Allow square element to be a rectangle

src/element.py

@@ -3,7 +3,7 @@ import math
 import sys
 
 from point import Point,l_infinity,l_2
-from tools import isint_nonzero,sgn,in_interval
+from tools import isint_nonzero,sgn,in_interval,ceil_grid,floor_grid
 from kivy.graphics import Rectangle,Ellipse,Line
 
 # parent class of all elements
@@ -55,11 +55,17 @@ class Element():
         return element
 
 
-# square elements
+# rectangular element
+# the size of the y component is specified by an aspect ratio: size_x=size, size_y=size*aspect
 class Element_square(Element):
+    def __init__(self,x,y,size,**kwargs):
+        self.pos=Point(x,y)
+        self.size=size
+        self.aspect=kwargs.get("aspect",1.0)
+
     # draw element
     def draw(self,painter):
-        Rectangle(pos=(painter.pos_tocoord_x(self.pos.x-0.5*self.size),painter.pos_tocoord_y(self.pos.y-0.5*self.size)),size=(self.size*painter.base_size,self.size*painter.base_size))
+        Rectangle(pos=(painter.pos_tocoord_x(self.pos.x-0.5*self.size),painter.pos_tocoord_y(self.pos.y-0.5*self.size*self.aspect)),size=(self.size*painter.base_size,self.size*self.aspect*painter.base_size))
 
     # draw boundary
     def stroke(self,painter):
@@ -68,53 +74,55 @@ class Element_square(Element):
         coordy=painter.pos_tocoord_y(square.pos.y)
 
         Line(points=(
-        *(coordx-0.5*self.size*painter.base_size,coordy-0.5*self.size*painter.base_size),
-        *(coordx-0.5*self.size*painter.base_size,coordy+0.5*self.size*painter.base_size),
-        *(coordx+0.5*self.size*painter.base_size,coordy+0.5*self.size*painter.base_size),
-        *(coordx+0.5*self.size*painter.base_size,coordy-0.5*self.size*painter.base_size),
-        *(coordx-0.5*self.size*painter.base_size,coordy-0.5*self.size*painter.base_size)
+        *(coordx-0.5*self.size*painter.base_size,coordy-0.5*self.size*self.aspect*painter.base_size),
+        *(coordx-0.5*self.size*painter.base_size,coordy+0.5*self.size*self.aspect*painter.base_size),
+        *(coordx+0.5*self.size*painter.base_size,coordy+0.5*self.size*self.aspect*painter.base_size),
+        *(coordx+0.5*self.size*painter.base_size,coordy-0.5*self.size*self.aspect*painter.base_size),
+        *(coordx-0.5*self.size*painter.base_size,coordy-0.5*self.size*self.aspect*painter.base_size)
         ))
 
     # check whether an element interacts with square
     # TODO: this only works if element is a square!
     def check_interaction(self,element):
         # allow for error
-        return l_infinity(element.pos-self.pos)<(self.size+element.size)/2-1e-11
+        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
 
     # whether x is in the support of the element
     def in_support(self,x):
-        return l_infinity(self.pos-x)<=1/2
+        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!
     def check_touch(self,element):
         # allow for error
-        if in_interval(l_infinity(element.pos-self.pos),(self.size+element.size)/2-1e-11,(self.size+element.size)/2+1e-11):
+        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):
                 return True
         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!
     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
         # compute intersections with four lines making up square
         if v.x!=0:
             if v.y!=0:
                 intersections=[\
-                Point(self.pos.x+(self.size+element.size)/2,element.pos.y+v.y/v.x*(self.pos.x+(self.size+element.size)/2-element.pos.x)),\
-                Point(self.pos.x-(self.size+element.size)/2,element.pos.y+v.y/v.x*(self.pos.x-(self.size+element.size)/2-element.pos.x)),\
-                Point(element.pos.x+v.x/v.y*(self.pos.y+(self.size+element.size)/2-element.pos.y),self.pos.y+(self.size+element.size)/2),\
-                Point(element.pos.x+v.x/v.y*(self.pos.y-(self.size+element.size)/2-element.pos.y),self.pos.y-(self.size+element.size)/2)\
+                Point(self.pos.x+size_x,element.pos.y+v.y/v.x*(self.pos.x+size_x-element.pos.x)),\
+                Point(self.pos.x-size_x,element.pos.y+v.y/v.x*(self.pos.x-size_x-element.pos.x)),\
+                Point(element.pos.x+v.x/v.y*(self.pos.y+size_y-element.pos.y),self.pos.y+size_y),\
+                Point(element.pos.x+v.x/v.y*(self.pos.y-size_y-element.pos.y),self.pos.y-size_y)\
                 ]
             else:
                 intersections=[\
-                Point(self.pos.x+(self.size+element.size)/2,element.pos.y+v.y/v.x*(self.pos.x+(self.size+element.size)/2-element.pos.x)),\
-                Point(self.pos.x-(self.size+element.size)/2,element.pos.y+v.y/v.x*(self.pos.x-(self.size+element.size)/2-element.pos.x))
+                Point(self.pos.x+size_x,element.pos.y),\
+                Point(self.pos.x-size_x,element.pos.y)
                 ]
         else:
             if v.y!=0:
                 intersections=[\
-                Point(element.pos.x+v.x/v.y*(self.pos.y+(self.size+element.size)/2-element.pos.y),self.pos.y+(self.size+element.size)/2),\
-                Point(element.pos.x+v.x/v.y*(self.pos.y-(self.size+element.size)/2-element.pos.y),self.pos.y-(self.size+element.size)/2)\
+                Point(element.pos.x,self.pos.y+size_y),\
+                Point(element.pos.x,self.pos.y-size_y)\
                 ]
             else:
                 print("error: move_on_line_to_stick called with v=0, please file a bug report with the developer",file=sys.stderr)
@@ -125,13 +133,13 @@ class Element_square(Element):
         dist=math.inf
         for i in range(0,len(intersections)):
             # check that it is on square
-            if abs(intersections[i].x-self.pos.x)<=(self.size+element.size)/2+1e-11 and abs(intersections[i].y-self.pos.y)<=(self.size+element.size)/2+1e-11:
+            if abs(intersections[i].x-self.pos.x)<=size_x+1e-11 and abs(intersections[i].y-self.pos.y)<=size_y+1e-11:
                 if (intersections[i]-element.pos)**2<dist:
                     closest=intersections[i]
                     dist=(intersections[i]-element.pos)**2
 
         if closest==None:
-            print("error: cannot move particle at (",pos.x,",",pos.y,") to the boundary of (",self.pos.x,",",self.pos.y,") in direction (",v.x,",",v.y,")",file=sys.stderr)
+            print("error: cannot move particle at (",element.pos.x,",",element.pos.y,") to the boundary of (",self.pos.x,",",self.pos.y,") in direction (",v.x,",",v.y,")",file=sys.stderr)
             exit(-1)
 
         # return difference to pos
@@ -140,11 +148,13 @@ class Element_square(Element):
     # move along edge of square
     # TODO: this only works if element is a square!
     def move_along(self,delta,element):
+        size_x=(self.size+element.size)/2
+        size_y=(self.size*self.aspect+element.size*element.aspect)/2
         rel=element.pos-self.pos
         # check if the particle is stuck in the x direction
-        if isint_nonzero(rel.x/((self.size+element.size)/2)):
+        if isint_nonzero(rel.x/size_x):
             # check y direction
-            if isint_nonzero(rel.y/((self.size+element.size)/2)):
+            if isint_nonzero(rel.y/size_y):
                 # in corner
                 if sgn(delta.y)==-sgn(rel.y):
                     # stuck in x direction
@@ -157,7 +167,7 @@ class Element_square(Element):
             else:
                 # stuck in x direction
                 return self.move_stuck_x(delta,element)
-        elif isint_nonzero(rel.y/((self.size+element.size)/2)):
+        elif isint_nonzero(rel.y/size_y):
             # stuck in y direction
             return self.move_stuck_y(delta,element)
         # this should never happen
@@ -166,33 +176,35 @@ class Element_square(Element):
             exit(-1)
     # move when stuck in the x direction
     def move_stuck_x(self,delta,element):
+        size_y=(self.size*self.aspect+element.size*element.aspect)/2
         # only move in y direction
         candidate=Point(0,delta.y)
         # do not move past corners
         rel=element.pos.y-self.pos.y
         if delta.y>0:
-            if rel<math.ceil(rel/((self.size+element.size)/2))*((self.size+element.size)/2)-1e-11 and delta.y+rel>math.ceil(rel/((self.size+element.size)/2))*((self.size+element.size)/2)+1e-11 and math.ceil(rel/((self.size+element.size)/2))*((self.size+element.size)/2)!=0:
+            if rel<ceil_grid(rel,size_y)-1e-11 and delta.y+rel>ceil_grid(rel,size_y)+1e-11 and ceil_grid(rel,size_y)!=0:
                 # stick to corner
-                candidate.y=math.ceil(rel/((self.size+element.size)/2))*((self.size+element.size)/2)+self.pos.y-element.pos.y
+                candidate.y=ceil_grid(rel,size_y)+self.pos.y-element.pos.y
         else:
-            if rel>math.floor(rel/((self.size+element.size)/2))*((self.size+element.size)/2)+1e-11 and delta.y+rel<math.floor(rel/((self.size+element.size)/2))*((self.size+element.size)/2)-1e-11 and math.floor(rel/((self.size+element.size)/2))*((self.size+element.size)/2)!=0:
+            if rel>floor_grid(rel,size_y)+1e-11 and delta.y+rel<floor_grid(rel,size_y)-1e-11 and floor_grid(rel,size_y)!=0:
                 # stick to corner
-                candidate.y=math.floor(rel/((self.size+element.size)/2))*((self.size+element.size)/2)+self.pos.y-element.pos.y
+                candidate.y=floor_grid(rel,size_y)+self.pos.y-element.pos.y
         return candidate
     # move when stuck in the y direction
     def move_stuck_y(self,delta,element):
+        size_x=(self.size+element.size)/2
         # onlx move in x direction
         candidate=Point(delta.x,0)
         # do not move past corners
         rel=element.pos.x-self.pos.x
         if delta.x>0:
-            if rel<math.ceil(rel/((self.size+element.size)/2))*((self.size+element.size)/2)-1e-11 and delta.x+rel>math.ceil(rel/((self.size+element.size)/2))*((self.size+element.size)/2)+1e-11 and math.ceil(rel/((self.size+element.size)/2))*((self.size+element.size)/2)!=0:
+            if rel<ceil_grid(rel,size_x)-1e-11 and delta.x+rel>ceil_grid(rel,size_x)+1e-11 and ceil_grid(rel,size_x)!=0:
                 # stick to corner
-                candidate.x=math.ceil(rel/((self.size+element.size)/2))*((self.size+element.size)/2)+self.pos.x-element.pos.x
+                candidate.x=ceil_grid(rel,size_x)+self.pos.x-element.pos.x
         else:
-            if rel>math.floor(rel/((self.size+element.size)/2))*((self.size+element.size)/2)+1e-11 and delta.x+rel<math.floor(rel/((self.size+element.size)/2))*((self.size+element.size)/2)-1e-11 and math.floor(rel/((self.size+element.size)/2))*((self.size+element.size)/2)!=0:
+            if rel>floor_grid(rel,size_x)+1e-11 and delta.x+rel<floor_grid(rel,size_x)-1e-11 and floor_grid(rel,size_x)!=0:
                 # stick to corner
-                candidate.x=math.floor(rel/((self.size+element.size)/2))*((self.size+element.size)/2)+self.pos.x-element.pos.x
+                candidate.x=floor_grid(rel,size_x)+self.pos.x-element.pos.x
         return candidate
 
 

src/painter.py

@@ -215,8 +215,8 @@ class Painter(Widget):
 
             # create new particle
             if touch.button=="right":
-                #new=Cross(touchx,touchy)
-                new=Disk(touchx,touchy)
+                new=Cross(touchx,touchy)
+                #new=Disk(touchx,touchy)
                 # snap to lattice
                 if self.lattice!=None:
                     new.move(self.lattice.nearest_delta(new.elements[0].pos))
@@ -529,7 +529,7 @@ class Painter(Widget):
                 continue
             if particle_type==CROSS_INDEX:
                 candidate=Cross(pos.x,pos.y,color=color)
-            elif particle_type==DISK_INDEX
+            elif particle_type==DISK_INDEX:
                 candidate=Disk(pos.x,pos.y,color=color)
             else:
                 print("warning: ignoring line "+str(i)+" in file '"+file+"': unrecognized particle type: '"+entries[0]+"'",file=sys.stderr)

src/polyomino.py

@@ -75,11 +75,9 @@ class Square(Polyomino):
 class Cross(Polyomino):
     def __init__(self,x,y,**kwargs):
         super(Cross,self).__init__(**kwargs,elements=[\
-        Element_square(x,y,1),\
+        Element_square(x,y,1,aspect=3),\
         Element_square(x+1,y,1),\
-        Element_square(x-1,y,1),\
-        Element_square(x,y+1,1),\
-        Element_square(x,y-1,1)\
+        Element_square(x-1,y,1)\
         ])
 
     # redefine stroke to avoid lines between touching elements

src/tools.py

@@ -1,3 +1,5 @@
+import math
+
 # sign function
 def sgn(x):
     if x>=0:
@@ -20,3 +22,10 @@ def remove_fromlist(a,x):
         a[a.index(x)]=a[len(a)-1]
         a=a[:len(a)-1]
     return a
+
+# snap to a grid: ceiling
+def ceil_grid(x,size):
+    return math.ceil(x/size)*size
+# snap to a grid: floor
+def floor_grid(x,size):
+    return math.floor(x/size)*size