commit ff6f8002c14b6a39146053d6ab15d94588963641
parent 843d9afdb48f1344bd1ab1473ee39be0cccb23ca
Author: Sebastiano Tronto <sebastiano.tronto@gmail.com>
Date: Fri, 15 Oct 2021 15:47:29 +0200
added function for computing multiplicities
Diffstat:
| M | billiard3d.py | | | 50 | ++++++++++++++++++++++++++++++++++++++++++++++++-- |
1 file changed, 48 insertions(+), 2 deletions(-)
diff --git 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":
