svg_hexaflexagon_editor: draw also the backfaces

Draw also the hexagons backfaces, to make it easier to visualize the
symmetry when folding the flexagon.

diff --git a/src/flexagon/hexaflexagon_diagram.py b/src/flexagon/hexaflexagon_diagram.py
index 4bb029b..7b09c94 100755 (executable)
--- a/src/flexagon/hexaflexagon_diagram.py
+++ b/src/flexagon/hexaflexagon_diagram.py
@@ -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)
@@ -91,6 +104,18 @@ class HexaflexagonDiagram(object):
         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:
             cx, cy = self.get_triangle_center(triangle)

diff --git a/src/flexagon/trihexaflexagon.py b/src/flexagon/trihexaflexagon.py
index 7bd4f72..ca21726 100755 (executable)
--- a/src/flexagon/trihexaflexagon.py
+++ b/src/flexagon/trihexaflexagon.py
@@ -37,6 +37,10 @@ class Triangle(object):
 
         return xoffset, yoffset
 
+    def get_backface_index(self):
+        # The backfaces have the triangles in the reverse rotational order
+        return 5 - self.index
+
     def get_angle_in_plan(self):
         """The angle of a triangle in the hexaflexagon plan."""
         return - ((self.index) % 2) * pi / 3.
@@ -61,6 +65,16 @@ class Triangle(object):
         # angle functions change this one can be left untouched.
         return self.get_angle_in_hexagon() - self.get_angle_in_plan()
 
+    def get_angle_in_backface_relative_to_hexagon(self):
+
+        """"Get the angle of the triangle in the backface relative to the
+        rotation of the same triangle in the hexagon."""
+
+        backface_triangle_index = self.get_backface_index()
+        # group triangles in couples
+        group = (((backface_triangle_index + 1) % 6) // 2)
+        return pi + pi * 2 / 3 * group
+
     def get_angle_in_hexagon(self):
         """Get the angle of the triangle in the hexagons.
 

diff --git a/src/svg_hexaflexagon_editor.py b/src/svg_hexaflexagon_editor.py
index 48c8646..d64468b 100755 (executable)
--- a/src/svg_hexaflexagon_editor.py
+++ b/src/svg_hexaflexagon_editor.py
@@ -32,6 +32,7 @@ class SvgwriteHexaflexagonDiagram(HexaflexagonDiagram):
         # create some layers and groups
         layers = {
             "Hexagons": svg.layer(label="Hexagons"),
+            "Backfaces": svg.layer(label="Backfaces"),
             "Hexaflexagon": svg.layer(label="Hexaflexagon"),
             "Folding guide": svg.layer(label="Folding guide"),
             "Template": svg.layer(label="Template")
@@ -110,6 +111,24 @@ class SvgwriteHexaflexagonDiagram(HexaflexagonDiagram):
                 ref['clip-path'] = "url(%s)" % (triangle_href + '-clip-path')
                 group.add(ref)
 
+        # draw the backfaces
+        group = self.groups["Backfaces"]
+        for hexagon in self.hexaflexagon.hexagons:
+            for triangle in hexagon.triangles:
+                m = self.get_triangle_backfaces_transform(triangle)
+                svg_matrix = "matrix(%f, %f, %f, %f, %f, %f)" % (m[0], m[3],
+                                                                 m[1], m[4],
+                                                                 m[2], m[5])
+
+                triangle_href = "#hexagon%d-triangle%d" % (hexagon.index, triangle.index)
+
+                # Reuse the content to draw the backface
+                content_href = "#hexagon%d-content" % hexagon.index
+                ref = self.backend.svg.use(content_href)
+                ref['transform'] = svg_matrix
+                ref['clip-path'] = "url(%s)" % (triangle_href + '-clip-path')
+                group.add(ref)
+
     def draw_triangle_template(self, triangle, cx, cy, theta):
         old_active_group = self.backend.active_group
         group_name = "hexagon%d-triangle%d" % (triangle.hexagon.index, triangle.index)