"Class of Drawn Ring. Output of Bubble.ringsToDraw()"

def __init__( self, noke, ring, fade= None ):

self.noke = noke

self.ring = ring

@staticmethod

def getDir( key ): # key is pair of Bubbles

return Vector2( key[0].ring.pos, key[1].ring.pos ).unit()

@staticmethod

def getArc( key ): # key is pair of Bubbles

a,b = key[0].ring, key[1].ring

return math.asin( 1.0 * b.r / (a.r + b.r) )

dirs = None # Cache

arcs = None

def __init__( self ):

# Group Topology

self.parent = None # Noke # not Bubble: for Group.buildGeometry()

self.childs = [] # Nokes

self.upper = False # Upper level - first child

self.group = None # Parent Group of Bubble

# Geometry and Correction

self.ring = Ring((0,0),1)

# For building Geometry

self.tight = 0 # Left (Parents) and right (Childs) Tights

self.corr = 0 # Correction of Radius

self.angles = {} # dict {Bubble:angle}

# Eating

self.fading = None # Fading object

def __repr__( self ):

return 'Bubble: %s' % self.ring

def neighbor( self, n ):

"Returns previous or next neighbor (or parent if not); n = -1 or 1"

if self.parent:

nokes = self.parent().childs + [self.parent]

bubbles = list(map( Noke.get, nokes ))

return nokes[ bubbles.index( self ) + n ]

def neighbors( self ):

"Iterates all neighbor Nokes"

if self.childs:

for n in self.childs:

yield n

if self.parent:

yield self.parent

for n in (-1,1):

neighbor = self.neighbor( n )

if neighbor != self.parent:

yield neighbor

#def strongParents( self ):

# "Skips first Parent if Bubble is not on upper level"

# return self.parents[ self.upper^1 :]

def lightCopy( self ):

"Copies main attributes of Bubble"

bubble = Bubble()

bubble.group = self.group

bubble.ring = self.ring.copy()

bubble.fading = self.fading

return bubble

def markUpperChilds( self, mark ):

self.upper = mark

if self.childs:

upper = self.childs[0]

for c in self.childs:

c().markUpperChilds( c == upper )

def detTights( self ):

def arc( noke ):

return Bubble.arcs[ ( self,noke() ) ]

if self.parent:

self.tight += arc( self.neighbor(-1) )

self.tight += arc( self.neighbor( 1) )

if self.childs:

self.tight += arc( self.childs[ 0] )

self.tight += arc( self.childs[-1] )

if not self.upper:

a = self.parent() # Bubbles: Parent

c = self.neighbor(-1)() # Prev Neighbor

ra = c.ring.r + self.ring.r # Radiuses

rb = a.ring.r + c.ring.r

rc = a.ring.r + self.ring.r

# Cosines

ca = 1.0 * ( rb**2 + rc**2 - ra**2 ) / ( 2 * rb * rc )

cc = 1.0 * ( ra**2 + rb**2 - rc**2 ) / ( 2 * ra * rb )

aa = math.acos( ca ) # Angles

ac = math.acos( cc )

ab = math.pi - (aa + ac)

a .tight += aa # Increase Tights

c .tight += ac

self.tight += ab

# Save angle aa for detPosition()

a.angles[ self ] = aa

def detCorrections( self ):

"Dets Correction values. Returns False if Correction is not needed."

if not ( self.parent or self.childs ): # Skip single Bubbles

return False

minChink = math.pi * 0.2 # ?? maybe to Constants

# Set tight as chink

self.tight = math.pi*2 - self.tight

self.tight /= 2

if self.tight < minChink: # Correction needed

self.corr += 2

for n in self.neighbors():

n().corr -= 0.2 # ?? Here may be wrong values, and some Figures may be unbuildable

return True

return False # Correction is not needed

def correct( self ):

"Corrects Radius of Ring."

if self.corr:

self.ring.r *= math.exp( self.corr * 0.06 )

def detPosition( self ):

"Dets Position of Bubble. Calculates initial values of Chinks."

if self.upper:

if not self.parent: # Root of Group

self.ring.pos = Vector2((0,0))

return

else:

parent = self.parent() # Parent Bubble

if not parent.parent:

dir = Vector2((1,0)) # Default direction

else:

parent1 = parent.neighbor( -1 )()

a = parent.tight + Bubble.arcs[(parent,self)] + Bubble.arcs[(parent,parent1)] - math.pi

dir = Bubble.dirs[(parent1,parent)]

dir = dir.rotate( Vector2( angle= -a ) ) # Det direction

else:

parent = self.parent()

prev = self.neighbor(-1)()

a = parent.angles[ self ]

dir = Bubble.dirs[(parent,prev)]

dir = dir.rotate( Vector2( angle= -a ) ) # Det direction

Bubble.dirs[(parent,self)] = dir

self.ring.pos = parent.ring.pos + dir * (parent.ring.r + self.ring.r)

def transform( self ):

"""

Returns transformation Matrix of Bubble,

includes transformation Matrix of Group if is.

"""

# Default transformation is Unit

# (Variable or Lambda inside another Lambda)

matrix = TransformMatrix()

matrix.unit()

# Group reference may not exist

# (Variable or Lambda inside fading Let-Bound Variable ??)

if self.group:

matrix *= self.group.transformMatrix

if self.ring:

matrix *= TransformMatrix( ring= self.ring )

def __init__( self ):

self.rootnoke = None

# Bounding Ring

self.boundingRing = None

self.boundingMatrix = None # Unit-Ring -> Bounding Ring

self.transformMatrix = None # Unit-Ring <- Bounding Ring

def bubbles( self, noke= None ): # ?? move to Bubble

"""

Iterates Nokes of Bubbles of Group

from root (reverse of order to draw)

#in strange Order (deeply, elder Parents before)

"""

noke = noke or self.rootnoke

yield noke

for p in noke().childs:

for n in self.bubbles( p ):

yield n

#yield noke

#for p in noke().strongParents():

# for n in self.bubbles( p ):

# yield n

#def bubblesDraw( self, bubble= None ):

# "Iterates Bubbles of Group in order of drawing"

# bubble = bubble or self.root

# yield bubble

# parents = bubble.strongParents()

# for p in parents[::-1]:

# for b in self.bubblesDraw( p ):

# yield b

@staticmethod

def getBounding( bubbles ):

"Returns Bounding Ring of Bubbles in Group"

center = Vector2((0,0))

ws = 0

for b in bubbles:

weight = b.ring.r ** 2

center += b.ring.pos * weight

ws += 1.0 * weight

center /= ws

radius = max([ Vector2( center, b.ring.pos ).length() + b.ring.r \

for b in bubbles ])

return Ring( center, radius )

def resetBoundingRing( self ):

"Resets Bounding Ring of Bubbles in Group"

bubbles = tuple( map( Noke.get, self.bubbles() ) )

self.boundingRing = Group.getBounding( bubbles )

def resetBoundingMatrix( self ):

"Resets Bounding Matrix of Bubbles in Group"

self.boundingMatrix = TransformMatrix( ring=self.boundingRing ) # Unit -> Bounding Ring

self.transformMatrix = self.boundingMatrix.inverse()

def balanceGroup( self ):

sum = Vector2((0,0))

for b in self.bubbles():

bubble = b()

for c in bubble.childs:

child = c()

sum += Bubble.dirs[ (bubble,child) ] * child.ring.r # Let it depend on radius of child

balance = sum.unit().conjugate()

for b in self.bubbles():

bubble = b()

bubble.ring.pos = bubble.ring.pos.rotate( balance )

drawing = {} # Feedback from Manipulator at drawing

# Geometry Constants

lambdaCoef = 1.22 # Constriction of Bubble by Abstraction

expandCoef = 1.07 # Expand all Rings for intersection of Bubbles (?? maybe move to Manipulator)

holeLens = 1.0

groupCoef = 0.8 # 0..1 Expand Bubble according Group inside

lambdaMatrix = TransformMatrix()

lambdaMatrix.setTranspose( 0,0, lambdaCoef )

isFigure = True

def __init__( self, expression ):

FieldItem.__init__( self )

# Parse Expression if needed

if type( expression ) is str:

expression = parse( expression )

debug( 2, 'init Figure', expression )

self.expression = expression.withRoot()

# History of Expression

self.history = history.History()

# Colorspace

self.detColorSpace()

# Size of Figure

self.sizeRing = Ring((0,0),1.0) # Ring for setting size of Figure (used in morphing)

self.refreshTransform()

self.groups = []

self.buildGroups()

self.buildGeometry()

self.history.step( self.expression.copy() )

# Eating Act

self.eating = None

def copy( self ):

copy = Figure( self.expression.copy().expr )

copy.position = self.position.copy()

copy.refreshTransform()

return copy

def detColorSpace( self ):

self.colorspace = color.ColorSpace( self.expression.expr )

def refreshTransform( self ):

self.transform = self.position * TransformMatrix( ring= self.sizeRing )

def root( self ):

"Root Noke of Figure"

return Noke( self.expression )['expr']

def detGroups( self, noke, childs, group= None ):

"Returns rootnoke of Group"

if APPL == noke.node.type:

debug('build','found APPL',noke,group)

if not group:

group = Group() # Create Group

self.groups.append( group )

child = self.detGroups( noke['arg' ].through(), [], group )

return self.detGroups( noke['func'].through(), [child]+childs, group )

else: # ABS or VAR

if group: # Bubble not needed if single

bubble = Bubble()

bubble.childs = copy.copy( childs )

bubble.group = group # Save Parent Group of Bubble ?? needed

noke.set( bubble )

debug('build','create Bubble',bubble,noke)

group.rootnoke = noke # rootnoke is overwritting (last func stays)

if ABS == noke.node.type:

self.detGroups( noke['expr'].through(), [] ) # Step inside

return noke # returns Noke

def buildGroups( self ):

# Det Groups, and Bubbles with 'childs' attribute

self.groups = [] # Nokes

self.detGroups( self.root().through(), [] )

debug('build','buildGroups groups:',self.groups)

for group in self.groups:

# Mark upper level of Bubbles (before bubbles() Iteration)

group.rootnoke().markUpperChilds( True )

# Det parents of Bubbles

for b in group.bubbles():

for n in b().childs:

n().parent = b

def buildGroupGeometry( self, group ):

"Det Configuration iteratively"

nokes = list( group.bubbles() )

bubbles = list(map( Noke.get, nokes ))

debug('build','buildGroupGeometry. nokes:',nokes)

# Det initial Radiuses of Bubbles

for b,n in zip( bubbles, nokes ):

b.ring.r = self.getRadius( n ) # Recursive call

# Iteratively det Radiuses (and angles) of Bubbles

for retries in range( 50,0,-1 ):

# Reset

Bubble.arcs.reset() # Reset Arcs Cache

for b in bubbles: # Reset Tights and Corrections

b.tight = 0

b.corr = 0

# Det Tights

for b in bubbles:

Bubble.detTights(b)

# Det Corrections

if not any( list(map( Bubble.detCorrections, bubbles )) ):

debug( 'build', "ok" )

break

debug( 'build', "retries", retries )

# Correct Radiuses of Bubbles

for b in bubbles:

Bubble.correct(b)

# Det positions of Bubbles

Bubble.dirs.reset() # Reset Dirs Cache

for b in bubbles:

Bubble.detPosition(b)

# Expand Radiuses for overlapping

for b in bubbles:

b.ring.r *= Figure.expandCoef

# Balance Group

group.balanceGroup()

# Set Bounding Ring and Matrix

group.resetBoundingRing()

group.resetBoundingMatrix()

def getRadius( self, noke ):

"""

Calculates Radius of (Sub)Figure

according to outside Lambdas and

building geometry of Group inside

"""

# Expand according to count of Lambdas

lambdas = 0

while ABS == noke.node.type:

lambdas += 1

noke = noke['expr'].through() # There must be no old Bubbles (clean Figure before!)

radius = Figure.lambdaCoef ** lambdas # Now radius=1.0 if no Lambdas

# Expand if Group inside

if APPL == noke.node.type:

group = noke.group()

self.buildGroupGeometry( group ) # Recursive call

radius *= group.boundingRing.r ** Figure.groupCoef

#debug('build','radius for',noke,radius)

return radius

def coordinateGroup( self, noke, dir ):

"dir is Matrix of Direction; noke is APPL-Noke"

group = noke.group()

# Co-ordinate inside Groups if are

for noke in group.bubbles():

bubble = noke()

bubble.ring = bubble.ring.transform( dir )

# Skip Lambdas

noke = noke.skipLambdas()

if APPL == noke.node.type: # Inside co-ordination needed

if not bubble.parent: # The same as parent group

dir1 = dir

else:

parent = bubble.parent()

dir1 = TransformMatrix()

dir1.setRotate( Bubble.getDir( (parent,bubble) ) )

self.coordinateGroup( noke, dir1 )

# Rotate Bounding Ring

group.boundingRing = group.boundingRing.transform( dir )

#group.resetBoundingRing()

group.resetBoundingMatrix()

def buildGeometry( self ):

noke = self.root().through()

# Build whole inside geometry

radius = self.getRadius( noke )

self.sizeRing.r = radius

self.refreshTransform()

# Co-ordinate all groups

# Skip Lambdas

noke = noke.skipLambdas()

if APPL == noke.node.type: # Co-ordination needed

dir = TransformMatrix()

dir.setRotate( Vector2( (1,0) ) )

self.coordinateGroup( noke, dir )

debug( 'build', "Geometry builded", self )

def clean( self ):

"Deletes Bubbles from Nokes"

for node in self.expression.allNodes():

node.fission = {}

def ringsToDraw( self, matrix, noke= None ): # ?? move to Noke class

noke = noke or self.root()

#debug('draw','ringsToDraw: draw',noke)

yielded = False

nokes = ()

type = noke.node.type

if VAR == type:

if noke.node.letbound():

# Check Fading Bubble

bubble = noke()

if bubble and bubble.fading:

# Do not change 'matrix'

matrix1 = matrix * bubble.transform()

yield Drawn( noke, Ring.unit.transform( matrix1 ), bubble.fading.fade )

yielded = True

nokes = noke['ref']['be'], # Here must be ['ref'], not .ref()

else: # Draw Bubble of Variable

bubble = noke()

if bubble:

matrix *= bubble.transform()

yield Drawn( noke, Ring.unit.transform( matrix ) )

return # Nothing to draw inside

elif ABS == type: # Draw Bubble of Lambda

bubble = noke()

if bubble:

matrix *= bubble.transform()

yield Drawn( noke, Ring.unit.transform( matrix ) )

yielded = True

matrix *= Figure.lambdaMatrix.inverse()

# Go inside Abstraction

nokes = noke['expr'],

elif LET == type:

# Check Fading Bubble

bubble = noke()

if bubble and bubble.fading:

# Do not change 'matrix'

yield Drawn( noke, bubble.ring.transform( matrix * bubble.group.transformMatrix ), bubble.fading.fade )

yielded = True

#debug( 'draw', 'drawn LET:', noke, bubble )

nokes = noke['expr'],

elif APPL == type:

nokes = noke['arg'], noke['func']

# Feedback from Manipulator

if yielded:

if not Figure.drawing['done']:

return # Skip other Bubbles inside (too small or out of view)

# Draw Bubbles inside

for noke in nokes:

for d in self.ringsToDraw( matrix, noke ):

yield d

def pick( self, matrix, cursor, noke= None ):

noke = noke and noke.through() or self.root().through()

type = noke.node.type

if APPL == type:

nokes = noke['arg'], noke['func']

else: # VAR or ABS

bubble = noke()

if bubble: # Bubble inside Group

matrix = matrix * bubble.transform() # create new matrix

if not Ring.unit.transform( matrix ).pick( cursor ):

return

yield noke # ABS or VAR

if VAR == type:

return

matrix = matrix * Figure.lambdaMatrix.inversion

nokes = noke['expr'],

# Pick Bubbles of Group or inside Lambda

for noke in nokes:

for n in self.pick( matrix, cursor, noke ):