource like copper should have. I gave it a value of 50 and as you can see squares within proximity get the full value after which the values rapidly deteriorate. The reason is that a village build close by or on top can easily harvest the resource, but the further away the village is placed the more difficult it is for them to harvest it until it just gets to be not worth it. So lets look at what happens when we combine the 2 grids.
So now we can see that the best place to build a new village (highlighted in red) is still close to the yellow line but now has the copper resource we just placed within it's range. So now what if we place down another resource, call it iron, and make it 3 times as valuable as copper?
Alright, now as we can see the best place to build a village now is by the iron deposit and that resource was valuable enough to justify building a bit further away from the yellow line. This might have the effect that travelers going between the 2 villages might have to walk in the dark a little bit, but hopefully won't be that big of a deal. Next lets talk about rivers.
Rivers are extremely important for trade, so as you can see in the above image I made them worth 250. I have also given them a much longer reach so that they will naturally pull new villages towards them. So lets see what happens when we combine it all together.
As you can see the river has pulled the best place to build a new village closer to it and further away from that yellow line. Although the village is still close enough to the yellow line that travel shouldn't be an issue, travelers may have to spend an hour or 2 in the dark when going between villages. On the upside, that iron is now much closer to the new village and much easier for it to harvest. The next village built after this one will quite likely be on the bank of that river.
In Minecraft the resource distribution is in such a way that that you have a little bit of everything everywhere. By that I mean that if you dig down anywhere your likely to easily find every resource you might need but in small pockets. This is perfect for a game that is primarily about construction and exploration as that anywhere you go you can easily find any resource that you might need to get started, but need to do a bit of exploring to amass the amount of resources needed for large scale construction. On the other hand for an RPG, this isn't so great. For the early game I want to force the player to run around and have to interact with NPC's in order to get the resources they need, while in the late game make the player figure out how to build where they need to instead of giving them the freedom to just build anywhere or in anyway they wish. To achieve this I want to put mine-able resources into large deposits that are big enough that if your can lay claim to one, you won't be needing any more of that particular resource for awhile and infrequent enough that if you just randomly dig down, your unlikely to find anything of value. This will give a reason to build mining villages strategically and incentivize trade between the the player and NPC as well as between NPCs. So with that in mind, village, towns, and cities can't just be placed any where and expect to receive a benefit, which leads us into the topic I was to talk about, AI city placement.
Alright, so the best way to get an AI to do what you want it to assign numbers to things, in this case places. Now while you could calculate things on a per-block level, that kind of resolution is unnecessary, so I'm going to use a chunk unit of measurement that's actual size is unspecified because it's not very important.
In the image above you can see I have made a 16x16 grid and placed a badly drawn village in one of the squares. There is also a yellow circle that represents the distance one can reasonably walk in a day. The optimal place to build another village is somewhere on that yellow line, the reason being that halfway between that line and the village is the furthest away someone who lives at that village can travel and expect to be home before sundown and thus is the furthest away they would be willing to go to farm or gather resources. So villages placed that far apart can optimally use the land without risk of overlap. This also gives travelers a fortified location in which to sleep at night, which benefits trade and the flow of resources. Now, there might be a resource or some other reason to not build perfectly on this line, so a little bit closer or somewhat farther might be acceptable. So now lets apply numbers to this so that an AI can understand it.
Ok, so I have gone though and applied a value to every square based on it's distance from the village and gave that yellow line a value of 300. Now because none of the squares are perfectly on that yellow line, none of them got exactly 300, instead the square with the highest value got 295 and is highlighted in red. I have also given any square too close to the village a negative number so that the AI will never build another village there. So now lets look at a resource.
Ok, so this image just shows the kind of effect I think a resource like copper should have. I gave it a value of 50 and as you can see squares within proximity get the full value after which the values rapidly deteriorate. The reason is that a village build close by or on top can easily harvest the resource, but the further away the village is placed the more difficult it is for them to harvest it until it just gets to be not worth it. So lets look at what happens when we combine the 2 grids.
So now we can see that the best place to build a new village (highlighted in red) is still close to the yellow line but now has the copper resource we just placed within it's range. So now what if we place down another resource, call it iron, and make it 3 times as valuable as copper?
Alright, now as we can see the best place to build a village now is by the iron deposit and that resource was valuable enough to justify building a bit further away from the yellow line. This might have the effect that travelers going between the 2 villages might have to walk in the dark a little bit, but hopefully won't be that big of a deal. Next lets talk about rivers.
Rivers are extremely important for trade, so as you can see in the above image I made them worth 250. I have also given them a much longer reach so that they will naturally pull new villages towards them. So lets see what happens when we combine it all together.
As you can see the river has pulled the best place to build a new village closer to it and further away from that yellow line. Although the village is still close enough to the yellow line that travel shouldn't be an issue, travelers may have to spend an hour or 2 in the dark when going between villages. On the upside, that iron is now much closer to the new village and much easier for it to harvest. The next village built after this one will quite likely be on the bank of that river.
I'm not sure what more to add to this, I just made up the numbers and rules on the fly, so there is quite likely lots of room for improvement on everything, but this should be enough to give you a rough idea of how I want this to work. For anyone wondering how I calculated and numbered every single square without fellating a 9mm, the answer is I made the following python script for GIMP:
# this is so i don't have to press enter
import math
townD = 200
oreMin = townD / 3
oreMax = townD * 2 / 3
riverMin = townD / 3
riverMax = townD * 2
def render(name, map):
img = gimp.image_list()[0]
# pdb.gimp_selection_none(img)
layer = gimp.Layer(img, name, 512, 512, RGBA_IMAGE, 0, NORMAL_MODE)
img.add_layer(layer, 0)
biggest = 0
for y in range(0, 16):
for x in range(0, 16):
if(map[y][x] > biggest):
biggest = map[y][x]
#couldn't get this to work, but i'll leave it in in-case i need it later
#pdb.gimp_context_swap_colors()
# for y in range(0, 16):
# for x in range(0, 16):
# if(1):#map[y][x] == biggest):
# pdb.gimp_image_select_rectangle(img, 2, x * 32 + 1, y * 32 + 1, 31, 31)
# pdb.gimp_image_select_rectangle(img, 1, x * 32 + 2, y * 32 + 2, 29, 29)
# pdb.gimp_edit_fill(layer, 1)
# pdb.gimp_edit_bucket_fill(layer, 1, 24, 100, 0, 0, x * 32 + 1, y * 32 + 1)
#pdb.gimp_context_swap_colors()
# pdb.gimp_selection_none(img)
for y in range(0, 16):
for x in range(0, 16):
if(map[y][x] == biggest):
pdb.gimp_context_swap_colors()
text = pdb.gimp_text_fontname(img, None, x * 32 + 2, y * 32 + 2, str(int(map[y][x])), -1, 1, 10, 0, 'Sans')
if(map[y][x] == biggest):
pdb.gimp_context_swap_colors()
pdb.gimp_image_merge_down(img, text, 1)
def dis(a, b):
return math.sqrt(math.pow(a[0] - b[0], 2) + math.pow(a[1] - b[1], 2))
def initMap():
map = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
return map
def calMap(map, rValue, rPos, rule):
for y in range(0, 16):
for x in range(0, 16):
testPos = [x * 32 + 16, y * 32 + 16]
for pos in rPos:
v = rule(testPos, pos, rValue)
if(v < 0 or map[y][x] < 0):
map[y][x] = -1
elif(v > map[y][x]):
map[y][x] = v
def mergeMaps(a, b):
map = initMap()
for y in range(0, 16):
for x in range(0, 16):
if(a[y][x] < 0 or b[y][x] < 0):
map[y][x] = -1
else:
map[y][x] = a[y][x] + b[y][x]
return map
def townRule(testPos, pos, value):
d = dis(testPos, pos)
if(d <= townD * 0.75):
return -1
elif(d < townD):
return max(math.floor(((d - townD * 0.75) * 4 * value) / townD), 0)
else:
return max(math.floor(((townD * 2 - d) * value) / townD), 0)
def oreRule(testPos, pos, value):
d = dis(testPos, pos)
if(d < oreMin):
return value
elif(d > oreMax):
return 0
else:
return max(math.floor(((oreMax - oreMin) - (d - oreMin)) * value / (oreMax - oreMin)), 0)
def riverRule(testPos, pos, value):
d = dis(testPos, pos)
if(d < riverMin):
return value
elif(d > riverMax):
return 0
else:
return max(math.floor(((riverMax - riverMin) - (d - riverMin)) * value / (riverMax - riverMin)), 0)
town = [[341, 21]]
iron = [[433, 309]]
copper = [[80, 108]]
river = [[16, 319], [56, 329], [93, 338], [130, 353], [161, 370], [191, 388], [221, 410], [254, 428], [288, 441], [323, 445], [357, 451], [389, 465], [424, 486], [455, 505]]
townMap = initMap()
copperMap = initMap()
ironMap = initMap()
riverMap = initMap()
calMap(townMap, 300, town, townRule)
calMap(copperMap, 50, copper, oreRule)
calMap(ironMap, 150, iron, oreRule)
calMap(riverMap, 250, river, riverRule)
tc = mergeMaps(townMap, copperMap)
tci = mergeMaps(tc, ironMap)
tcir = mergeMaps(tci, riverMap)
render('town map', townMap)
render('copper map', copperMap)
render('river map', riverMap)
render('tc map', tc)
render('tci map', tci)
render('tcir map', tcir)
# this is so i don't have to press enter
import math
townD = 200
oreMin = townD / 3
oreMax = townD * 2 / 3
riverMin = townD / 3
riverMax = townD * 2
def render(name, map):
img = gimp.image_list()[0]
# pdb.gimp_selection_none(img)
layer = gimp.Layer(img, name, 512, 512, RGBA_IMAGE, 0, NORMAL_MODE)
img.add_layer(layer, 0)
biggest = 0
for y in range(0, 16):
for x in range(0, 16):
if(map[y][x] > biggest):
biggest = map[y][x]
#couldn't get this to work, but i'll leave it in in-case i need it later
#pdb.gimp_context_swap_colors()
# for y in range(0, 16):
# for x in range(0, 16):
# if(1):#map[y][x] == biggest):
# pdb.gimp_image_select_rectangle(img, 2, x * 32 + 1, y * 32 + 1, 31, 31)
# pdb.gimp_image_select_rectangle(img, 1, x * 32 + 2, y * 32 + 2, 29, 29)
# pdb.gimp_edit_fill(layer, 1)
# pdb.gimp_edit_bucket_fill(layer, 1, 24, 100, 0, 0, x * 32 + 1, y * 32 + 1)
#pdb.gimp_context_swap_colors()
# pdb.gimp_selection_none(img)
for y in range(0, 16):
for x in range(0, 16):
if(map[y][x] == biggest):
pdb.gimp_context_swap_colors()
text = pdb.gimp_text_fontname(img, None, x * 32 + 2, y * 32 + 2, str(int(map[y][x])), -1, 1, 10, 0, 'Sans')
if(map[y][x] == biggest):
pdb.gimp_context_swap_colors()
pdb.gimp_image_merge_down(img, text, 1)
def dis(a, b):
return math.sqrt(math.pow(a[0] - b[0], 2) + math.pow(a[1] - b[1], 2))
def initMap():
map = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
return map
def calMap(map, rValue, rPos, rule):
for y in range(0, 16):
for x in range(0, 16):
testPos = [x * 32 + 16, y * 32 + 16]
for pos in rPos:
v = rule(testPos, pos, rValue)
if(v < 0 or map[y][x] < 0):
map[y][x] = -1
elif(v > map[y][x]):
map[y][x] = v
def mergeMaps(a, b):
map = initMap()
for y in range(0, 16):
for x in range(0, 16):
if(a[y][x] < 0 or b[y][x] < 0):
map[y][x] = -1
else:
map[y][x] = a[y][x] + b[y][x]
return map
def townRule(testPos, pos, value):
d = dis(testPos, pos)
if(d <= townD * 0.75):
return -1
elif(d < townD):
return max(math.floor(((d - townD * 0.75) * 4 * value) / townD), 0)
else:
return max(math.floor(((townD * 2 - d) * value) / townD), 0)
def oreRule(testPos, pos, value):
d = dis(testPos, pos)
if(d < oreMin):
return value
elif(d > oreMax):
return 0
else:
return max(math.floor(((oreMax - oreMin) - (d - oreMin)) * value / (oreMax - oreMin)), 0)
def riverRule(testPos, pos, value):
d = dis(testPos, pos)
if(d < riverMin):
return value
elif(d > riverMax):
return 0
else:
return max(math.floor(((riverMax - riverMin) - (d - riverMin)) * value / (riverMax - riverMin)), 0)
town = [[341, 21]]
iron = [[433, 309]]
copper = [[80, 108]]
river = [[16, 319], [56, 329], [93, 338], [130, 353], [161, 370], [191, 388], [221, 410], [254, 428], [288, 441], [323, 445], [357, 451], [389, 465], [424, 486], [455, 505]]
townMap = initMap()
copperMap = initMap()
ironMap = initMap()
riverMap = initMap()
calMap(townMap, 300, town, townRule)
calMap(copperMap, 50, copper, oreRule)
calMap(ironMap, 150, iron, oreRule)
calMap(riverMap, 250, river, riverRule)
tc = mergeMaps(townMap, copperMap)
tci = mergeMaps(tc, ironMap)
tcir = mergeMaps(tci, riverMap)
render('town map', townMap)
render('copper map', copperMap)
render('river map', riverMap)
render('tc map', tc)
render('tci map', tci)
render('tcir map', tcir)
# this is so i don't have to press enter
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