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whirlpool.py
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whirlpool.py
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# Generate a whirlpool (or screw shell) from triangles
# This method is based in the one described in Spirals
# by Tomoko Fuse for Whirlpool Spirals.
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.path import Path
import matplotlib as mpl
from math import *
import copy
def distance(a, b):
x2 = (a[0] - b[0])**2
y2 = (a[1] - b[1])**2
return sqrt(x2 + y2)
class wp_angles:
def __init__(self):
self.beta = 0
self.alpha = 0
self.gamma = 0
class point:
def __init__(self, x, y):
self.x = x
self.y = y
def lengthTo(self, p):
x2 = (self.x-p.x)**2
y2 = (self.y-p.y)**2
return sqrt(x2 + y2)
def pts(self):
return [self.x, self.y]
def negative(self):
return point(self.x, -self.y)
def pointFrom(self, length, angle):
x = self.x + length*sin(radians(angle))
y = self.y + length*cos(radians(angle))
return point(x, y)
def atan_deg(pt1, pt2):
x = pt2[0] - pt1[0]
y = pt2[1] - pt1[1]
print("atan %f %f => %f"%(x, y, degrees(atan2(x,y))))
return degrees(atan2(x,y))
def law_sines(length, ang_denom, ang_mult):
val = length*sin(radians(ang_mult)) / sin(radians(ang_denom))
return abs(val)
def update_angle_offset(angle_offset, rho):
for i in range(len(angle_offset)):
if angle_offset[i] > 0.0001: # epsilon
angle_offset[i] = rho
return angle_offset
def make_basic_triangle_path(origin, ac_len, basic):
a = point(origin[0], origin[1])
c = a.pointFrom(ac_len, 0.0)
ab_len = law_sines(ac_len, basic.beta, basic.gamma)
b = a.pointFrom(ab_len, basic.alpha)
vertices = [(a.x, a.y), (b.x, b.y), (c.x, c.y), (a.x, a.y)]
path = Path(vertices)
return path
def make_plot(prefix='wp', show_plot=True, polygon_sides=3, rotation_rho=10, spirality_sigma=20,
N=10, glue_tab = False,
cut_tip = True, cut_bottom_func=None,
angle_offsets = None):
fig, ax = plt.subplots()
name = '{}_poly{}_rho{}_sig{}_N{}'.format(prefix,
polygon_sides, int(rotation_rho), int(spirality_sigma), N)
exterior_base = 90.0 + rotation_rho/2.0
poly = wp_angles()
poly.beta = 360.0/polygon_sides
poly.alpha = (180.0 - poly.beta)/2.0
poly.gamma = 2.0 * poly.alpha
basic = wp_angles()
basic.beta = exterior_base - poly.alpha
basic.alpha = spirality_sigma
basic.gamma = 180.0 - basic.alpha - basic.beta
print(basic.alpha, basic.beta, basic.gamma)
#FIXME: Check validity
# standard whirlpool
if angle_offsets is None:
original_angle_offsets = [rotation_rho*x for x in list(range(polygon_sides))]
angle_offsets = [rotation_rho*x for x in list(range(polygon_sides))]
ac_len = 10.0
row_origin = [0.0, 0.0]
rows = []
triangles = []
for layer in range(N):
# create a basic triangle of ac_len with angles given
path = make_basic_triangle_path(row_origin, ac_len, basic)
print(path.vertices)
color = ["red", "green", "blue", "orange", "yellow", "cyan"]
start = row_origin
row = []
for n in range(polygon_sides):
r = mpl.transforms.Affine2D().rotate_deg_around(
path.vertices[0][0], path.vertices[0][1],
-angle_offsets[n])
path = path.transformed(r)
# put triangle in position at the angle_offset and position
row.append(path)
print(color[n])
print(path)
path = make_basic_triangle_path(origin = path.vertices[2], ac_len=ac_len, basic=basic)
# end poly for
rows.append(row) # big matrix of paths so we can make a cut path
# Calculate angle offsets then move row_origin
ac_len = distance(row[0].vertices[1], row[1].vertices[1])
angoff = atan_deg(row[0].vertices[1], row[1].vertices[1]) - original_angle_offsets[1]
for n in range(polygon_sides):
angle_offsets[n] = original_angle_offsets[n] + angoff
b = point(row[0].vertices[1][0],row[0].vertices[1][1])
a = b.pointFrom(-ac_len, angoff)
row_origin = [a.x, a.y]
print(row_origin, ac_len)
print(angle_offsets)
# end for each layer of triangles
# make an outline for cutting, use cut_tip and cut_bottom to control it
cut_vertices = []
for r in rows: # start at 0,0 and go clockwise, adding each A point in the column
cut_vertices.append(r[0].vertices[0])
if cut_tip:
path = rows[-1][0]
pta = path.vertices[0]
ptb = path.vertices[1]
ab_mid = (pta + ptb)/2.0
rot = mpl.transforms.Affine2D().rotate_deg_around(ab_mid[0], ab_mid[1], 180.0)
v = path.transformed(rot).vertices[2]
cut_vertices.append(v)
for n in range(polygon_sides): # add B points of the top (smallest) row
cut_vertices.append(rows[-1][n].vertices[1])
# else calculate the meeting point and use that
# Fixme: add that
# calculate the tip point, rho angle and then isoceles triangle
# will need the vertical scores to tip point, ok to aappend a row to rows
# add tip point to cut_vertices
# add B point of the last triangle rows[-1][-1]
for i in range(N): # back down the column using the C points on this side
cut_vertices.append(rows[-(i+1)][-1].vertices[2])
if cut_bottom_func is None:
for n in range(polygon_sides): # along the wide bottom until back to start
cut_vertices.append(rows[0][-(n+1)].vertices[0])
cut_path = Path(cut_vertices)
patch = patches.PathPatch(cut_path, facecolor='k', alpha=0.05, edgecolor='k')
ax.add_patch(patch)
# add all the trangles to the plot
for r in rows:
for n in range(polygon_sides):
patch = patches.PathPatch(r[n], facecolor=color[n], alpha=0.75, edgecolor='k')
ax.add_patch(patch)
plt.axis('off')
plt.box(False)
ax.set_aspect(1), ax.autoscale()
plt.savefig(name + ".svg")
if show_plot: plt.title(name), plt.show()
make_plot(prefix='wp', show_plot=True, polygon_sides=4,
rotation_rho=20, spirality_sigma=40,
N=8, glue_tab = False,
cut_tip = True, angle_offsets = None)