Change how a trihexaflexagon is drawn

Change how a trihexaflexagon is drawn to obtain a hexaflexagon more
aligned with conventions used elsewhere.

Now the hexagons are drawn with a "vertical orientation", opposed to the
previous horizontal one where they looked like they were laying on the
x axis.

This shows more clearly that the triangles are grouped in couples and
these couples only change orientation on one axis when shown on the
"opposite" face.

To have a clearer view of hat that means take a look at "The symmetry
within the trihexaflexagon, with Simon Pampena":
https://www.youtube.com/watch?v=NBJrGbbxceU

diff --git a/src/flexagon/hexaflexagon_diagram.py b/src/flexagon/hexaflexagon_diagram.py
index 09e8fc9..cdd636b 100755 (executable)
--- a/src/flexagon/hexaflexagon_diagram.py
+++ b/src/flexagon/hexaflexagon_diagram.py
@@ -56,7 +56,7 @@ class HexaflexagonDiagram(object):
             cx = self.x_border + self.hexagon_radius + (2 * self.hexagon_radius + self.x_border) * hexagon.index
             self.hexagons_centers[hexagon.index] = (cx, cy)
 
-            triangles_centers = self.backend.get_regular_polygon(cx, cy, 6, self.triangle_radius)
+            triangles_centers = self.backend.get_regular_polygon(cx, cy, 6, self.triangle_radius, pi / 6)
             for triangle in hexagon.triangles:
                 self.triangles_centers[hexagon.index][triangle.index] = triangles_centers[triangle.index]
 

diff --git a/src/flexagon/trihexaflexagon.py b/src/flexagon/trihexaflexagon.py
index d79875e..e3aab5c 100755 (executable)
--- a/src/flexagon/trihexaflexagon.py
+++ b/src/flexagon/trihexaflexagon.py
@@ -39,19 +39,19 @@ class Triangle(object):
 
     def get_angle_in_plan(self):
         """The angle of a triangle in the hexaflexagon plan."""
-        return - ((self.index + 1) % 2) * pi / 3.
+        return - ((self.index) % 2) * pi / 3.
 
     def get_angle_in_plan_relative_to_hexagon(self):
         """"Get the angle of the triangle in the plan relative to the rotation
         of the same triangle in the hexagon."""
-        return ((self.index + 4) % 6 // 2) * pi * 2. / 3.
+        return ((self.index + 5) % 6 // 2) * pi * 2 / 3 - pi / 6
 
     def get_angle_in_hexagon(self):
         """Get the angle of the triangle in the hexagons.
 
         NOTE: the angle is rotated by pi to have the first triangle with the
         base on the bottom."""
-        return pi + self.index * pi / 3.
+        return pi + pi / 6. + self.index * pi / 3.
 
     def __str__(self):
         return "%d,%d" % (self.hexagon.index, self.index)
@@ -88,8 +88,8 @@ class TriHexaflexagon(object):
         # a pair (h, t), where 'h' is the index of the hexagon, and 't' is the
         # index of the triangle in that hexagon.
         plan_map = [
-            [(0, 0), (1, 5), (1, 4), (2, 3), (2, 2), (0, 3), (0, 2), (1, 1), (1, 0)],
-            [(2, 5), (2, 4), (0, 5), (0, 4), (1, 3), (1, 2), (2, 1), (2, 0), (0, 1)]
+            [(0, 5), (1, 4), (1, 3), (2, 2), (2, 1), (0, 2), (0, 1), (1, 0), (1, 5)],
+            [(2, 4), (2, 3), (0, 4), (0, 3), (1, 2), (1, 1), (2, 0), (2, 5), (0, 0)]
         ]
 
         # Preallocate a bi-dimensional array for an inverse mapping, this is

diff --git a/src/svg_hexaflexagon_editor.py b/src/svg_hexaflexagon_editor.py
index f86ad13..48c8646 100755 (executable)
--- a/src/svg_hexaflexagon_editor.py
+++ b/src/svg_hexaflexagon_editor.py
@@ -17,7 +17,6 @@
 # You should have received a copy of the GNU General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
-from math import pi
 import svgwrite
 
 from diagram.svgwrite_diagram import SvgwriteDiagram
@@ -61,7 +60,7 @@ class SvgwriteHexaflexagonDiagram(HexaflexagonDiagram):
             # Draw some default content
             old_active_group = self.backend.active_group
             self.backend.active_group = self.groups["hexagon%d-content" % hexagon.index]
-            self.backend.draw_regular_polygon(cx, cy, 6, self.hexagon_radius, pi / 6., fill_color=(0.5, 0.5, 0.5, 0.2), stroke_color=None)
+            self.backend.draw_regular_polygon(cx, cy, 6, self.hexagon_radius, fill_color=(0.5, 0.5, 0.5, 0.2), stroke_color=None)
             self.backend.active_group = old_active_group
 
             # Add folding guides