Compute discrete Voronoi cell

src/command_prompt.py

@@ -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:

src/element.py

@@ -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

src/lattice.py

@@ -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
         

src/painter.py

@@ -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):

src/polyomino.py

@@ -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)