Fix write: color

README.md

@@ -9,10 +9,17 @@ particles overlap.
 
 Run with
 ```bash
-  ./src/jam [configuration_file]
+  ./src/jam [configuration_file] [-L lattice]
 ```
-where `[configuration_file]` is an optional argument that specifies a file with
-a list of particle positions that will be loaded on initial execution.
+
+* `[configuration_file]` is an optional argument that specifies a file with
+    a list of particle positions that will be loaded on initial execution.
+
+* `[-L lattice]` is an optional argument that specifies a background grid that
+  constrains the position of the particles. So far, the `lattice` argument must
+  be `square` for the square lattice, or, to specify the unit length of the
+  lattice: `square:<unit_length>`.
+  
 
 
 # Dependencies
@@ -59,11 +66,8 @@ Commands can be executed by typing `:` (similarly to vim).
 
 # Current developments
 
-So far, Jam only supports cross-shaped particles, but work is in progress to
-support arbitrary shapes consisting of rectangles, circle arcs and triangles
-(check out the `dev` branch to follow the progress).
-
-Support for lattice configurations is also ongoing.
+So far, Jam supports particles made of combinations of rectangles, but there is
+no infrastructure to set the shape of the particle at runtime.
 
 
 # License

TeX/jam.sty

@@ -28,3 +28,21 @@
   \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
   \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0);
 }
+
+% 3-staircase (color #1, position #2)
+\def\staircase#1#2{
+  \fill[color=#1]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
+  \draw[color=black]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
+}
+
+% disk (color #1, position #2)
+\def\disk#1#2{
+  \fill[color=#1]#2circle(2.5);
+  \draw[color=black]#2circle(2.5);
+}
+
+% square (color #1, position #2)
+\def\square#1#2{
+  \fill[color=#1]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
+  \draw[color=black]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle;
+}

src/command_prompt.py

@@ -20,6 +20,7 @@ import os.path
 
 import filecheck
 import colors
+from polyomino import Cross,Disk,Staircase,Square2
 
 class Command_prompt(Label):
     
@@ -338,9 +339,15 @@ class Command_prompt(Label):
         if argv[1]=="color":
             self.run_set_color(argv)
             return
+        elif argv[1]=="shape":
+            self.run_set_shape(argv)
+            return
         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:
@@ -350,7 +357,7 @@ class Command_prompt(Label):
     # set color
     def run_set_color(self,argv):
         if len(argv)<3:
-            self.message="error: 'set color' command was run with without anargument -- usage: 'set color <color_descriptor>'"
+            self.message="error: 'set color' command was run with without an argument -- usage: 'set color <color_descriptor>'"
             return
         # find color name in list
         for color in colors.xcolor_names:
@@ -372,6 +379,23 @@ class Command_prompt(Label):
             return
         self.app.painter.set_color(color)
 
+    # set particle shape
+    def run_set_shape(self,argv):
+        if len(argv)<3:
+            self.message="error: 'set shape' command was run with without an argument -- usage: 'set shape <shape_descriptor>'"
+            return
+        elif argv[2]=="cross":
+            self.app.painter.shape=Cross
+        elif argv[2]=="disk":
+            self.app.painter.shape=Disk
+        elif argv[2]=="staircase":
+            self.app.painter.shape=Staircase
+        elif argv[2]=="2square":
+            self.app.painter.shape=Square2
+        else:
+            self.message="error: unrecognized shape '"+argv[2]+"'; supported shapes are cross|disk"
+            return
+
     # toggle grid
     def run_set_grid(self,argv):
         if len(argv)==2:
@@ -392,6 +416,19 @@ 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

@@ -0,0 +1,297 @@
+# Copyright 2021-2023 Ian Jauslin
+# 
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+# 
+#     http://www.apache.org/licenses/LICENSE-2.0
+# 
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+## 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)
+        ))
+
+    # 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 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
+
+    # 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 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):
+                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 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
+        # 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 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
+        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
+
+    # 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)
+        for i in range(-dx,dx+1):
+            for j in range(-dx,dx+1):
+                if lattice.spacing*lattice.spacing*(i*i+j*j)<=self.size*self.size/4:
+                    out.append(Point(self.pos.x+i*lattice.spacing,self.pos.y+j*lattice.spacing))
+        return out
+
+

src/filecheck.py

@@ -12,6 +12,8 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+# check that a file is creatable/writable/editable
+
 import os.path
 
 # check that a file can be edited

src/jam

@@ -14,18 +14,119 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+import sys
+import os.path,os
+import filecheck
+from lattice import Lattice
+
+## read cli before loading kivy, in case there are errors
+
+# read cli
+openfile=""
+lattice=""
+def read_cli():
+    global openfile
+    global lattice
+
+    # init flag
+    flag=""
+
+    # loop over arguments
+    for arg in sys.argv[1:]:
+        # option flag
+        if arg[0]=='-':
+            # loop over options
+            for c in arg[1:]:
+                # lattice
+                if c=='L':
+                    flag="lattice"
+                else:
+                    print("error: unrecognized option '"+c+"'\n", file=sys.stderr)
+                    exit(-1)
+
+
+        else:
+            # read lattice argument
+            if flag=="lattice":
+                # test the specification
+                (obj,message)=Lattice.new(arg)
+                if obj==None:
+                    print(message,file=sys.stderr)
+                    exit(-1)
+                lattice=arg
+                # reset flag
+                flag=""
+
+            # no flags
+            else:
+                openfile=arg
+                (ret,message)=filecheck.check_edit(openfile)
+                if ret<0:
+                    print(message,file=sys.stderr)
+                    exit(-1)
+                preread_conf(openfile)
+
+# read command line arguments from configuration file
+def preread_conf(file):
+    global lattice
+    try:
+        ff=open(file,"r")
+    except:
+        return
+
+    # counter
+    i=0
+    try:
+        lines=ff.readlines()
+    except:
+        print("error: could not read the contents of file '"+file+"'", file=sys.stderr)
+        exit(-1)
+
+    for line in lines:
+        i+=1
+        # remove newline
+        line=line[:len(line)-1]
+        # ignore comments
+        if '#' in line:
+            line=line[:line.find('#')]
+        # ignore empty lines
+        if len(line)==0:
+            continue
+
+        # read options
+        if line[0]=='%':
+            # ignore empty line
+            if len(line)==1:
+                continue
+            [key,val]=line[1:].split('=',1)
+            if key=="lattice":
+                # test the specification
+                (obj,message)=Lattice.new(val)
+                if obj==None:
+                    print("error: line "+str(i)+" in file '"+file+"': "+message,file=sys.stderr)
+                    exit(-1)
+                lattice=val
+
+    ff.close()
+
+
+# read cli
+read_cli()
+
+
+## import kivy
+
+# disable kivy argument parser
+os.environ["KIVY_NO_ARGS"] = "1"
 
 from kivy.app import App
 from kivy.uix.widget import Widget
 from kivy.uix.boxlayout import BoxLayout
 from kivy.config import Config
-import sys
-import os.path
 
 from painter import Painter
 from status_bar import Status_bar
 from command_prompt import Command_prompt
-import filecheck
 
 # App class
 class Jam_app(App):
@@ -36,6 +137,9 @@ class Jam_app(App):
         # the file open for editing
         self.openfile=kwargs.get("openfile","")
 
+        # the lattice open for editing
+        self.lattice=kwargs.get("lattice","")
+
         # readonly mode
         self.readonly=False
 
@@ -63,24 +167,20 @@ class Jam_app(App):
             # set readonly mode
             self.readonly=not os.access(self.openfile,os.W_OK)
 
+        # load lattice
+        if self.lattice!="":
+            (obj,message)=Lattice.new(self.lattice)
+            self.painter.set_lattice(obj)
+
         return layout
 
 
+
 # disable red circles on right click
 Config.set('input', 'mouse', 'mouse,disable_multitouch')
 # do not exit on escape
 Config.set('kivy', 'exit_on_escape', 0)
 
-# read cli
-openfile=""
-if len(sys.argv)==2:
-    openfile=sys.argv[1]
-    # check file
-    (ret,message)=filecheck.check_edit(openfile)
-    if ret<0:
-        print(message,file=sys.stderr)
-        exit(-1)
-
 # run
 if __name__ == '__main__':
-    Jam_app(openfile=openfile).run()
+    Jam_app(openfile=openfile,lattice=lattice).run()

src/lattice.py

@@ -0,0 +1,94 @@
+# Copyright 2021-2023 Ian Jauslin
+# 
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+# 
+#     http://www.apache.org/licenses/LICENSE-2.0
+# 
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# define background lattices
+
+from point import Point
+
+# parent class of all lattices
+class Lattice():
+    def __init__(self,**kwargs):
+        self.type=kwargs.get("type","")
+
+    # lattice point nearest to point
+    # overwrite in subclasses
+    def nearest(self,point):
+        return point
+
+    # delta to nearest point
+    def nearest_delta(self,point):
+        return self.nearest(point)-point
+
+    # draw lattice
+    # overwrite in subclasses
+    def draw(self,painter):
+        return
+
+    # return the lattice according to a specification
+    def new(spec):
+        specs=spec.split(":")
+        # check type of lattice
+        if specs[0]=="square":
+            return Lattice_square.new_square(specs[1:],spec)
+        else:
+            return(None,"error: unrecognized lattice type: '"+specs[0]+"'")
+
+
+# square lattice
+class Lattice_square(Lattice):
+    def __init__(self,**kwargs):
+
+        self.spacing=kwargs.get("spacing",1.)
+
+        super(Lattice_square,self).__init__(**kwargs,type="square")
+
+    # lattice point nearest to point
+    def nearest(self,point):
+        return Point(round(point.x/self.spacing)*self.spacing,round(point.y/self.spacing)*self.spacing)
+
+    # draw
+    def draw(self,painter):
+        painter.draw_grid(Point(self.spacing/2,self.spacing/2),self.spacing)
+
+    # return the lattice according to a specification
+    def new_square(specs,spec):
+        # no optional args
+        if len(specs)==0:
+            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 (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

@@ -12,15 +12,16 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+# main drawing class
+
 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
-from polyomino import Square_element
+from polyomino import Cross,Disk,Staircase,Square2
 
 from tools import remove_fromlist
 
@@ -34,6 +35,15 @@ class Painter(Widget):
         # list of particles
         self.particles=[]
 
+        # shape of particle to add next
+        self.shape=Cross
+
+        # color of particle to add next
+        self.color=(0,0,1)
+
+        # underlying lattice
+        self.lattice=None
+
         # particle under mouse
         self.undermouse=None
 
@@ -54,6 +64,9 @@ class Painter(Widget):
         # modifiers
         self.modifiers=[]
 
+        # base size for all particles
+        self.base_size=50
+
         # init Widget
         super(Painter,self).__init__(**kwargs)
 
@@ -61,21 +74,38 @@ class Painter(Widget):
         self.keyboard = Window.request_keyboard(None,self,"text")
         self.keyboard.bind(on_key_down=self.on_key_down,on_key_up=self.on_key_up,on_textinput=self.on_textinput)
 
+        # redraw on resize
+        self.bind(size=lambda obj,value: self.draw())
+
     
     def reset(self):
         self.particles=[]
         self.undermouse=None
         self.draw()
 
+    # set lattice
+    def set_lattice(self,lattice):
+        self.lattice=lattice
+
+        # draw
+        self.draw()
+
+        # snap all existing particles to grid
+        for particle in self.particles:
+            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
         
 
 
@@ -88,10 +118,20 @@ class Painter(Widget):
             for particle in self.particles:
                 particle.draw(self)
 
+            # draw lattice
+            if self.lattice!=None:
+                self.lattice.draw(self)
+
             # 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)
+
+            # 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)
@@ -101,17 +141,79 @@ class Painter(Widget):
         # height offset due to status bar and command prompt
         height_offset=self.app.status_bar.height+self.app.command_prompt.height
         # vertical lines
-        # offest wrt 0
-        offset=(pos.x-0.5)%mesh
-        for i in range(math.floor((self.width/Square_element.size-offset)/mesh)+1):
+        # lines right of pos
+        xx=pos.x+mesh/2
+        while self.pos_tocoord_x(xx)<self.width:
             Color(1,1,1)
-            Line(points=((i*mesh+offset)*Square_element.size,height_offset,(i*mesh+offset)*Square_element.size,self.height+height_offset))
-        # horizontal lines
-        # offset wrt 0
-        offset=(pos.y-0.5)%1-height_offset/Square_element.size
-        for i in range(math.floor((self.height/Square_element.size-offset)/mesh)+1):
+            Line(points=(self.pos_tocoord_x(xx),height_offset,self.pos_tocoord_x(xx),self.height+height_offset))
+            xx+=mesh
+        # lines left of pos
+        xx=pos.x-mesh/2
+        while self.pos_tocoord_x(xx)>0:
             Color(1,1,1)
-            Line(points=(0,(i*mesh+offset)*Square_element.size+height_offset,self.width,(i*mesh+offset)*Square_element.size+height_offset))
+            Line(points=(self.pos_tocoord_x(xx),height_offset,self.pos_tocoord_x(xx),self.height+height_offset))
+            xx-=mesh
+        # lines above pos
+        yy=pos.y+mesh/2
+        while self.pos_tocoord_y(yy)<self.height:
+            Color(1,1,1)
+            Line(points=(0,self.pos_tocoord_y(yy),self.width,self.pos_tocoord_y(yy)))
+            yy+=mesh
+        # lines below pos
+        yy=pos.y-mesh/2
+        while self.pos_tocoord_y(yy)>0:
+            Color(1,1,1)
+            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:
+                    self.draw_voronoi_site(xx,yy,particle.color,self.is_in_voronoi(xx,yy,particle))
+                    yy+=self.lattice.spacing
+                yy=pos.y-self.lattice.spacing
+                while self.pos_tocoord_y(yy)>0:
+                    self.draw_voronoi_site(xx,yy,particle.color,self.is_in_voronoi(xx,yy,particle))
+                    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:
+                    self.draw_voronoi_site(xx,yy,particle.color,self.is_in_voronoi(xx,yy,particle))
+                    yy+=self.lattice.spacing
+                yy=pos.y-self.lattice.spacing
+                while self.pos_tocoord_y(yy)>0:
+                    self.draw_voronoi_site(xx,yy,particle.color,self.is_in_voronoi(xx,yy,particle))
+                    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)
+        # count how many are in voronoi cell
+        count=1
+        # TODO: start  with a particle that is close to x,y
+        for q in self.particles:
+            dd=self.lattice.distance_to_particle(x,y,q)
+            if q!=particle and dd<d_to_particle:
+                return 0
+            if dd==d_to_particle:
+                count+=1
+        return count
+    # draw a site in a Voronoi cell
+    def draw_voronoi_site(self,x,y,color,count):
+        if count==0:
+            return
+        Color(color[0],color[1],color[2],1-count*0.1)
+        Rectangle(pos=(self.pos_tocoord_x(x-0.5*self.lattice.spacing),self.pos_tocoord_y(y-0.5*self.lattice.spacing)),size=(self.base_size*self.lattice.spacing,self.base_size*self.lattice.spacing))
+
 
 
     # respond to keyboard
@@ -153,10 +255,10 @@ 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)
@@ -186,9 +288,13 @@ 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=self.shape(touchx,touchy,color=self.color)
+                # snap to lattice
+                if self.lattice!=None:
+                    new.move(self.lattice.nearest_delta(new.elements[0].pos))
+
                 if not self.check_interaction_any(new,Point(0,0)):
                     # add to list
                     self.particles.append(new)
@@ -208,7 +314,10 @@ 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
+                    # snap to lattice
+                    if self.lattice!=None:
+                        self.offset=self.lattice.nearest(self.offset)
 
                 # no modifiers
                 if self.modifiers==[]:
@@ -251,18 +360,34 @@ class Painter(Widget):
 
     # respond to drag
     def on_touch_move(self,touch):
-        # convert to logical
-        touchx=self.coord_topos_x(touch.x)
-        touchy=self.coord_topos_y(touch.y)
 
         # only respond to touch in drawing area
         if self.collide_point(*touch.pos):
+            # convert to logical
+            touchc=Point(self.coord_topos_x(touch.x),self.coord_topos_y(touch.y))
+
+            # snap to lattice
+            if self.lattice!=None:
+                touchc=self.lattice.nearest(touchc)
+
             # 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)
-                for particle in self.selected:
-                    particle.move(delta)
+                delta=self.adjust_move(touchc-(self.offset+self.undermouse.elements[0].pos),0)
+
+
+                # snap to lattice
+                if self.lattice!=None:
+                    delta=self.lattice.nearest(delta)
+                    # check that the move is possible (which is not guaranteed after snapping to lattice)
+                    if not self.check_interaction_unselected_list(self.selected,delta):
+                        for particle in self.selected:
+                            particle.move(delta)
+
+                # no lattice, move is guaranteed to be acceptable
+                else:
+                    for particle in self.selected:
+                        particle.move(delta)
 
                 # redraw
                 self.draw()
@@ -305,9 +430,15 @@ 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
 
 
@@ -317,7 +448,7 @@ 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)
@@ -343,18 +474,23 @@ 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:
@@ -369,6 +505,9 @@ class Painter(Widget):
 
     # set color of selected particles
     def set_color(self,color):
+        # set color for next particles
+        self.color=color
+        # set color of selected particles
         for particle in self.selected:
             particle.color=color
         # redraw
@@ -388,14 +527,46 @@ 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):
         ff=open(file,"w")
+        # save state (particle shape, zoom, lattice)
+        if self.shape==Cross:
+            ff.write("%shape=cross\n")
+        elif self.shape==Disk:
+            ff.write("%shape=disk\n")
+        elif self.shape==Staircase:
+            ff.write("%shape=staircase\n")
+        elif self.shape==Square2:
+            ff.write("%shape=2square\n")
+        else:
+            print("bug: unrecognized shape in write: '"+str(self.shape)+"'")
+        ff.write("%zoom={:1.1f}\n".format(self.base_size/50))
+        ff.write("%color={:1.1f},{:1.1f},{:1.1f}\n".format(self.color[0],self.color[1],self.color[2]))
+        if self.lattice != None:
+            ff.write("%lattice="+self.lattice.type+':'+str(self.lattice.spacing)+"\n")
         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))
+            elif type(particle)==Staircase:
+                ff.write("{:d};".format(STAIRCASE_INDEX))
+            elif type(particle)==Square2:
+                ff.write("{:d};".format(SQUARE2_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
@@ -429,12 +600,35 @@ class Painter(Widget):
             if len(line)==0:
                 continue
 
+            # read options
+            if line[0]=='%':
+                # ignore empty line
+                if len(line)==1:
+                    continue
+                [key,val]=line[1:].split('=',1)
+                if key=="shape":
+                    self.app.command_prompt.run_set_shape(["set","shape",val])
+                elif key=="zoom":
+                    self.app.command_prompt.run_set_zoom(["set","zoom",val])
+                elif key=="color":
+                    color_str=val.split(',')
+                    try:
+                        self.set_color((float(color_str[0]),float(color_str[1]),float(color_str[2])))
+                    except:
+                        print("warning: ignoring line "+str(i)+" in file '"+file+"': color '"+color_str+"' cannot be read",file=sys.stderr)
+                # lattice is handled by main function
+                elif key=="lattice":
+                    continue
+                else:
+                    print("warning: ignoring line "+str(i)+" in file '"+file+"': unrecognized option '"+key+"'",file=sys.stderr)
+                continue
+
             entries=line.split(";")
             # skip line if improperly formatted
             if len(entries)>3:
-                print("warning: ignoring line "+str(i)+" in file '"+file+"': more than three ';' spearated entries in '"+line+"'",file=sys.stderr)
+                print("warning: ignoring line "+str(i)+" in file '"+file+"': more than three ';' separated entries in '"+line+"'",file=sys.stderr)
             if len(entries)<2:
-                print("warning: ignoring line "+str(i)+" in file '"+file+"': fewer than two ';' spearated entries in '"+line+"'",file=sys.stderr)
+                print("warning: ignoring line "+str(i)+" in file '"+file+"': fewer than two ';' separated entries in '"+line+"'",file=sys.stderr)
                 continue
 
             # position
@@ -472,6 +666,12 @@ 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)
+            elif particle_type==STAIRCASE_INDEX:
+                candidate=Staircase(pos.x,pos.y,color=color)
+            elif particle_type==SQUARE2_INDEX:
+                candidate=Square2(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
@@ -508,7 +708,13 @@ 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))
+            elif type(particle)==Disk:
+                ff.write("\disk{"+colors.closest_color(particle.color,colors.xcolor_names)+"}")
+            elif type(particle)==Staircase:
+                ff.write("\staircase{"+colors.closest_color(particle.color,colors.xcolor_names)+"}")
+            elif type(particle)==Square2:
+                ff.write("\square{"+colors.closest_color(particle.color,colors.xcolor_names)+"}")
+            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")
@@ -518,11 +724,14 @@ 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
+STAIRCASE_INDEX=3
+SQUARE2_INDEX=4
 
 

src/point.py

@@ -12,6 +12,8 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+# two-dimensional point structure
+
 import math
 
 # point in two dimensions
@@ -61,3 +63,7 @@ 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

@@ -12,18 +12,16 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-import math
-import sys
-from kivy.graphics import Color,Line,Rectangle
-
-from point import Point,l_infinity
-from tools import isint_nonzero,sgn,in_interval
+# a polyomino is a collection of elements, defined in elements.py
+from kivy.graphics import Color,Line
+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 maje 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
@@ -31,6 +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)
@@ -42,212 +43,137 @@ 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)
+        super(Disk,self).__init__(**kwargs,elements=[Element_circle(x,y,size=kwargs.get("size",1.0))])
 
-    # set position
-    def setpos(self,x,y):
-        self.pos.x=x
-        self.pos.y=y
+# 3-staircase
+class Staircase(Polyomino):
+    def __init__(self,x,y,**kwargs):
+        super(Staircase,self).__init__(**kwargs,elements=[\
+        Element_square(x,y+1,1,aspect=3),\
+        Element_square(x+1,y,1),\
+        Element_square(x+1,y+1,1),\
+        Element_square(x+2,y,1)\
+        ])
 
+    # redefine stroke to avoid lines between touching elements
+    def stroke(self,painter):
+        # convert to graphical coordinates
+        coordx=painter.pos_tocoord_x(self.elements[0].pos.x)
+        coordy=painter.pos_tocoord_y(self.elements[0].pos.y)
 
-    # check whether a square at pos interacts with square
-    def check_interaction(self,pos):
-        return l_infinity(pos-self.pos)<1
+        Color(1,1,1)
+        Line(points=(
+        *(coordx-0.5*painter.base_size,coordy-1.5*painter.base_size),
+        *(coordx+2.5*painter.base_size,coordy-1.5*painter.base_size),
+        *(coordx+2.5*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-1.5*painter.base_size),
+        ))
 
-    # 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
+# 2-square
+class Square2(Polyomino):
+    def __init__(self,x,y,**kwargs):
+        super(Square2,self).__init__(**kwargs,elements=[\
+        Element_square(x,y,1),\
+        Element_square(x+1,y,1),\
+        Element_square(x,y+1,1),\
+        Element_square(x+1,y+1,1)\
+        ])
 
-    # 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
+    # redefine stroke to avoid lines between touching elements
+    def stroke(self,painter):
+        # convert to graphical coordinates
+        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*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+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),
+        ))

src/status_bar.py

@@ -1,3 +1,17 @@
+# Copyright 2021-2023 Ian Jauslin
+# 
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+# 
+#     http://www.apache.org/licenses/LICENSE-2.0
+# 
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
 from kivy.uix.label import Label
 from kivy.graphics import Color,Rectangle
 from kivy.utils import escape_markup
@@ -45,9 +59,9 @@ 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 +1,19 @@
+# Copyright 2021-2023 Ian Jauslin
+# 
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+# 
+#     http://www.apache.org/licenses/LICENSE-2.0
+# 
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import math
+
 # sign function
 def sgn(x):
     if x>=0:
@@ -20,3 +36,10 @@ 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