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Core algorithm for procedural city generation article (http://www.tmwhere.com)
# author: tmwhere.com
# --- third party dependencies
PIXI = require('pixi.dev')
_ = require('lodash')
noise = require('perlin').noise
Quadtree = require('quadtree').Quadtree
seedrandom = require('seedrandom')
# ---
math = require('modules/math')
util = require('modules/utility')
collision = require('modules/collision')
config = require('game_modules/config')
class Segment extends collision.CollisionObject
@End:
START: "start"
END: "end"
constructor: (start, end, t, q) ->
obj = @
start = _.cloneDeep(start)
end = _.cloneDeep(end)
t = util.defaultFor(t, 0)
q = util.defaultFor(q, {}, true)
@width = if q.highway then config.mapGeneration.HIGHWAY_SEGMENT_WIDTH else config.mapGeneration.DEFAULT_SEGMENT_WIDTH
@collider = new collision.CollisionObject(this, collision.CollisionObject.Type.LINE, {start: start, end: end, width: @width})
@roadRevision = 0
@dirRevision = undefined
@lengthRevision = undefined
@cachedDir = undefined
@cachedLength = undefined
# representation of road
@r =
start: start
end: end
setStart: (val) ->
@start = val
obj.collider.updateCollisionProperties({start: @start})
obj.roadRevision++
setEnd: (val) ->
@end = val
obj.collider.updateCollisionProperties({end: @end})
obj.roadRevision++
# time-step delay before this road is evaluated
@t = t
# meta-information relevant to global goals
@q = q
# links backwards and forwards
@links =
b: []
f: []
@users = []
[@maxSpeed, @capacity] =
if (q.highway)
[1200, 12]
else
[800, 6]
currentSpeed: ->
# subtract 1 from user's length so that a single user can go full speed
Math.min(config.gameLogic.MIN_SPEED_PROPORTION, 1 - Math.max(0, @users.length - 1) / @capacity) * @maxSpeed
# clockwise direction
dir: ->
if (@dirRevision != @roadRevision)
@dirRevision = @roadRevision
vector = math.subtractPoints(@r.end, @r.start)
@cachedDir = -1 * math.sign(math.crossProduct({x:0, y: 1}, vector)) * math.angleBetween({x: 0, y: 1}, vector)
return @cachedDir
length: ->
if (@lengthRevision != @roadRevision)
@lengthRevision = @roadRevision
@cachedLength = math.length(@r.start, @r.end)
return @cachedLength
debugLinks: ->
@q.color = 0x00FF00
_.each(@links.b, (backwards) ->
backwards.q.color = 0xFF0000
)
_.each(@links.f, (forwards) ->
forwards.q.color = 0x0000FF
)
startIsBackwards: ->
if (@links.b.length > 0)
math.equalV(@links.b[0].r.start, @r.start) ||
math.equalV(@links.b[0].r.end, @r.start)
else
math.equalV(@links.f[0].r.start, @r.end) ||
math.equalV(@links.f[0].r.end, @r.end)
cost: ->
@length() / @currentSpeed()
costTo: (other, fromFraction) ->
segmentEnd = @endContaining(other)
return @cost() *
if fromFraction?
switch segmentEnd
when Segment.End.START then fromFraction
when Segment.End.END then (1-fromFraction)
else
0.5
neighbours: ->
@links.f.concat(@links.b)
endContaining: (segment) ->
startBackwards = @startIsBackwards()
if @links.b.indexOf(segment) != -1
return if startBackwards then Segment.End.START else Segment.End.END
else if @links.f.indexOf(segment) != -1
return if startBackwards then Segment.End.END else Segment.End.START
else
undefined
linksForEndContaining: (segment) ->
if @links.b.indexOf(segment) != -1
@links.b
else if @links.f.indexOf(segment) != -1
@links.f
else
undefined
split: (point, segment, segmentList, qTree) ->
startIsBackwards = @startIsBackwards()
splitPart = segmentFactory.fromExisting(this)
addSegment(splitPart, segmentList, qTree)
splitPart.r.setEnd(point)
@r.setStart(point)
# links are not copied using the preceding factory method.
# copy link array for the split part, keeping references the same
splitPart.links.b = @links.b.slice(0)
splitPart.links.f = @links.f.slice(0)
# determine which links correspond to which end of the split segment
if (startIsBackwards)
firstSplit = splitPart
secondSplit = this
fixLinks = splitPart.links.b
else
firstSplit = this
secondSplit = splitPart
fixLinks = splitPart.links.f
_.each(fixLinks, (link) ->
index = link.links.b.indexOf(this)
if (index != -1)
link.links.b[index] = splitPart
else
index = link.links.f.indexOf(this)
link.links.f[index] = splitPart
, this)
firstSplit.links.f = []
firstSplit.links.f.push(segment)
firstSplit.links.f.push(secondSplit)
secondSplit.links.b = []
secondSplit.links.b.push(segment)
secondSplit.links.b.push(firstSplit)
segment.links.f.push(firstSplit)
segment.links.f.push(secondSplit)
segmentFactory = do ->
return {
fromExisting: (segment, t, r, q) ->
t = util.defaultFor(t, segment.t)
r = util.defaultFor(r, segment.r)
q = util.defaultFor(q, segment.q)
return new Segment(r.start, r.end, t, q)
,
usingDirection: (start, dir, length, t, q) ->
# default to east
dir = util.defaultFor(dir, 90)
length = util.defaultFor(length, config.mapGeneration.DEFAULT_SEGMENT_LENGTH)
end =
x: start.x + length*math.sinDegrees(dir),
y: start.y + length*math.cosDegrees(dir)
return new Segment(start, end, t, q)
}
heatmap = do ->
{
popOnRoad: (r) ->
(@populationAt(r.start.x, r.start.y) + @populationAt(r.end.x, r.end.y))/2
populationAt: (x, y) ->
value1 = (noise.simplex2(x/10000, y/10000) + 1) / 2
value2 = (noise.simplex2(x/20000 + 500, y/20000 + 500) + 1) / 2
value3 = (noise.simplex2(x/20000 + 1000, y/20000 + 1000) + 1) / 2
Math.pow((value1 * value2 + value3) / 2, 2)
}
doRoadSegmentsIntersect = (r1, r2) ->
math.doLineSegmentsIntersect(r1.start, r1.end, r2.start, r2.end, true)
localConstraints = (segment, segments, qTree, debugData) ->
action =
priority: 0,
func: undefined,
q: {}
matches = qTree.retrieve(segment.collider.limits())
for i in [0..matches.length-1] by 1
other = matches[i].o
# intersection check
if (action.priority <= 4)
intersection = doRoadSegmentsIntersect(segment.r, other.r)
if (intersection)
if (!action.q.t? || intersection.t < action.q.t)
action.q.t = intersection.t
do (other, intersection) ->
action.priority = 4
action.func = ->
# if intersecting lines are too similar don't continue
if util.minDegreeDifference(other.dir(), segment.dir()) < config.mapGeneration.MINIMUM_INTERSECTION_DEVIATION
return false
other.split(intersection, segment, segments, qTree)
segment.r.end = intersection
segment.q.severed = true
if (debugData?)
if (!debugData.intersections?)
debugData.intersections = []
debugData.intersections.push(
x: intersection.x
y: intersection.y
)
return true
# snap to crossing within radius check
if (action.priority <= 3)
# current segment's start must have been checked to have been created.
# other segment's start must have a corresponding end.
if (math.length(segment.r.end, other.r.end) <= config.mapGeneration.ROAD_SNAP_DISTANCE)
do (other) ->
point = other.r.end
action.priority = 3
action.func = ->
segment.r.end = point
segment.q.severed = true
# update links of otherSegment corresponding to other.r.end
links = if other.startIsBackwards() then other.links.f else other.links.b
# check for duplicate lines, don't add if it exists
# this should be done before links are setup, to avoid having to undo that step
if _.any(links, (link) ->
((math.equalV(link.r.start, segment.r.end) && math.equalV(link.r.end, segment.r.start)) ||
(math.equalV(link.r.start, segment.r.start) && math.equalV(link.r.end, segment.r.end))))
return false
_.each(links, (link) ->
# pick links of remaining segments at junction corresponding to other.r.end
link.linksForEndContaining(other).push(segment)
# add junction segments to snapped segment
segment.links.f.push(link)
)
links.push(segment)
segment.links.f.push(other)
if (debugData?)
if (!debugData.snaps?)
debugData.snaps = []
debugData.snaps.push(
x: point.x
y: point.y
)
return true
# intersection within radius check
if (action.priority <= 2)
{distance2, pointOnLine, lineProj2, length2} = math.distanceToLine(segment.r.end, other.r.start, other.r.end)
if (distance2 < config.mapGeneration.ROAD_SNAP_DISTANCE * config.mapGeneration.ROAD_SNAP_DISTANCE &&
lineProj2 >= 0 && lineProj2 <= length2)
do (other) ->
point = pointOnLine
action.priority = 2
action.func = ->
segment.r.end = point
segment.q.severed = true
# if intersecting lines are too closely aligned don't continue
if util.minDegreeDifference(other.dir(), segment.dir()) < config.mapGeneration.MINIMUM_INTERSECTION_DEVIATION
return false
other.split(point, segment, segments, qTree)
if (debugData?)
if (!debugData.intersectionsRadius?)
debugData.intersectionsRadius = []
debugData.intersectionsRadius.push(
x: point.x
y: point.y
)
return true
if (action.func)
return action.func()
return true
globalGoals = do ->
return {
generate: (previousSegment) ->
newBranches = []
if (!previousSegment.q.severed)
template = (direction, length, t, q) ->
segmentFactory.usingDirection(previousSegment.r.end, direction, length, t, q)
# used for highways or going straight on a normal branch
templateContinue = _.partialRight(template, previousSegment.length(), 0, previousSegment.q)
# not using q, i.e. not highways
templateBranch = _.partialRight(
template, config.mapGeneration.DEFAULT_SEGMENT_LENGTH, if previousSegment.q.highway then config.mapGeneration.NORMAL_BRANCH_TIME_DELAY_FROM_HIGHWAY else 0)
continueStraight = templateContinue(previousSegment.dir())
straightPop = heatmap.popOnRoad(continueStraight.r)
if (previousSegment.q.highway)
randomStraight = templateContinue(previousSegment.dir() + config.mapGeneration.RANDOM_STRAIGHT_ANGLE())
randomPop = heatmap.popOnRoad(randomStraight.r)
roadPop
if (randomPop > straightPop)
newBranches.push(randomStraight)
roadPop = randomPop
else
newBranches.push(continueStraight)
roadPop = straightPop
if (roadPop > config.mapGeneration.HIGHWAY_BRANCH_POPULATION_THRESHOLD)
if (Math.random() < config.mapGeneration.HIGHWAY_BRANCH_PROBABILITY)
leftHighwayBranch = templateContinue(previousSegment.dir() - 90 + config.mapGeneration.RANDOM_BRANCH_ANGLE())
newBranches.push(leftHighwayBranch)
else if (Math.random() < config.mapGeneration.HIGHWAY_BRANCH_PROBABILITY)
rightHighwayBranch = templateContinue(previousSegment.dir() + 90 + config.mapGeneration.RANDOM_BRANCH_ANGLE())
newBranches.push(rightHighwayBranch)
else if (straightPop > config.mapGeneration.NORMAL_BRANCH_POPULATION_THRESHOLD)
newBranches.push(continueStraight)
if (straightPop > config.mapGeneration.NORMAL_BRANCH_POPULATION_THRESHOLD)
if (Math.random() < config.mapGeneration.DEFAULT_BRANCH_PROBABILITY)
leftBranch = templateBranch(previousSegment.dir() - 90 + config.mapGeneration.RANDOM_BRANCH_ANGLE())
newBranches.push(leftBranch)
else if (Math.random() < config.mapGeneration.DEFAULT_BRANCH_PROBABILITY)
rightBranch = templateBranch(previousSegment.dir() + 90 + config.mapGeneration.RANDOM_BRANCH_ANGLE())
newBranches.push(rightBranch)
for i in [0..newBranches.length-1] by 1
do (branch = newBranches[i]) ->
branch.setupBranchLinks = ->
# setup links between each current branch and each existing branch stemming from the previous segment
_.each(previousSegment.links.f, (link) ->
@links.b.push(link)
link.linksForEndContaining(previousSegment).push(this)
, @)
previousSegment.links.f.push(@)
@links.b.push(previousSegment)
return newBranches
}
addSegment = (segment, segmentList, qTree) ->
segmentList.push(segment)
qTree.insert(segment.collider.limits())
generate = (seed) ->
debugData = {}
Math.seedrandom(seed)
# NB: this perlin noise library only supports 65536 different seeds
noise.seed(Math.random())
priorityQ = []
# setup first segments in queue
do ->
rootSegment = new Segment({x: 0, y: 0}, {x: config.mapGeneration.HIGHWAY_SEGMENT_LENGTH, y: 0}, 0, {highway: true})
oppositeDirection = segmentFactory.fromExisting(rootSegment)
newEnd =
x: rootSegment.r.start.x - config.mapGeneration.HIGHWAY_SEGMENT_LENGTH
y: oppositeDirection.r.end.y
oppositeDirection.r.setEnd(newEnd)
oppositeDirection.links.b.push(rootSegment)
rootSegment.links.b.push(oppositeDirection)
priorityQ.push(rootSegment)
priorityQ.push(oppositeDirection)
segments = []
qTree = new Quadtree(config.mapGeneration.QUADTREE_PARAMS,
config.mapGeneration.QUADTREE_MAX_OBJECTS, config.mapGeneration.QUADTREE_MAX_LEVELS)
while (priorityQ.length > 0 && segments.length < config.mapGeneration.SEGMENT_COUNT_LIMIT)
# pop smallest r(ti, ri, qi) from Q (i.e., smallest 't')
minT = undefined
minT_i = 0
_.each(priorityQ, (segment, i) ->
if (!minT? || segment.t < minT)
minT = segment.t
minT_i = i
)
minSegment = priorityQ.splice(minT_i, 1)[0]
accepted = localConstraints(minSegment, segments, qTree, debugData)
if (accepted)
if (minSegment.setupBranchLinks?)
minSegment.setupBranchLinks()
addSegment(minSegment, segments, qTree)
_.each(globalGoals.generate(minSegment), (newSegment) ->
newSegment.t = minSegment.t + 1 + newSegment.t
priorityQ.push(newSegment)
)
id = 0
for segment in segments
segment.id = id++
console.log("#{segments.length} segments generated.")
return {
segments: segments
qTree: qTree
heatmap: heatmap
debugData: debugData
}
module.exports = {
Segment: Segment
generate: generate
}
@t-mw
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t-mw commented Dec 14, 2015

The full source for the project can be found here: https://github.com/t-mw/citygen

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