154 lines
6.8 KiB
Python
154 lines
6.8 KiB
Python
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#! /usr/bin/env python3
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from math import pi, sin, cos, tan, acos, sqrt
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import inkex
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from Path import Path
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from Pattern import Pattern
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class Kresling(Pattern):
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def __init__(self):
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Pattern.__init__(self) # Must be called in order to parse common options
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self.add_argument("-p", "--pattern", default="kresling", help="Origami pattern")
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self.add_argument("--lines", type=int, default=1, help="Number of lines")
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self.add_argument("--sides", type=int, default=3, help="Number of polygon sides")
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self.add_argument("--add_attachment", type=inkex.Boolean, default=False, help="Add attachment?")
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self.add_argument("--attachment_percentage", type=float, default=100., help="Length percentage of extra facet")
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self.add_argument("--mirror_cells", type=inkex.Boolean, default=False, help="Mirror odd cells?")
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@staticmethod
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def generate_kresling_zigzag(sides, radius, angle_ratio, add_attachment):
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theta = (pi / 2.) * (1 - 2. / sides)
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l = 2. * radius * cos(theta * (1. - angle_ratio))
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a = 2. * radius * sin(pi / sides)
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# b = sqrt(a * a + l * l - 2 * a * l * cos(angle_ratio * theta))
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# phi = abs(acos((l * l + b * b - a * a) / (2 * l * b)))
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# gamma = pi / 2 - angle_ratio * theta - phi
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dy = l * sin(theta * angle_ratio)
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dx = l * cos(theta * angle_ratio) - a
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points = []
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styles = []
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for i in range(sides):
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points.append((i * a, 0))
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points.append(((i + 1) * a + dx, -dy))
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styles.append('v')
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if i != sides - 1:
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styles.append('m')
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elif add_attachment:
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points.append((sides * a, 0))
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styles.append('m')
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path = Path.generate_separated_paths(points, styles)
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return path
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def generate_path_tree(self):
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""" Specialized path generation for Waterbomb tesselation pattern
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"""
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unit_factor = self.calc_unit_factor()
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vertex_radius = self.options.vertex_radius * unit_factor
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lines = self.options.lines
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sides = self.options.sides
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radius = self.options.radius * unit_factor
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angle_ratio = self.options.angle_ratio
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mirror_cells = self.options.mirror_cells
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theta = (pi/2.)*(1 - 2./sides)
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l = 2.*radius*cos(theta*(1.-angle_ratio))
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a = 2.*radius*sin(pi/sides)
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# b = sqrt(a*a + l*l - 2*a*l*cos(angle_ratio*theta))
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# phi = abs(acos((l*l + b*b - a*a)/(2*l*b)))
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# gamma = pi/2 - angle_ratio*theta - phi
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# dy = b*cos(gamma)
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# dx = b*sin(gamma)
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dy = l * sin(theta * angle_ratio)
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dx = l * cos(theta * angle_ratio) - a
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add_attachment = self.options.add_attachment
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attachment_percentage = self.options.attachment_percentage/100.
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attachment_height = a*(attachment_percentage-1)*tan(angle_ratio*theta)
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vertices = []
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for i in range(sides + 1):
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for j in range(lines + 1):
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if mirror_cells:
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vertices.append(Path((dx*((lines - j)%2) + a*i, dy*j), style='p', radius=vertex_radius))
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else:
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vertices.append(Path((dx*(lines - j) + a*i, dy*j), style='p', radius=vertex_radius))
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# create a horizontal grid, then offset each line according to angle
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grid_h = Path.generate_hgrid([0, a * sides], [0, dy * lines], lines, 'm')
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if not mirror_cells:
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# shift every mountain line of the grid to the right by increasing amounts
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grid_h = Path.list_add(grid_h, [(i * dx, 0) for i in range(lines - 1, 0, -1)])
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else:
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# shift every OTHER mountain line of the grid a bit to the right
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grid_h = Path.list_add(grid_h, [((i%2)*dx, 0) for i in range(lines-1, 0, -1)])
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if add_attachment:
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for i in range(lines%2, lines-1, 2):
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# hacky solution, changes length of every other mountain line
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grid_h[i].points[1-i%2] = (grid_h[i].points[1-i%2][0] + a*attachment_percentage, grid_h[i].points[1-i%2][1])
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# create MV zigzag for Kresling pattern
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zigzag = Kresling.generate_kresling_zigzag(sides, radius, angle_ratio, add_attachment)
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zigzags = []
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# duplicate zigzag pattern for desired number of cells
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if not mirror_cells:
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for i in range(lines):
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zigzags.append(Path.list_add(zigzag, (i * dx, (lines - i) * dy)))
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else:
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zigzag_mirror = Path.list_reflect(zigzag, (0, lines * dy / 2), (dx, lines * dy / 2))
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for i in range(lines):
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if i % 2 == 1:
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zigzags.append(Path.list_add(zigzag_mirror, (0, -(lines - i + (lines-1)%2) * dy)))
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else:
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zigzags.append(Path.list_add(zigzag, (0, (lines - i) * dy)))
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# create edge strokes
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if not mirror_cells:
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self.edge_points = [
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(a * sides , dy * lines), # bottom right
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(0 , dy * lines), # bottom left
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(dx * lines , 0), # top left
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(dx * lines + a * sides, 0)] # top right
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if add_attachment:
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for i in range(lines):
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x = dx * (lines - i) + a * (sides + attachment_percentage)
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self.edge_points.append((x, dy * i))
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self.edge_points.append((x, dy * i - attachment_height))
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if i != lines - 1:
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self.edge_points.append((x-dx-a*attachment_percentage, dy * (i + 1)))
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pass
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else:
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self.edge_points = [(a * sides + (lines % 2)*dx, 0)]
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for i in range(lines+1):
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self.edge_points.append([((lines+i) % 2)*dx, dy*i])
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self.edge_points.append([a * sides + ((lines+i) %2)*dx, lines*dy])
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if add_attachment:
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for i in range(lines + 1):
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if not i%2 == 0:
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self.edge_points.append([a*sides + (i%2)*(dx+a*attachment_percentage), dy*(lines - i) - (i%2)*attachment_height])
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self.edge_points.append([a*sides + (i%2)*(dx+a*attachment_percentage), dy*(lines - i)])
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if (i != lines):
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self.edge_points.append([a * sides + (i % 2) * (dx + a * attachment_percentage), dy * (lines - i) + (i % 2) * attachment_height])
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else:
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self.edge_points.append([a * sides + (i % 2) * (dx + a * attachment_percentage), dy * (lines - i)])
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else:
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for i in range(lines + 1):
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self.edge_points.append([a*sides + (i%2)*dx, dy*(lines - i)])
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self.path_tree = [grid_h, zigzags, vertices]
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if __name__ == '__main__':
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Kresling().run()
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