# Author: alexn11 (alexn11.gh@gmail.com)
# Created: 2019-05-18
# Copyright (C) 2019, 2020 Alexandre De Zotti
# License: MIT License
import sys
import math
import cmath
import mathsvg
smallest_interval = 0.0003
density = 0.5
max_length = 1.
allowed_object_types = [ "disconnected-straight-brush", "compact-cantor-bouquet", "one-sided-hairy-circle" ]
def print_help_and_leave():
print("\nUsage:\n")
print("> " + sys.argv [0] + " object-type " + " --smallest-interval float --density float --max-length float")
print("\nObject type must one of these: " + str(allowed_object_types) + "\n")
sys.exit()
object_type = allowed_object_types [0]
if(len(sys.argv) > 1):
object_type = sys.argv [1]
if(object_type not in allowed_object_types):
if(sys.argv [1] == "--help"):
print_help_and_leave()
message = "Object type should be one from: "
for object_type in allowed_object_types:
message += object_type + ", "
print(message)
raise Exception("Wrong command line argument")
if(len(sys.argv) > 2):
argc = len(sys.argv)
arg_index = 2
while(arg_index < argc):
if(sys.argv [arg_index] == "--smallest-interval"):
smallest_interval = float(sys.argv [arg_index + 1])
arg_index += 2
elif(sys.argv [arg_index] == "--density"):
density = float(sys.argv [arg_index + 1])
arg_index += 2
elif(sys.argv [arg_index] == "--max-length"):
max_length = float(sys.argv [arg_index + 1])
arg_index += 2
elif(sys.argv [arg_index] == "--help"):
print_help_and_leave()
arg_index += 1
def generate_intermediate_lengths(left_element, right_element, smallest_interval, density):
lengths = []
left_x = left_element [0]
left_length = left_element [1]
right_x = right_element [0]
right_length = right_element [1]
width = right_x - left_x
next_width = density * width
while(abs(next_width) > smallest_interval):
next_x = left_x + next_width
next_length = (next_width * left_length + (width - next_width) * right_length) / width
lengths.append(( next_x, next_length, True ))
right_x = next_x
right_length = next_length
width = next_width
next_width = density * width
if(width > 0):
lengths.reverse()
#print(lengths)
return lengths
def compute_lengths(max_length, smallest_interval, density, max_level = 188):
# last coordinate indicate if an intermediate length can fit in between (given the smallest_interval restriction)
level = 0
left_element = (0., max_length, True)
right_element = (1., max_length, True)
lengths_list = [ left_element, right_element ]
while(level < max_level):
next_level = level + 1
left_index = 0
right_index = 1
interval_count = 0
while(left_index < len(lengths_list) - 1):
right_index = left_index + 1
left_element = lengths_list [left_index]
right_element = lengths_list [right_index]
if((not left_element [2]) and (not right_element [2])):
left_index = right_index
else:
interval_count += 1
middle_coordinate = 0.5 * (right_element [0] + left_element [0])
middle_element = (middle_coordinate, 0, True)
new_lengths_list = generate_intermediate_lengths(left_element, middle_element, smallest_interval, density)
new_lengths_list += (generate_intermediate_lengths(right_element, middle_element, smallest_interval, density))
if(len(new_lengths_list) == 0):
lengths_list [left_index] = (lengths_list [left_index] [0], lengths_list [left_index] [1], False)
lengths_list [right_index] = (lengths_list [right_index] [0], lengths_list [right_index] [1], False)
left_index = right_index
else:
lengths_list = lengths_list [ : left_index + 1 ] + new_lengths_list + lengths_list [ right_index : ]
left_index = right_index + len(new_lengths_list)
if(interval_count == 0):
break
return lengths_list
image_name = object_type + ".svg"
image_main_scale = 800
padding = 0.1
lengths = compute_lengths(max_length, smallest_interval, density)
#print(lengths)
if(object_type == "disconnected-straight-brush"):
view_window = ((-padding, -padding), (1 + padding, 1 + padding))
image = mathsvg.SvgImage(pixel_density = image_main_scale, view_window = view_window)
for element in lengths:
image.draw_line_segment( [ element [0], 0 ], [ element [0], element [1] ] )
elif(object_type == "compact-cantor-bouquet"):
view_window = ((-1 - padding, -1 - padding), (1 + padding, 1 + padding))
image = mathsvg.SvgImage(pixel_density = image_main_scale, view_window = view_window)
for element in lengths:
endpoint = element [1] * cmath.exp(2. * math.pi * element [0] * 1.j)
image.draw_line_segment( [ 0, 0 ], [ endpoint. real, endpoint.imag ] )
elif(object_type == "one-sided-hairy-circle"):
view_window = ((-1 - padding, -1 - padding), (1 + padding, 1 + padding))
image = mathsvg.SvgImage(pixel_density = image_main_scale, view_window = view_window)
image.draw_circle((0, 0), 0.5)
for element in lengths:
direction = cmath.exp(2. * math.pi * element [0] * 1.j)
start_point = 0.5 * direction
endpoint = start_point + 0.5 * element [1] * direction
image.draw_line_segment( [ start_point.real, start_point.imag ], [ endpoint. real, endpoint.imag ] )
image.save(image_name)
