added function for computing multiplicities

1 files changed, 48 insertions, 2 deletions

diff --git a/billiard3d.py b/billiard3d.py
index d77fc1a..b9eb143 100644
--- a/billiard3d.py
+++ b/billiard3d.py
@@ -36,7 +36,7 @@ def get_path(n, sizes, r):
         path = [r]
         p = r
         d = [1] * n
-        steps = 0
+        steps = 1
         while steps < 2*lcm_list(sizes):
                 p = [p[i] + d[i] for i in range(n)]
                 path.append(p)
@@ -44,6 +44,46 @@ def get_path(n, sizes, r):
                 d = [d[i] if p[i] % sizes[i] != 0 else -d[i] for i in range(n)]
         return path
 
+def is_double(path):
+        # A path is double if and only at some point the ball bounces on a
+        # corner and bounces back in the opposite direction. This happens if
+        # and only if for some i we have path[i] = path[i+2]
+        for i in range(0, len(path)-2):
+                if path[i] == path[i+2]:
+                        return True
+
+        return False
+
+def print_multiplicities(n, sizes, r):
+        print("")
+        print("Points with multiplicity > 1:")
+        print("")
+
+        d = dict()
+        path = [tuple(x) for x in get_path(n, sizes, r)]
+
+        for point in path:
+                if point in d:
+                        d[point] += 1
+                else:
+                        d[point] = 1
+
+        if is_double(path):
+                for p in d:
+                        d[p] //= 2
+
+        for i in range(2, max(d.values())+1):
+                L = []
+                for point in d:
+                        if d[point] == i:
+                                L.append(point)
+
+                if len(L) != 0:
+                        print(len(L), "point of multiplicity", i)
+                        print(L)
+                        print("")
+
+
 ###############################################################################
 # This part is specific for 2d drawings
 ###############################################################################
@@ -180,14 +220,20 @@ def user_input():
         ra = int(input("a-coordinate of r: "))
         rb = int(input("b-coordinate of r: "))
         rc = int(input("c-coordinate of r: "))
-        pic = input("Choose p for projections or 3 for 3d (empty = both): ")
+        pic = input("Choose p for projections or 3 for 3d (empty = all, one after the other): ")
         return [a,b,c], [ra,rb,rc], pic
 
+###############################################################################
+# Main routine below
+###############################################################################
+
 # You can choose to write your input here or to get it interactively
 #sizes, r, pic = [15, 9, 7], [2, 0, 0], "p"
 #sizes, r, pic = [2, 3, 4], [0, 0, 0], "3"
 sizes, r, pic = user_input()
 
+print_multiplicities(len(sizes), sizes, r)
+
 if pic == "p":
         draw_3d_projections(sizes, r)
 elif pic == "3":