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Compute discrete Voronoi cell

This commit is contained in:
Ian Jauslin 2024-02-21 19:12:07 -05:00
parent 0070094b94
commit fd61a4620f
5 changed files with 118 additions and 5 deletions
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16
src/command_prompt.py
View File

@ -345,6 +345,9 @@ class Command_prompt(Label):
elif argv[1]=="grid":
self.run_set_grid(argv)
return
elif argv[1]=="voronoi":
self.run_set_voronoi(argv)
return
elif argv[1]=="zoom":
self.run_set_zoom(argv)
else:
@ -409,6 +412,19 @@ class Command_prompt(Label):
return
self.app.painter.set_grid(mesh)
# toggle Voronoi cells
def run_set_voronoi(self,argv):
if len(argv)==2:
# no argument: set to toggle
self.app.painter.set_voronoi(-1)
elif argv[2]=="on":
self.app.painter.set_voronoi(1)
elif argv[2]=="off":
self.app.painter.set_voronoi(0)
else:
self.message="error: unrecognized argument '"+argv[2]+"' -- usage 'set voronoi [on|off]'"
return
# set zoom level (changes size of elements)
def run_set_zoom(self,argv):
if len(argv)==2:

20
src/element.py
View File

@ -95,8 +95,20 @@ class Element_square(Element):
*(coordx-0.5*self.size*painter.base_size,coordy-0.5*self.size*self.aspect*painter.base_size)
))
# for use with lattices
# list of lattice points covered by square
def lattice_points(self,lattice):
out=[]
dx=math.floor(0.5*self.size/lattice.spacing)
dy=math.floor(0.5*self.size*self.aspect/lattice.spacing)
for i in range(-dx,dx+1):
for j in range(-dy,dy+1):
out.append(Point(self.pos.x+i*lattice.spacing,self.pos.y+j*lattice.spacing))
return out
# check whether an element interacts with square
# TODO: this only works if element is a square!
# TODO: this only works if element is a rectangle!
def check_interaction(self,element):
# allow for error
return max(abs(element.pos.x-self.pos.x)/(self.size+element.size),abs(element.pos.y-self.pos.y)/(self.size*self.aspect+element.size*element.aspect))<1/2-1e-11
@ -106,7 +118,7 @@ class Element_square(Element):
return max(abs(self.pos.x-x.x),abs(self.pos.y-x.y)/self.aspect)<=1/2
# check whether an element is touching self
# TODO: this only works if element is a square!
# TODO: this only works if element is a rectangle!
def check_touch(self,element):
# allow for error
if in_interval(max(abs(element.pos.x-self.pos.x)/(self.size+element.size),abs(element.pos.y-self.pos.y)/(self.size*self.aspect+element.size*element.aspect)),1/2-1e-11,1/2+1e-11):
@ -114,7 +126,7 @@ class Element_square(Element):
return False
# find position along a line that comes in contact with the line going through element.pos in direction v
# TODO: this only works if element is a square!
# TODO: this only works if element is a rectangle!
def move_on_line_to_stick(self,element,v):
size_x=(self.size+element.size)/2
size_y=(self.size*self.aspect+element.size*element.aspect)/2
@ -160,7 +172,7 @@ class Element_square(Element):
return closest-element.pos
# move along edge of square
# TODO: this only works if element is a square!
# TODO: this only works if element is a rectangle!
def move_along(self,delta,element):
size_x=(self.size+element.size)/2
size_y=(self.size*self.aspect+element.size*element.aspect)/2

18
src/lattice.py
View File

@ -73,4 +73,22 @@ class Lattice_square(Lattice):
return (Lattice_square(spacing=spacing),"")
except:
return (None,"error: '"+spec+"' is not a valid specification for the square lattice: should be 'square[:spacing]'")
# distance on the lattice between (x1,x2) and (y1,y2)
def distance(self, x1, x2, y1, y2):
return round((abs(x1-y1)+abs(x2-y2))/self.spacing)
# distance between a lattice site and a particle
def distance_to_particle(self, x1, x2, particle):
mindist=self.distance_to_element(x1, x2, particle.elements[0])
for i in range(1,len(particle.elements)):
mindist=min(self.distance_to_element(x1, x2, particle.elements[i]),mindist)
return mindist
# distance between a lattice site and an element
def distance_to_element(self, x1, x2, element):
pts=element.lattice_points(self)
mindist=self.distance(x1, x2, pts[0].x, pts[0].y)
for i in range(1,len(pts)):
mindist=min(self.distance(x1, x2, pts[i].x, pts[i].y),mindist)
return mindist

66
src/painter.py
View File

@ -18,7 +18,7 @@ import sys
import math
from kivy.uix.widget import Widget
from kivy.core.window import Window
from kivy.graphics import Color,Line
from kivy.graphics import Color,Line,Rectangle
from point import Point
from polyomino import Cross,Disk
@ -127,6 +127,12 @@ class Painter(Widget):
if particle.grid>0:
self.draw_grid(particle.elements[0].pos,particle.grid)
# draw Voronoi cells
if self.lattice!=None:
for particle in self.particles:
if particle.voronoi>0:
self.draw_voronoi(particle)
for particle in self.particles:
particle.draw(self,alpha=0.5)
@ -160,6 +166,53 @@ class Painter(Widget):
Line(points=(0,self.pos_tocoord_y(yy),self.width,self.pos_tocoord_y(yy)))
yy-=mesh
# draw the discrete Voronoi cell of a particle
def draw_voronoi(self,particle):
# only works for lattices
if self.lattice!=None:
pos=particle.elements[0].pos
# loop over all points
xx=pos.x
while self.pos_tocoord_x(xx)<self.width:
yy=pos.y
while self.pos_tocoord_y(yy)<self.height:
if self.is_in_voronoi(xx,yy,particle):
self.draw_voronoi_site(xx,yy,particle.color)
yy+=self.lattice.spacing
yy=pos.y-self.lattice.spacing
while self.pos_tocoord_y(yy)>0:
if self.is_in_voronoi(xx,yy,particle):
self.draw_voronoi_site(xx,yy,particle.color)
yy-=self.lattice.spacing
xx+=self.lattice.spacing
xx=pos.x-self.lattice.spacing
while self.pos_tocoord_x(xx)>0:
yy=pos.y
while self.pos_tocoord_y(yy)<self.height:
if self.is_in_voronoi(xx,yy,particle):
self.draw_voronoi_site(xx,yy,particle.color)
yy+=self.lattice.spacing
yy=pos.y-self.lattice.spacing
while self.pos_tocoord_y(yy)>0:
if self.is_in_voronoi(xx,yy,particle):
self.draw_voronoi_site(xx,yy,particle.color)
yy-=self.lattice.spacing
xx-=self.lattice.spacing
# check whether a site is in the Voronoi cell of a particle
def is_in_voronoi(self,x,y,particle):
d_to_particle=self.lattice.distance_to_particle(x,y,particle)
# TODO: start with a particle that is close to x,y
for q in self.particles:
if q!=particle and self.lattice.distance_to_particle(x,y,q)<d_to_particle:
return False
return True
# draw a site in a Voronoi cell
def draw_voronoi_site(self,x,y,color):
Color(color[0],color[1],color[2],0.25)
#Color(1,0,0,alpha=0.25)
Rectangle(pos=(self.pos_tocoord_x(x-0.5),self.pos_tocoord_y(y-0.5)),size=(self.base_size,self.base_size))
# respond to keyboard
def on_key_down(self, keyboard, keycode, text, modifiers):
@ -465,6 +518,17 @@ class Painter(Widget):
# redraw
self.draw()
# set voronoi for selected particles
def set_voronoi(self, onoff):
for particle in self.selected:
if onoff==0:
particle.voronoi=False
elif onoff==1:
particle.voronoi=True
elif onoff==-1:
particle.voronoi=not particle.voronoi
# redraw
self.draw()
# write configuration to file
def write(self,file):

3
src/polyomino.py
View File

@ -29,6 +29,9 @@ class Polyomino():
# mesh of background grid (no grid for mesh size 0)
self.grid=kwargs.get("grid",0)
# draw Voronoi cell
self.voronoi=kwargs.get("voronoi",False)
# draw function
def draw(self,painter,**kwargs):
alpha=kwargs.get("alpha",1)