--- /dev/null
+#!/usr/bin/env python
+#
+# An class to draw tetraflexagons
+#
+# Copyright (C) 2018 Antonio Ospite <ao2@ao2.it>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# 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
+from .tritetraflexagon import TriTetraflexagon
+
+
+class TetraflexagonDiagram(object):
+ def __init__(self, x_border, backend=None):
+ self.x_border = x_border
+ self.backend = backend
+
+ self.tetraflexagon = TriTetraflexagon()
+
+ num_squares = len(self.tetraflexagon.squares)
+ self.square_side = (self.backend.height - (x_border * 3)) / (num_squares)
+ self.square_radius = self.square_side / 2
+ self.tile_side = self.square_radius
+ self.tile_radius = self.tile_side / 2
+
+ self._init_centers()
+
+ # draw the plan centered wrt. the squares
+ self.plan_origin = ((self.backend.width - self.tile_side * 5) / 2,
+ self.x_border)
+
+ self.squares_color_map = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
+
+ def _init_centers(self):
+ # Preallocate the lists to be able to access them by indices in the
+ # loops below.
+ self.squares_centers = [None for h in self.tetraflexagon.squares]
+ self.tiles_centers = [[None for t in h.tiles] for h in self.tetraflexagon.squares]
+
+ cy = self.backend.height - (self.square_radius + self.x_border)
+ for square in self.tetraflexagon.squares:
+ cx = self.x_border + (2 * self.square_radius + self.x_border) * (square.index + 1)
+ self.squares_centers[square.index] = (cx, cy)
+
+ for tile in square.tiles:
+ # offset by 1 or -1 times the tile radius
+ tile_cx = cx + self.tile_radius * ((tile.index % 2) * 2 - 1)
+ tile_cy = cy + self.tile_radius * ((tile.index > 1) * 2 - 1)
+ self.tiles_centers[square.index][tile.index] = (tile_cx, tile_cy)
+
+ def get_square_center(self, square):
+ return self.squares_centers[square.index]
+
+ def get_tile_center(self, tile):
+ return self.tiles_centers[tile.square.index][tile.index]
+
+ def get_tile_center_in_plan(self, tile):
+ x0, y0 = self.plan_origin
+ i, j = self.tetraflexagon.get_tile_plan_position(tile)
+ x, y = tile.calc_plan_coordinates(self.tile_side, i, j)
+ return x0 + x, y0 + y
+
+ def get_tile_transform(self, tile):
+ """Calculate the transformation matrix from a tile in an square to
+ the correspondent tile in the plan.
+
+ Return the matrix as a list of values sorted in row-major order."""
+
+ src_x, src_y = self.get_tile_center(tile)
+ dest_x, dest_y = self.get_tile_center_in_plan(tile)
+
+ i, j = self.tetraflexagon.get_tile_plan_position(tile)
+ theta = tile.get_angle_in_plan(i, j)
+
+ # The transformation from a tile in the square to the correspondent
+ # tile 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
+
+ def draw_square_template(self, square):
+ for tile in square.tiles:
+ cx, cy = self.get_tile_center(tile)
+ self.draw_tile_template(tile, cx, cy, 0)
+
+ def draw_tile_template(self, tile, cx, cy, theta):
+ side = self.tile_side
+ color = self.squares_color_map[tile.square.index]
+
+ self.backend.draw_rect_from_center(cx, cy, side, side, theta, color)
+
+ corners_labels = "ABC"
+ corner_text = corners_labels[tile.square.index] + str(tile.index + 1)
+ self.backend.draw_centered_text(cx, cy, corner_text, 0, color)
+
+ def draw_plan_template(self):
+ x0, y0 = self.plan_origin
+ for square in self.tetraflexagon.squares:
+ for tile in square.tiles:
+ i, j = self.tetraflexagon.get_tile_plan_position(tile)
+ x, y = tile.calc_plan_coordinates(self.tile_radius, i, j)
+ theta = tile.get_angle_in_plan(i, j)
+ self.draw_tile_template(tile, x0 + x, y0 + y, theta)
+
+ def draw_template(self):
+ for square in self.tetraflexagon.squares:
+ self.draw_square_template(square)
+
+ self.draw_plan_template()
--- /dev/null
+#!/usr/bin/env python
+#
+# A generic model for a tri-tetraflexagon
+#
+# Copyright (C) 2018 Antonio Ospite <ao2@ao2.it>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# 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
+
+
+class Tile(object):
+ def __init__(self, square, index):
+ self.square = square
+ self.index = index
+
+ @staticmethod
+ def calc_plan_coordinates(side, i, j):
+ xoffset = side / 2 + j * side
+ yoffset = side / 2 + i * side
+
+ return xoffset, yoffset
+
+ @staticmethod
+ def calc_angle_in_plan(i, j):
+ """The angle of a tile in the tetraflexagon plan."""
+ return pi * (i > 1)
+
+ def __str__(self):
+ return "%d,%d" % (self.square.index, self.index)
+
+
+class Square(object):
+ def __init__(self, index):
+ self.index = index
+ self.tiles = []
+ for i in range(4):
+ tile = Tile(self, i)
+ self.tiles.append(tile)
+
+ def __str__(self):
+ output = ""
+ for i in range(0, 4):
+ output += str(self.tiles[i])
+ output += "\t"
+
+ return output
+
+
+class TriTetraflexagon(object):
+ def __init__(self):
+ self.squares = []
+ for i in range(0, 3):
+ square = Square(i)
+ self.squares.append(square)
+
+ # A plan is described by a mapping of the tiles in the squares,
+ # repositioned on a 2d grid.
+ #
+ # In the map below, the grid has two rows, each element of the grid is
+ # a pair (s, t), where 's' is the index of the square, and 't' is the
+ # index of the tile in that square.
+ plan_map = [
+ [(2, 0), (2, 1), (0, 1), None, None],
+ [None, None, (0, 3), (1, 2), (1, 3)],
+ [None, None, (2, 3), (2, 2), (0, 2)],
+ [(0, 0), (1, 1), (1, 0), None, None],
+ ]
+
+ # Preallocate a bi-dimensional array for an inverse mapping, this is
+ # useful to retrieve the position in the plan given a tile.
+ self.plan_map_inv = [[-1 for t in h.tiles] for h in self.squares]
+
+ self.plan = []
+ for i, plan_map_row in enumerate(plan_map):
+ plan_row = []
+ for j, mapping in enumerate(plan_map_row):
+ if mapping:
+ square_index, tile_index = mapping
+ square = self.squares[square_index]
+ tile = square.tiles[tile_index]
+ self.plan_map_inv[square_index][tile_index] = (i, j)
+ else:
+ tile = None
+
+ plan_row.append(tile)
+
+ self.plan.append(plan_row)
+
+ def get_tile_plan_position(self, tile):
+ return self.plan_map_inv[tile.square.index][tile.index]
+
+ def __str__(self):
+ output = ""
+
+ for row in self.plan:
+ for tile in row:
+ output += "%s\t" % str(tile)
+ output += "\n"
+
+ return output
+
+
+def test():
+ tritetraflexagon = TriTetraflexagon()
+ print(tritetraflexagon)
+
+
+if __name__ == "__main__":
+ test()
--- /dev/null
+#!/usr/bin/env python3
+#
+# Draw an SVG tetraflexagon which can be edited live in Inkscape.
+#
+# Copyright (C) 2018 Antonio Ospite <ao2@ao2.it>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+import svgwrite
+
+from diagram.svgwrite_diagram import SvgwriteDiagram
+from flexagon.tetraflexagon_diagram import TetraflexagonDiagram
+
+
+class SvgwriteTetraflexagonDiagram(TetraflexagonDiagram):
+ def __init__(self, *args, **kwargs):
+ super(SvgwriteTetraflexagonDiagram, self).__init__(*args, **kwargs)
+
+ svg = self.backend.svg
+
+ # create some layers and groups
+ layers = {
+ "Squares": svg.layer(label="Squares"),
+ "Tetraflexagon": svg.layer(label="Tetraflexagon"),
+ "Template": svg.layer(label="Template")
+ }
+ for layer in layers.values():
+ svg.add(layer)
+
+ self.groups = layers
+
+ for square in self.tetraflexagon.squares:
+ name = "square%d-content" % square.index
+ layer = svg.layer(id=name, label="Square %d" % (square.index + 1))
+ self.groups[name] = layer
+ layers['Squares'].add(layer)
+
+ for tile in square.tiles:
+ name = "square%d-tile%d" % (square.index, tile.index)
+ group = svg.g(id=name)
+ self.groups[name] = group
+ layers['Template'].add(group)
+
+ def draw(self):
+ for square in self.tetraflexagon.squares:
+ cx, cy = self.get_square_center(square)
+
+ # Draw some default content
+ old_active_group = self.backend.active_group
+ self.backend.active_group = self.groups["square%d-content" % square.index]
+ self.backend.draw_rect_from_center(cx, cy, self.square_side, self.square_side, 0,
+ fill_color=(0.5, 0.5, 0.5, 0.2))
+ self.backend.active_group = old_active_group
+
+ self.backend.active_group = old_active_group
+
+ # Draw the normal template for squares
+ for square in self.tetraflexagon.squares:
+ self.draw_square_template(square)
+
+ # draw plan using references
+ for square in self.tetraflexagon.squares:
+ for tile in square.tiles:
+ m = self.get_tile_transform(tile)
+ svg_matrix = "matrix(%f, %f, %f, %f, %f, %f)" % (m[0], m[3],
+ m[1], m[4],
+ m[2], m[5])
+
+ # Reuse the squares tile for the tetraflexagon template
+ group = self.groups["Template"]
+ tile_href = "#square%d-tile%d" % (square.index, tile.index)
+ ref = self.backend.svg.use(tile_href)
+ ref['transform'] = svg_matrix
+ group.add(ref)
+
+ # Reuse the content to draw the final tetraflexagon
+ group = self.groups["Tetraflexagon"]
+ content_href = "#square%d-content" % square.index
+ ref = self.backend.svg.use(content_href)
+ ref['transform'] = svg_matrix
+ ref['clip-path'] = "url(%s)" % (tile_href + '-clip-path')
+ group.add(ref)
+
+ def draw_tile_template(self, tile, cx, cy, theta):
+ old_active_group = self.backend.active_group
+ group_name = "square%d-tile%d" % (tile.square.index, tile.index)
+ self.backend.active_group = self.groups[group_name]
+
+ super(SvgwriteTetraflexagonDiagram, self).draw_tile_template(tile, cx, cy, theta)
+
+ # The tile outline in the active group's element is the only polygon
+ # element, so get it and set its id so that it can be reused as
+ # a clip-path
+ for element in self.backend.active_group.elements:
+ if isinstance(element, svgwrite.shapes.Rect):
+ element['id'] = group_name + "-outline"
+ break
+
+ clip_path = self.backend.svg.clipPath(id=group_name + '-clip-path')
+ self.backend.svg.defs.add(clip_path)
+ ref = self.backend.svg.use('#%s-outline' % group_name)
+ clip_path.add(ref)
+
+ self.backend.active_group = old_active_group
+
+def main():
+ width = 3508
+ height = 2480
+
+ x_border = width / 50
+ font_size = width / 80
+ stroke_width = width / 480
+
+ svg_backend = SvgwriteDiagram(width, height, font_size=font_size, stroke_width=stroke_width)
+ tetraflexagon = SvgwriteTetraflexagonDiagram(x_border, backend=svg_backend)
+ tetraflexagon.draw()
+ svg_backend.save_svg("inkscape-tetraflexagon-editor.svg")
+
+
+if __name__ == "__main__":
+ main()
projects / flexagon-toolkit.git / commitdiff