move along cross

cross.py

@@ -1,8 +1,10 @@
 import math
+import sys
 from kivy.graphics import Color,Line,Rectangle
 from kivy.uix.widget import Widget
 
 from point import Point
+from tools import isint_nonzero,sgn
 
 class Cross():
     # size of central square
@@ -12,6 +14,7 @@ class Cross():
         self.pos=Point(x,y)
         self.color=kwargs.get("color",(0,0,1))
         self.selected=False
+        self.stuckto=None
 
     # set position
     def setpos(self,x,y):
@@ -89,6 +92,87 @@ class Cross():
             closest=self.move_on_line_to_stick_relative(Point(-x.x,x.y),Point(-v.x,v.y))
             return Point(-closest.x,closest.y)
 
+    # move along edge of cross while remaining stuck
+    def move_along(self,newpos,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
+                # two types of corners: |x|_1=3 or |x|_1=4
+                if abs(rel.x)+abs(rel.y)<3.5:
+                    if sgn(newpos.y-pos.y)==sgn(rel.y):
+                        # stuck in x direction
+                        return self.move_stuck_x(newpos,pos)
+                    elif sgn(newpos.x-pos.x)==sgn(rel.x):
+                        # stuck in y direction
+                        return self.move_stuck_y(newpos,pos)
+                else:
+                    if sgn(newpos.y-pos.y)==-sgn(rel.y):
+                        # stuck in x direction
+                        return self.move_stuck_x(newpos,pos)
+                    elif sgn(newpos.x-pos.x)==-sgn(rel.x):
+                        # stuck in y direction
+                        return self.move_stuck_y(newpos,pos)
+                # stuck in both directions
+                return pos
+            else:
+                # stuck in x direction
+                return self.move_stuck_x(newpos,pos)
+        elif isint_nonzero(rel.y):
+            # stuck in y direction
+            return self.move_stuck_y(newpos,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,newpos,pos):
+        # only move in y direction
+        candidate=Point(pos.x,newpos.y)
+        # do not move past corners
+        rel=pos.y-self.pos.y
+        newrel=newpos.y-self.pos.y
+        if newpos.y>pos.y:
+            if self.check_interaction(candidate)==False or (rel<math.ceil(rel)-1e-11 and newrel>math.ceil(rel)+1e-11 and math.ceil(rel)!=0):
+                # in open corner
+                if rel>math.ceil(rel)-1e-11:
+                    candidate.y=math.ceil(rel)+1+self.pos.y
+                else:
+                    candidate.y=math.ceil(rel)+self.pos.y
+        else:
+            if self.check_interaction(candidate)==False or (rel>math.floor(rel)+1e-11 and newrel<math.floor(rel)-1e-11 and math.floor(rel)!=0):
+                # in open corner
+                if rel<math.floor(rel)+1e-11:
+                    candidate.y=math.floor(rel)-1+self.pos.y
+                else:
+                    candidate.y=math.floor(rel)+self.pos.y
+        return candidate
+    # move when stuck in the y direction
+    def move_stuck_y(self,newpos,pos):
+        # only move in x direction
+        candidate=Point(newpos.x,pos.y)
+        # do not move past corners
+        rel=pos.x-self.pos.x
+        newrel=newpos.x-self.pos.x
+        if newpos.x>pos.x:
+            if self.check_interaction(candidate)==False or (rel<math.ceil(rel)-1e-11 and newrel>math.ceil(rel)+1e-11 and math.ceil(rel)!=0):
+                # in open corner
+                if rel>math.ceil(rel)-1e-11:
+                    candidate.x=math.ceil(rel)+1+self.pos.x
+                else:
+                    candidate.x=math.ceil(rel)+self.pos.x
+        else:
+            if self.check_interaction(candidate)==False or (rel>math.floor(rel)+1e-11 and newrel<math.floor(rel)-1e-11 and math.floor(rel)!=0):
+                # in open corner
+                if rel<math.floor(rel)+1e-11:
+                    candidate.x=math.floor(rel)-1+self.pos.x
+                else:
+                    candidate.x=math.floor(rel)+self.pos.x
+        return candidate
+        
+
 
 # L_infinity distance rescalled by 3 in the x direction
 def cross_distx(x,y):
@@ -181,8 +265,16 @@ class Cross_painter(Widget):
             if other!=cross:
                 # move would make cross overlap with other
                 if other.check_interaction(newpos)==False:
-                    # stick to the cross
+                    # check if cross is stuck to other
-                    return other.move_on_line_to_stick(cross.pos,newpos-cross.pos)
+                    if cross.stuckto==other:
+                        # move along other while remaining stuck
+                        return other.move_along(newpos,cross.pos)
+                    else:
+                        # stick to the cross
+                        cross.stuckto=other
+                        return other.move_on_line_to_stick(cross.pos,newpos-cross.pos)
+        # reset stuckto if move is allowed
+        cross.stuckto=None
         return newpos
 
     # check that a cross can be added at position

tools.py

@@ -1,6 +1,11 @@
-
 # sign function
 def sgn(x):
     if x>=0:
         return 1
     return -1
+
+# check whether a number is an integer (with tolerance)
+def isint_nonzero(x):
+    if abs(x)<1e-11:
+        return False
+    return abs(round(x)-x)<1e-11