Compute discrete Voronoi cell

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):