README.md: mention also the tetraflexagon example

[flexagon-toolkit.git] / src / flexagon / hexaflexagon_diagram.py

diff --git a/src/flexagon/hexaflexagon_diagram.py b/src/flexagon/hexaflexagon_diagram.py
index cdd636b..7b09c94 100755 (executable)
--- a/src/flexagon/hexaflexagon_diagram.py
+++ b/src/flexagon/hexaflexagon_diagram.py
@@ -1,6 +1,6 @@
 #!/usr/bin/env python
 #
-# An class to draw hexaflexagons
+# A class to draw hexaflexagons
 #
 # Copyright (C) 2018  Antonio Ospite <ao2@ao2.it>
 #
@@ -17,7 +17,7 @@
 # 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 sin, cos, pi
+from math import cos, pi
 from .trihexaflexagon import TriHexaflexagon
 
 
@@ -43,6 +43,10 @@ class HexaflexagonDiagram(object):
         self.plan_origin = (self.x_border * 2. + self.hexagon_radius / 2.,
                             self.x_border + self.triangle_radius / 3.)
 
+        # The offset of the backfaces relative to the first hexagon
+        self.backfaces_offsets = (0,
+                                  (self.hexagon_radius + self.x_border) * 2)
+
         self.hexagons_color_map = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
 
     def _init_centers(self):
@@ -66,6 +70,15 @@ class HexaflexagonDiagram(object):
     def get_triangle_center(self, triangle):
         return self.triangles_centers[triangle.hexagon.index][triangle.index]
 
+    def get_triangle_center_in_backfaces(self, triangle):
+        """Get the center of this triangle but in the backface"""
+        x0, y0 = self.backfaces_offsets
+
+        backface_triangle_index = triangle.get_backface_index()
+        x, y = self.triangles_centers[triangle.hexagon.index][backface_triangle_index]
+
+        return x0 + x, y0 + y
+
     def get_triangle_center_in_plan(self, triangle):
         x0, y0 = self.plan_origin
         i, j = self.hexaflexagon.get_triangle_plan_position(triangle)
@@ -88,59 +101,20 @@ class HexaflexagonDiagram(object):
         dest_x, dest_y = self.get_triangle_center_in_plan(triangle)
         theta = triangle.get_angle_in_plan_relative_to_hexagon()
 
-        # The transformation from a triangle in the hexagon to the correspondent
-        # triangle in the plan is composed by these steps:
-        #
-        #   1. rotate by 'theta' around (src_x, src_y);
-        #   2. move to (dest_x, dest_y).
-        #
-        # Step 1 can be expressed by these sub-steps:
-        #
-        #  1a. translate by (-src_x, -src_y)
-        #  1b. rotate by 'theta'
-        #  1c. translate by (src_x, src_y)
-        #
-        # Step 2. can be expressed by a translation like:
-        #
-        #  2a. translate by (dest_x - src_x, dest_y - src_y)
-        #
-        # The consecutive translations 1c and 2a can be easily combined, so
-        # the final steps are:
-        #
-        #  T1 -> translate by (-src_x, -src_y)
-        #  R  -> rotate by 'theta'
-        #  T2 -> translate by (dest_x, dest_y)
-        #
-        # Using affine transformations these are expressed as:
-        #
-        #      | 1  0  -src_x |
-        # T1 = | 0  1  -src_y |
-        #      | 0  0       1 |
-        #
-        #      | cos(theta)  -sin(theta)  0 |
-        # R  = | sin(theta)   con(theta)  0 |
-        #      |          0            0  1 |
-        #
-        #      | 1  0  dest_x |
-        # T2 = | 0  1  dest_y |
-        #      | 0  0       1 |
-        #
-        # Composing these transformations into one is achieved by multiplying
-        # the matrices from right to left:
-        #
-        #   T = T2 * R * T1
-        #
-        # NOTE: To remember this think about composing functions: T2(R(T1())),
-        # the inner one is performed first.
-        #
-        # The resulting  T matrix is the one below.
-        matrix = [
-            cos(theta), -sin(theta), -src_x * cos(theta) + src_y * sin(theta) + dest_x,
-            sin(theta),  cos(theta), -src_x * sin(theta) - src_y * cos(theta) + dest_y,
-                     0,           0,                                                 1
-        ]
-
-        return matrix
+        return self.backend.calc_rotate_translate_transform(src_x, src_y,
+                                                            dest_x, dest_y, theta)
+
+    def get_triangle_backfaces_transform(self, triangle):
+        """Calculate the transformation matrix from a triangle in an hexagon to
+        the correspondent triangle in a backface.
+
+        Return the matrix as a list of values sorted in row-major order."""
+        src_x, src_y = self.get_triangle_center(triangle)
+        dest_x, dest_y = self.get_triangle_center_in_backfaces(triangle)
+        theta = triangle.get_angle_in_backface_relative_to_hexagon()
+
+        return self.backend.calc_rotate_translate_transform(src_x, src_y,
+                                                            dest_x, dest_y, theta)
 
     def draw_hexagon_template(self, hexagon):
         for triangle in hexagon.triangles: