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mightyscape-1.1-deprecated/extensions/fablabchemnitz/origami_patterns/OrigamiPatterns/Kresling.py

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2021-07-23 02:36:56 +02:00
#! /usr/bin/env python3
from math import pi, sin, cos, tan, acos, sqrt
import inkex
from Path import Path
from Pattern import Pattern
class Kresling(Pattern):
def __init__(self):
Pattern.__init__(self) # Must be called in order to parse common options
self.add_argument("-p", "--pattern", default="kresling", help="Origami pattern")
self.add_argument("--lines", type=int, default=1, help="Number of lines")
self.add_argument("--sides", type=int, default=3, help="Number of polygon sides")
self.add_argument("--add_attachment", type=inkex.Boolean, default=False, help="Add attachment?")
self.add_argument("--attachment_percentage", type=float, default=100., help="Length percentage of extra facet")
self.add_argument("--mirror_cells", type=inkex.Boolean, default=False, help="Mirror odd cells?")
@staticmethod
def generate_kresling_zigzag(sides, radius, angle_ratio, add_attachment):
theta = (pi / 2.) * (1 - 2. / sides)
l = 2. * radius * cos(theta * (1. - angle_ratio))
a = 2. * radius * sin(pi / sides)
# b = sqrt(a * a + l * l - 2 * a * l * cos(angle_ratio * theta))
# phi = abs(acos((l * l + b * b - a * a) / (2 * l * b)))
# gamma = pi / 2 - angle_ratio * theta - phi
dy = l * sin(theta * angle_ratio)
dx = l * cos(theta * angle_ratio) - a
points = []
styles = []
for i in range(sides):
points.append((i * a, 0))
points.append(((i + 1) * a + dx, -dy))
styles.append('v')
if i != sides - 1:
styles.append('m')
elif add_attachment:
points.append((sides * a, 0))
styles.append('m')
path = Path.generate_separated_paths(points, styles)
return path
def generate_path_tree(self):
""" Specialized path generation for Waterbomb tesselation pattern
"""
unit_factor = self.calc_unit_factor()
vertex_radius = self.options.vertex_radius * unit_factor
lines = self.options.lines
sides = self.options.sides
radius = self.options.radius * unit_factor
angle_ratio = self.options.angle_ratio
mirror_cells = self.options.mirror_cells
theta = (pi/2.)*(1 - 2./sides)
l = 2.*radius*cos(theta*(1.-angle_ratio))
a = 2.*radius*sin(pi/sides)
# b = sqrt(a*a + l*l - 2*a*l*cos(angle_ratio*theta))
# phi = abs(acos((l*l + b*b - a*a)/(2*l*b)))
# gamma = pi/2 - angle_ratio*theta - phi
# dy = b*cos(gamma)
# dx = b*sin(gamma)
dy = l * sin(theta * angle_ratio)
dx = l * cos(theta * angle_ratio) - a
add_attachment = self.options.add_attachment
attachment_percentage = self.options.attachment_percentage/100.
attachment_height = a*(attachment_percentage-1)*tan(angle_ratio*theta)
vertices = []
for i in range(sides + 1):
for j in range(lines + 1):
if mirror_cells:
vertices.append(Path((dx*((lines - j)%2) + a*i, dy*j), style='p', radius=vertex_radius))
else:
vertices.append(Path((dx*(lines - j) + a*i, dy*j), style='p', radius=vertex_radius))
# create a horizontal grid, then offset each line according to angle
grid_h = Path.generate_hgrid([0, a * sides], [0, dy * lines], lines, 'm')
if not mirror_cells:
# shift every mountain line of the grid to the right by increasing amounts
grid_h = Path.list_add(grid_h, [(i * dx, 0) for i in range(lines - 1, 0, -1)])
else:
# shift every OTHER mountain line of the grid a bit to the right
grid_h = Path.list_add(grid_h, [((i%2)*dx, 0) for i in range(lines-1, 0, -1)])
if add_attachment:
for i in range(lines%2, lines-1, 2):
# hacky solution, changes length of every other mountain line
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])
# create MV zigzag for Kresling pattern
zigzag = Kresling.generate_kresling_zigzag(sides, radius, angle_ratio, add_attachment)
zigzags = []
# duplicate zigzag pattern for desired number of cells
if not mirror_cells:
for i in range(lines):
zigzags.append(Path.list_add(zigzag, (i * dx, (lines - i) * dy)))
else:
zigzag_mirror = Path.list_reflect(zigzag, (0, lines * dy / 2), (dx, lines * dy / 2))
for i in range(lines):
if i % 2 == 1:
zigzags.append(Path.list_add(zigzag_mirror, (0, -(lines - i + (lines-1)%2) * dy)))
else:
zigzags.append(Path.list_add(zigzag, (0, (lines - i) * dy)))
# create edge strokes
if not mirror_cells:
self.edge_points = [
(a * sides , dy * lines), # bottom right
(0 , dy * lines), # bottom left
(dx * lines , 0), # top left
(dx * lines + a * sides, 0)] # top right
if add_attachment:
for i in range(lines):
x = dx * (lines - i) + a * (sides + attachment_percentage)
self.edge_points.append((x, dy * i))
self.edge_points.append((x, dy * i - attachment_height))
if i != lines - 1:
self.edge_points.append((x-dx-a*attachment_percentage, dy * (i + 1)))
pass
else:
self.edge_points = [(a * sides + (lines % 2)*dx, 0)]
for i in range(lines+1):
self.edge_points.append([((lines+i) % 2)*dx, dy*i])
self.edge_points.append([a * sides + ((lines+i) %2)*dx, lines*dy])
if add_attachment:
for i in range(lines + 1):
if not i%2 == 0:
self.edge_points.append([a*sides + (i%2)*(dx+a*attachment_percentage), dy*(lines - i) - (i%2)*attachment_height])
self.edge_points.append([a*sides + (i%2)*(dx+a*attachment_percentage), dy*(lines - i)])
if (i != lines):
self.edge_points.append([a * sides + (i % 2) * (dx + a * attachment_percentage), dy * (lines - i) + (i % 2) * attachment_height])
else:
self.edge_points.append([a * sides + (i % 2) * (dx + a * attachment_percentage), dy * (lines - i)])
else:
for i in range(lines + 1):
self.edge_points.append([a*sides + (i%2)*dx, dy*(lines - i)])
self.path_tree = [grid_h, zigzags, vertices]
if __name__ == '__main__':
Kresling().run()