Allow square element to be a rectangle

src/element.py

@@ -0,0 +1,258 @@
+## elements that polyominoes are made of
+import math
+import sys
+
+from point import Point,l_infinity,l_2
+from tools import isint_nonzero,sgn,in_interval,ceil_grid,floor_grid
+from kivy.graphics import Rectangle,Ellipse,Line
+
+# parent class of all elements
+class Element():
+    def __init__(self,x,y,size,**kwargs):
+        self.pos=Point(x,y)
+        self.size=size
+
+    # set position
+    def setpos(self,x,y):
+        self.pos.x=x
+        self.pos.y=y
+
+
+    # override in each subclass
+    # draw element
+    def draw(self,painter):
+        return
+
+    # override in each subclass
+    # draw boundary
+    def stroke(self,painter):
+        return
+
+    # override in each subclass
+    # check whether an element interacts with square
+    def check_interaction(self,element):
+        return False
+
+    # override in each subclass
+    # whether x is in the support of the element
+    def in_support(self,x):
+        return False
+
+    # override in each subclass
+    # check whether an element is touching self
+    def check_touch(self,element):
+        return False
+
+    # override in each subclass
+    # find position along a line that comes in contact with the line going through element.pos in direction v
+    def move_on_line_to_stick(self,element,v):
+        return Point(0,0)
+
+    # override in each subclass
+    # move along edge of element
+    # delta is the impossible move that was asked for
+    def move_along(self,delta,element):
+        return element
+
+
+# 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*self.aspect)),size=(self.size*painter.base_size,self.size*self.aspect*painter.base_size))
+
+    # draw boundary
+    def stroke(self,painter):
+        # convert to graphical coordinates
+        coordx=painter.pos_tocoord_x(square.pos.x)
+        coordy=painter.pos_tocoord_y(square.pos.y)
+
+        Line(points=(
+        *(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 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 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(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+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+size_x,element.pos.y),\
+                Point(self.pos.x-size_x,element.pos.y)
+                ]
+        else:
+            if v.y!=0:
+                intersections=[\
+                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)
+                exit(-1)
+
+        # compute closest one, on square
+        closest=None
+        dist=math.inf
+        for i in range(0,len(intersections)):
+            # check that it is on square
+            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 (",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
+        return closest-element.pos
+
+    # 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/size_x):
+            # check y direction
+            if isint_nonzero(rel.y/size_y):
+                # in corner
+                if sgn(delta.y)==-sgn(rel.y):
+                    # stuck in x direction
+                    return self.move_stuck_x(delta,element)
+                elif sgn(delta.x)==-sgn(rel.x):
+                    # stuck in y direction
+                    return self.move_stuck_y(delta,element)
+                # stuck in both directions
+                return element.pos
+            else:
+                # stuck in x direction
+                return self.move_stuck_x(delta,element)
+        elif isint_nonzero(rel.y/size_y):
+            # stuck in y direction
+            return self.move_stuck_y(delta,element)
+        # this should never happen
+        else:
+            print("error: stuck particle has non-integer relative position: (",rel.x,",",rel.y,")",file=sys.stderr)
+            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<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=ceil_grid(rel,size_y)+self.pos.y-element.pos.y
+        else:
+            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=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<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=ceil_grid(rel,size_x)+self.pos.x-element.pos.x
+        else:
+            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=floor_grid(rel,size_x)+self.pos.x-element.pos.x
+        return candidate
+
+
+# circular elements
+# (size is the diameter)
+class Element_circle(Element):
+    # draw element
+    def draw(self,painter):
+        Ellipse(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))
+
+    # draw boundary
+    def stroke(self,painter):
+        Line(circle=(painter.pos_tocoord_x(self.pos.x),painter.pos_tocoord_y(self.pos.y),self.size*0.5*painter.base_size))
+
+    # check whether an element interacts with square
+    # TODO: this only works if element is a circle!
+    def check_interaction(self,element):
+        # allow for error
+        return l_2(element.pos-self.pos)<(self.size+element.size)/2-1e-11
+
+    # whether x is in the support of the element
+    def in_support(self,x):
+        return l_2(self.pos-x)<=1/2
+
+    # check whether an element is touching self
+    # TODO: this only works if element is a circle!
+    def check_touch(self,element):
+        # allow for error
+        if in_interval(l_2(element.pos-self.pos),(self.size+element.size)/2-1e-11,(self.size+element.size)/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 circle!
+    def move_on_line_to_stick(self,element,v):
+        # relative position
+        x=element.pos-self.pos
+        # radius of collision circle
+        R=(element.size+self.size)/2
+
+        # smallest root of t^2 v^2+2x.v t+x^2-R^2
+        t=(-v.dot(x)-math.sqrt(v.dot(x)*v.dot(x)-v.dot(v)*(x.dot(x)-R*R)))/v.dot(v)
+
+        # return difference to pos
+        return v*t
+
+    # move along edge of circle
+    # TODO: this only works if element is a circle!
+    def move_along(self,delta,element):
+        x=element.pos-self.pos+delta
+        return x/l_2(x)*(element.size+self.size)/2+self.pos-element.pos

src/filecheck.py

@@ -1,3 +1,5 @@
+# check that a file is creatable/writable/editable
+
 import os.path
 
 # check that a file can be edited

src/lattice.py

@@ -1,3 +1,5 @@
+# define background lattices
+
 from point import Point
 
 # parent class of all lattices
@@ -24,18 +26,18 @@ class Lattice():
         specs=spec.split(":")
         # check type of lattice
         if specs[0]=="square":
-            return Square_lattice.new_square(specs[1:],spec)
+            return Lattice_square.new_square(specs[1:],spec)
         else:
             return(None,"error: unrecognized lattice type: '"+specs[0]+"'")
 
 
 # square lattice
-class Square_lattice(Lattice):
+class Lattice_square(Lattice):
     def __init__(self,**kwargs):
 
         self.spacing=kwargs.get("spacing",1.)
 
-        super(Square_lattice,self).__init__(**kwargs,type="square")
+        super(Lattice_square,self).__init__(**kwargs,type="square")
 
     # lattice point nearest to point
     def nearest(self,point):
@@ -49,12 +51,12 @@ class Square_lattice(Lattice):
     def new_square(specs,spec):
         # no optional args
         if len(specs)==0:
-            return (Square_lattice(),"")
+            return (Lattice_square(),"")
         if len(specs)>1:
             return (None,"error: '"+spec+"' is not a valid specification for the square lattice: should be 'square[:spacing]'")
         try:
             spacing=float(specs[0])
-            return (Square_lattice(spacing=spacing),"")
+            return (Lattice_square(spacing=spacing),"")
         except:
             return (None,"error: '"+spec+"' is not a valid specification for the square lattice: should be 'square[:spacing]'")
         

src/painter.py

@@ -1,3 +1,5 @@
+# main drawing class
+
 import sys
 import math
 from kivy.uix.widget import Widget
@@ -5,9 +7,7 @@ from kivy.core.window import Window
 from kivy.graphics import Color,Line
 
 from point import Point
-from polyomino import Cross
-from polyomino import Square_element
-from lattice import Square_lattice
+from polyomino import Cross,Disk
 
 from tools import remove_fromlist
 
@@ -44,6 +44,9 @@ class Painter(Widget):
         # modifiers
         self.modifiers=[]
 
+        # base size for all particles
+        self.base_size=50
+
         # init Widget
         super(Painter,self).__init__(**kwargs)
 
@@ -69,20 +72,20 @@ class Painter(Widget):
 
         # snap all existing particles to grid
         for particle in self.particles:
-            delta=self.lattice.nearest_delta(particle.squares[0].pos)
+            delta=self.lattice.nearest_delta(particle.elements[0].pos)
             if not self.check_interaction_any(particle,delta):
                 particle.move(delta)
 
 
     # convert logical coordinates (normalized and centered) to the ones that are plotted
     def pos_tocoord_x(self,x):
-        return self.width/2+x*Square_element.size
+        return self.width/2+x*self.base_size
     def pos_tocoord_y(self,y):
-        return self.height/2+y*Square_element.size
+        return self.height/2+y*self.base_size
     def coord_topos_x(self,x):
-        return (x-self.width/2)/Square_element.size
+        return (x-self.width/2)/self.base_size
     def coord_topos_y(self,y):
-        return (y-self.height/2)/Square_element.size
+        return (y-self.height/2)/self.base_size
         
 
 
@@ -102,7 +105,7 @@ class Painter(Widget):
             # draw grids
             for particle in self.particles:
                 if particle.grid>0:
-                    self.draw_grid(particle.squares[0].pos,particle.grid)
+                    self.draw_grid(particle.elements[0].pos,particle.grid)
 
             for particle in self.particles:
                 particle.draw(self,alpha=0.5)
@@ -177,10 +180,10 @@ class Painter(Widget):
             # zoom
             elif text=="+":
                 # increment by 10%
-                self.set_zoom(Square_element.size/50*1.1)
+                self.set_zoom(self.base_size/50*1.1)
             elif text=="-":
                 # decrease by 10%
-                self.set_zoom(Square_element.size/50*0.9)
+                self.set_zoom(self.base_size/50*0.9)
             elif text=="=":
                 # reset
                 self.set_zoom(1)
@@ -210,12 +213,13 @@ class Painter(Widget):
             touchx=self.coord_topos_x(touch.x)
             touchy=self.coord_topos_y(touch.y)
 
-            # create new cross
+            # create new particle
             if touch.button=="right":
                 new=Cross(touchx,touchy)
+                #new=Disk(touchx,touchy)
                 # snap to lattice
                 if self.lattice!=None:
-                    new.move(self.lattice.nearest_delta(new.squares[0].pos))
+                    new.move(self.lattice.nearest_delta(new.elements[0].pos))
 
                 if not self.check_interaction_any(new,Point(0,0)):
                     # add to list
@@ -236,7 +240,7 @@ class Painter(Widget):
 
                 # record relative position of click with respect to reference
                 if self.undermouse!=None:
-                    self.offset=Point(touchx,touchy)-self.undermouse.squares[0].pos
+                    self.offset=Point(touchx,touchy)-self.undermouse.elements[0].pos
 
                 # no modifiers
                 if self.modifiers==[]:
@@ -289,7 +293,7 @@ class Painter(Widget):
             # only move on left click
             if touch.button=="left" and self.modifiers==[] and self.undermouse!=None:
                 # attempted move determined by the relative position to the relative position of click within self.undermouse
-                delta=self.adjust_move(Point(touchx,touchy)-(self.offset+self.undermouse.squares[0].pos),0)
+                delta=self.adjust_move(Point(touchx,touchy)-(self.offset+self.undermouse.elements[0].pos),0)
 
                 # snap to lattice
                 if self.lattice!=None:
@@ -345,9 +349,15 @@ class Painter(Widget):
     # check whether a candidate particle element with any of the unselected particles
     def check_interaction_unselected_element(self,element,offset):
         for particle in self.unselected:
-            for square in particle.squares:
-                if square.check_interaction(element.pos+offset):
+            for elt in particle.elements:
+                # add offset
+                element.pos+=offset
+                if elt.check_interaction(element):
+                    # reset offset
+                    element.pos-=offset
                     return True
+                # reset offset
+                element.pos-=offset
         return False
 
 
@@ -357,7 +367,7 @@ class Painter(Widget):
         # actual_delta is the smallest (componentwise) of all the computed delta's
         actual_delta=Point(math.inf,math.inf)
         for particle in self.selected:
-            for element in particle.squares:
+            for element in particle.elements:
                 # compute adjustment move due to unselected obstacles
                 adjusted_delta=self.adjust_move_element(delta,element,0)
                 # only keep the smallest delta's (in absolute value)
@@ -383,18 +393,23 @@ class Painter(Widget):
         # whether newpos is acceptable
         accept_newpos=True
         for other in self.unselected:
-            for obstacle in other.squares:
+            for obstacle in other.elements:
                 # move would make element overlap with obstacle
-                if obstacle.check_interaction(element.pos+delta):
+                element.pos+=delta
+                if obstacle.check_interaction(element):
+                    element.pos-=delta
                     accept_newpos=False
                     # check if particle already touches obstacle
-                    if obstacle.check_touch(element.pos):
+                    if obstacle.check_touch(element):
                         # move along obstacle while remaining stuck
-                        newdelta=obstacle.move_along(delta,element.pos)
+                        newdelta=obstacle.move_along(delta,element)
                     else:
-                        newdelta=obstacle.move_on_line_to_stick(element.pos,delta)
+                        newdelta=obstacle.move_on_line_to_stick(element,delta)
                     if not self.check_interaction_unselected_element(element,newdelta):
                         return newdelta
+                else:
+                    # reset offset
+                    element.pos-=delta
         if accept_newpos:
             return delta
         else:
@@ -435,7 +450,9 @@ class Painter(Widget):
         for particle in self.particles:
             if type(particle)==Cross:
                 ff.write("{:d};".format(CROSS_INDEX))
-            ff.write("{:05.2f},{:05.2f};{:3.1f},{:3.1f},{:3.1f}\n".format(particle.squares[0].pos.x,particle.squares[0].pos.y,particle.color[0],particle.color[1],particle.color[2]))
+            elif type(particle)==Disk:
+                ff.write("{:d};".format(DISK_INDEX))
+            ff.write("{:05.2f},{:05.2f};{:3.1f},{:3.1f},{:3.1f}\n".format(particle.elements[0].pos.x,particle.elements[0].pos.y,particle.color[0],particle.color[1],particle.color[2]))
         ff.close()
 
     # read configuration from file
@@ -512,6 +529,8 @@ class Painter(Widget):
                 continue
             if particle_type==CROSS_INDEX:
                 candidate=Cross(pos.x,pos.y,color=color)
+            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)
                 continue
@@ -548,7 +567,7 @@ class Painter(Widget):
         for particle in self.particles:
             if type(particle)==Cross:
                 ff.write("\cross{"+colors.closest_color(particle.color,colors.xcolor_names)+"}")
-            ff.write("{{({:05.2f},{:05.2f})}};\n".format(particle.squares[0].pos.x-self.particles[0].squares[0].pos.x,particle.squares[0].pos.y-self.particles[0].squares[0].pos.y))
+            ff.write("{{({:05.2f},{:05.2f})}};\n".format(particle.elements[0].pos.x-self.particles[0].elements[0].pos.x,particle.elements[0].pos.y-self.particles[0].elements[0].pos.y))
 
         ff.write("\\end{tikzpicture}\n")
         ff.write("\\end{document}\n")
@@ -558,11 +577,12 @@ class Painter(Widget):
 
     # set zoom level
     def set_zoom(self,level):
-        Square_element.size=level*50
+        self.base_size=level*50
         self.draw()
 
 
 # global variables (used like precompiler variables)
 CROSS_INDEX=1
+DISK_INDEX=2
 
 

src/point.py

@@ -1,3 +1,5 @@
+# two-dimensional point structure
+
 import math
 
 # point in two dimensions
@@ -47,3 +49,7 @@ class Point:
 # L infinity norm
 def l_infinity(x):
     return max(abs(x.x),abs(x.y))
+
+# L 2 norm
+def l_2(x):
+    return math.sqrt(x.x*x.x+x.y*x.y)

src/polyomino.py

@@ -1,15 +1,14 @@
-import math
-import sys
-from kivy.graphics import Color,Line,Rectangle
+# a polyomino is a collection of elements, defined in elements.py
+from kivy.graphics import Color,Line
 
-from point import Point,l_infinity
-from tools import isint_nonzero,sgn,in_interval
+from point import l_infinity
+from element import Element_square,Element_circle
 
 # parent class of all polyominos
 class Polyomino():
     def __init__(self,**kwargs):
-        # square elements that make up the polyomino 
-        self.squares=kwargs.get("squares",[])
+        # elements that make up the polyomino 
+        self.elements=kwargs.get("elements",[])
 
         self.color=kwargs.get("color",(0,0,1))
         self.selected=False
@@ -28,212 +27,83 @@ class Polyomino():
             # darken selected
             Color(r/2,g/2,b/2,alpha)
 
-        for square in self.squares:
-            Rectangle(pos=(painter.pos_tocoord_x(square.pos.x-0.5),painter.pos_tocoord_y(square.pos.y-0.5)),size=(square.size,square.size))
+        for element in self.elements:
+            element.draw(painter)
 
         # draw boundary
         self.stroke(painter)
 
     # draw boundary (override for connected polyominos)
     def stroke(self,painter):
-        # convert to graphical coordinates
-        coordx=painter.pos_tocoord_x(square.pos.x)
-        coordy=painter.pos_tocoord_y(square.pos.y)
-
         # white
         Color(1,1,1)
-        for square in self.squares:
-            Line(points=(
-            *(coordx-0.5*square.size,coordy-0.5*square.size),
-            *(coordx-0.5*square.size,coordy+0.5*square.size),
-            *(coordx+0.5*square.size,coordy+0.5*square.size),
-            *(coordx+0.5*square.size,coordy-0.5*square.size),
-            *(coordx-0.5*square.size,coordy-0.5*square.size)
-            ))
+        for element in self.elements:
+            element.stroke(painter)
 
     # move by delta
     def move(self,delta):
-        for square in self.squares:
-            square.pos+=delta
+        for element in self.elements:
+            element.pos+=delta
 
     # whether x is in the support of the polyomino
     def in_support(self,x):
-        for square in self.squares:
-            if l_infinity(square.pos-x)<=1/2:
+        for element in self.elements:
+            if element.in_support(x):
                 return True
         return False
 
     # check whether self interacts with candidate if candidate were moved by offset
     def check_interaction(self,candidate,offset):
-        for square1 in self.squares:
-            for square2 in candidate.squares:
-                if square1.check_interaction(square2.pos+offset):
+        for element1 in self.elements:
+            for element2 in candidate.elements:
+                # add offset
+                element2.pos+=offset
+                if element1.check_interaction(element2):
+                    # reset offset
+                    element2.pos-=offset
                     return True
+                # reset offset
+                element2.pos-=offset
         return False
 
 # square
 class Square(Polyomino):
     def __init__(self,x,y,**kwargs):
-        super(Square,self).__init__(**kwargs,squares=[Square_element(x,y)])
+        super(Square,self).__init__(**kwargs,elements=[Element_square(x,y,size=kwargs.get("size",1.0))])
 
 # cross
 class Cross(Polyomino):
     def __init__(self,x,y,**kwargs):
-        super(Cross,self).__init__(**kwargs,squares=[\
-        Square_element(x,y),\
-        Square_element(x+1,y),\
-        Square_element(x-1,y),\
-        Square_element(x,y+1),\
-        Square_element(x,y-1)\
+        super(Cross,self).__init__(**kwargs,elements=[\
+        Element_square(x,y,1,aspect=3),\
+        Element_square(x+1,y,1),\
+        Element_square(x-1,y,1)\
         ])
 
-    # redefine stroke to avoid lines between touching squares
+    # redefine stroke to avoid lines between touching elements
     def stroke(self,painter):
         # convert to graphical coordinates
-        coordx=painter.pos_tocoord_x(self.squares[0].pos.x)
-        coordy=painter.pos_tocoord_y(self.squares[0].pos.y)
+        coordx=painter.pos_tocoord_x(self.elements[0].pos.x)
+        coordy=painter.pos_tocoord_y(self.elements[0].pos.y)
 
         Color(1,1,1)
         Line(points=(
-        *(coordx-0.5*Square_element.size,coordy-0.5*Square_element.size),
-        *(coordx-0.5*Square_element.size,coordy-1.5*Square_element.size),
-        *(coordx+0.5*Square_element.size,coordy-1.5*Square_element.size),
-        *(coordx+0.5*Square_element.size,coordy-0.5*Square_element.size),
-        *(coordx+1.5*Square_element.size,coordy-0.5*Square_element.size),
-        *(coordx+1.5*Square_element.size,coordy+0.5*Square_element.size),
-        *(coordx+0.5*Square_element.size,coordy+0.5*Square_element.size),
-        *(coordx+0.5*Square_element.size,coordy+1.5*Square_element.size),
-        *(coordx-0.5*Square_element.size,coordy+1.5*Square_element.size),
-        *(coordx-0.5*Square_element.size,coordy+0.5*Square_element.size),
-        *(coordx-1.5*Square_element.size,coordy+0.5*Square_element.size),
-        *(coordx-1.5*Square_element.size,coordy-0.5*Square_element.size),
-        *(coordx-0.5*Square_element.size,coordy-0.5*Square_element.size),
+        *(coordx-0.5*painter.base_size,coordy-0.5*painter.base_size),
+        *(coordx-0.5*painter.base_size,coordy-1.5*painter.base_size),
+        *(coordx+0.5*painter.base_size,coordy-1.5*painter.base_size),
+        *(coordx+0.5*painter.base_size,coordy-0.5*painter.base_size),
+        *(coordx+1.5*painter.base_size,coordy-0.5*painter.base_size),
+        *(coordx+1.5*painter.base_size,coordy+0.5*painter.base_size),
+        *(coordx+0.5*painter.base_size,coordy+0.5*painter.base_size),
+        *(coordx+0.5*painter.base_size,coordy+1.5*painter.base_size),
+        *(coordx-0.5*painter.base_size,coordy+1.5*painter.base_size),
+        *(coordx-0.5*painter.base_size,coordy+0.5*painter.base_size),
+        *(coordx-1.5*painter.base_size,coordy+0.5*painter.base_size),
+        *(coordx-1.5*painter.base_size,coordy-0.5*painter.base_size),
+        *(coordx-0.5*painter.base_size,coordy-0.5*painter.base_size),
         ))
 
-
-
-# square building block of polyominos
-class Square_element():
-    # size
-    size=50
-
+# disk
+class Disk(Polyomino):
     def __init__(self,x,y,**kwargs):
-        self.pos=Point(x,y)
-
-    # set position
-    def setpos(self,x,y):
-        self.pos.x=x
-        self.pos.y=y
-
-
-    # check whether a square at pos interacts with square
-    def check_interaction(self,pos):
-        return l_infinity(pos-self.pos)<1
-
-    # check whether a square at position pos is touching self
-    def check_touch(self,pos):
-        # allow for error
-        if in_interval(l_infinity(pos-self.pos),1-1e-11,1+1e-11):
-                return True
-        return False
-
-    # find position along a line that comes in contact with the line going through pos in direction v
-    def move_on_line_to_stick(self,pos,v):
-        # compute intersections with four lines making up square
-        if v.x!=0:
-            if v.y!=0:
-                intersections=[\
-                Point(self.pos.x+1,pos.y+v.y/v.x*(self.pos.x+1-pos.x)),\
-                Point(self.pos.x-1,pos.y+v.y/v.x*(self.pos.x-1-pos.x)),\
-                Point(pos.x+v.x/v.y*(self.pos.y+1-pos.y),self.pos.y+1),\
-                Point(pos.x+v.x/v.y*(self.pos.y-1-pos.y),self.pos.y-1)\
-                ]
-            else:
-                intersections=[\
-                Point(self.pos.x+1,pos.y+v.y/v.x*(self.pos.x+1-pos.x)),\
-                Point(self.pos.x-1,pos.y+v.y/v.x*(self.pos.x-1-pos.x))
-                ]
-        else:
-            if v.y!=0:
-                intersections=[\
-                Point(pos.x+v.x/v.y*(self.pos.y+1-pos.y),self.pos.y+1),\
-                Point(pos.x+v.x/v.y*(self.pos.y-1-pos.y),self.pos.y-1)\
-                ]
-            else:
-                print("error: move_on_line_to_stick called with v=0, please file a bug report with the developer",file=sys.stderr)
-                exit(-1)
-
-        # compute closest one, on square
-        closest=None
-        dist=math.inf
-        for i in range(0,len(intersections)):
-            # check that it is on square
-            if abs(intersections[i].x-self.pos.x)<=1+1e-11 and abs(intersections[i].y-self.pos.y)<=1+1e-11:
-                if (intersections[i]-pos)**2<dist:
-                    closest=intersections[i]
-                    dist=(intersections[i]-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)
-            exit(-1)
-
-        # return difference to pos
-        return closest-pos
-
-    # move along edge of square
-    def move_along(self,delta,pos):
-        rel=pos-self.pos
-        # check if the particle is stuck in the x direction
-        if isint_nonzero(rel.x):
-            # check y direction
-            if isint_nonzero(rel.y):
-                # in corner
-                if sgn(delta.y)==-sgn(rel.y):
-                    # stuck in x direction
-                    return self.move_stuck_x(delta,pos)
-                elif sgn(delta.x)==-sgn(rel.x):
-                    # stuck in y direction
-                    return self.move_stuck_y(delta,pos)
-                # stuck in both directions
-                return pos
-            else:
-                # stuck in x direction
-                return self.move_stuck_x(delta,pos)
-        elif isint_nonzero(rel.y):
-            # stuck in y direction
-            return self.move_stuck_y(delta,pos)
-        # this should never happen
-        else:
-            print("error: stuck particle has non-integer relative position: (",rel.x,",",rel.y,")",file=sys.stderr)
-            exit(-1)
-    # move when stuck in the x direction
-    def move_stuck_x(self,delta,pos):
-        # only move in y direction
-        candidate=Point(0,delta.y)
-        # do not move past corners
-        rel=pos.y-self.pos.y
-        if delta.y>0:
-            if rel<math.ceil(rel)-1e-11 and delta.y+rel>math.ceil(rel)+1e-11 and math.ceil(rel)!=0:
-                # stick to corner
-                candidate.y=math.ceil(rel)+self.pos.y-pos.y
-        else:
-            if rel>math.floor(rel)+1e-11 and delta.y+rel<math.floor(rel)-1e-11 and math.floor(rel)!=0:
-                # stick to corner
-                candidate.y=math.floor(rel)+self.pos.y-pos.y
-        return candidate
-    # move when stuck in the y direction
-    def move_stuck_y(self,delta,pos):
-        # onlx move in x direction
-        candidate=Point(delta.x,0)
-        # do not move past corners
-        rel=pos.x-self.pos.x
-        if delta.x>0:
-            if rel<math.ceil(rel)-1e-11 and delta.x+rel>math.ceil(rel)+1e-11 and math.ceil(rel)!=0:
-                # stick to corner
-                candidate.x=math.ceil(rel)+self.pos.x-pos.x
-        else:
-            if rel>math.floor(rel)+1e-11 and delta.x+rel<math.floor(rel)-1e-11 and math.floor(rel)!=0:
-                # stick to corner
-                candidate.x=math.floor(rel)+self.pos.x-pos.x
-        return candidate
-
+        super(Disk,self).__init__(**kwargs,elements=[Element_circle(x,y,size=kwargs.get("size",1.0))])

src/status_bar.py

@@ -45,9 +45,9 @@ class Status_bar(Label):
             spaces=int(self.width/self.char_width)-len(self.raw_text)-13
             if spaces>0:
                 if self.app.painter.reference==None:
-                    self.raw_text+=" "*spaces+"({:05.2f},{:05.2f})\n".format(self.app.painter.selected[0].squares[0].pos.x,self.app.painter.selected[0].squares[0].pos.y)
+                    self.raw_text+=" "*spaces+"({:05.2f},{:05.2f})\n".format(self.app.painter.selected[0].elements[0].pos.x,self.app.painter.selected[0].elements[0].pos.y)
                 else:
-                    self.raw_text+=" "*spaces+"({:05.2f},{:05.2f})\n".format(self.app.painter.selected[0].squares[0].pos.x-self.app.painter.reference.squares[0].pos.x,self.app.painter.selected[0].squares[0].pos.y-self.app.painter.reference.squares[0].pos.y)
+                    self.raw_text+=" "*spaces+"({:05.2f},{:05.2f})\n".format(self.app.painter.selected[0].elements[0].pos.x-self.app.painter.reference.elements[0].pos.x,self.app.painter.selected[0].elements[0].pos.y-self.app.painter.reference.elements[0].pos.y)
 
         # do not wrap
         self.text=self.raw_text[:min(len(self.raw_text),int(self.width/self.char_width))]

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