diff --git a/main.py b/main.py
index 2ef4987..b780f44 100644
--- a/main.py
+++ b/main.py
@@ -135,7 +135,7 @@ class Cross():
 
     # check whether a cross at pos interacts with cross
     def check_interaction(self,pos):
-        return int((pos.x-self.pos.x)/self.size)**2+int((pos.y-self.pos.y)/self.size)**2>=5
+        return ((pos-self.pos)/self.size).int()**2>=5
 
     # find position along a line that comes in contact with the line
     #def move_on_line_to_stick(self,x,v):
@@ -148,9 +148,31 @@ class Point:
     def __add__(self,point):
         return Point(self.x+point.x,self.y+point.y)
 
-    def __neg__(self):
-        return Point(-self.x,self.y)
+    def __sub__(self,point):
+        return Point(self.x-point.x,self.y-point.y)
 
+    def __neg__(self):
+        return Point(-self.x,-self.y)
+
+    def __mul__(self,a):
+        return Point(a*self.x,a*self.y)
+
+    def __truediv__(self,a):
+        return Point(self.x/a,self.y/a)
+
+    def __pow__(self,a):
+        if a==2:
+            return self.dot(self)
+
+    # dot product
+    def dot(self,x):
+        return self.x*x.x+self.y*x.y
+
+    # integer part
+    def int(self):
+        return Point(int(self.x),int(self.y))
+
+    # set position
     def setpos(self,x,y):
         self.x=x
         self.y=y