#!/usr/bin/env python # # An class to draw tetraflexagons # # Copyright (C) 2018 Antonio Ospite # # 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 . 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.calc_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()