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‎solid/examples/koch.py‎

Lines changed: 95 additions & 92 deletions
Original file line numberDiff line numberDiff line change
@@ -1,34 +1,38 @@
11
#! /usr/bin/env python
22
# -*- coding: utf-8 -*-
3-
import os, sys, re
3+
import os
4+
import sys
5+
import re
46

57
from solid import *
68
from solid.utils import *
79

810
from euclid import *
911

10-
ONE_THIRD = 1/3.0
12+
ONE_THIRD = 1 / 3.0
13+
1114

1215
def affine_combination(a, b, weight=0.5):
1316
'''
1417
Note that weight is a fraction of the distance between self and other.
1518
So... 0.33 is a point .33 of the way between self and other.
1619
'''
1720
if hasattr(a, 'z'):
18-
return Point3( (1-weight)*a.x + weight*b.x,
19-
(1-weight)*a.y + weight*b.y,
20-
(1-weight)*a.z + weight*b.z,
21-
)
21+
return Point3((1 - weight) * a.x + weight * b.x,
22+
(1 - weight) * a.y + weight * b.y,
23+
(1 - weight) * a.z + weight * b.z,
24+
)
2225
else:
23-
return Point2( (1-weight)*a.x + weight*b.x,
24-
(1-weight)*a.y + weight*b.y,
25-
)
26-
27-
def kochify_3d(a, b, c,
28-
ab_weight=0.5, bc_weight=0.5, ca_weight=0.5,
29-
pyr_a_weight=ONE_THIRD, pyr_b_weight=ONE_THIRD, pyr_c_weight=ONE_THIRD,
30-
pyr_height_weight=ONE_THIRD
31-
):
26+
return Point2((1 - weight) * a.x + weight * b.x,
27+
(1 - weight) * a.y + weight * b.y,
28+
)
29+
30+
31+
def kochify_3d(a, b, c,
32+
ab_weight=0.5, bc_weight=0.5, ca_weight=0.5,
33+
pyr_a_weight=ONE_THIRD, pyr_b_weight=ONE_THIRD, pyr_c_weight=ONE_THIRD,
34+
pyr_height_weight=ONE_THIRD
35+
):
3236
'''
3337
Point3s a, b, and c must be coplanar and define a face
3438
ab_weight, etc define the subdivision of the original face
@@ -39,52 +43,52 @@ def kochify_3d(a, b, c,
3943
new_a = affine_combination(a, b, ab_weight)
4044
new_b = affine_combination(b, c, bc_weight)
4145
new_c = affine_combination(c, a, ca_weight)
42-
43-
triangles.extend( [[a, new_a, new_c], [b, new_b, new_a], [c, new_c, new_b]])
44-
45-
avg_pt_x = a.x*pyr_a_weight + b.x*pyr_b_weight + c.x*pyr_c_weight
46-
avg_pt_y = a.y*pyr_a_weight + b.y*pyr_b_weight + c.y*pyr_c_weight
47-
avg_pt_z = a.z*pyr_a_weight + b.z*pyr_b_weight + c.z*pyr_c_weight
48-
46+
47+
triangles.extend([[a, new_a, new_c], [b, new_b, new_a], [c, new_c, new_b]])
48+
49+
avg_pt_x = a.x * pyr_a_weight + b.x * pyr_b_weight + c.x * pyr_c_weight
50+
avg_pt_y = a.y * pyr_a_weight + b.y * pyr_b_weight + c.y * pyr_c_weight
51+
avg_pt_z = a.z * pyr_a_weight + b.z * pyr_b_weight + c.z * pyr_c_weight
52+
4953
center_pt = Point3(avg_pt_x, avg_pt_y, avg_pt_z)
50-
51-
# The top of the pyramid will be on a normal
54+
55+
# The top of the pyramid will be on a normal
5256
ab_vec = b - a
5357
bc_vec = c - b
5458
ca_vec = a - c
5559
normal = ab_vec.cross(bc_vec).normalized()
56-
avg_side_length = (abs(ab_vec) + abs(bc_vec) + abs(ca_vec))/3
60+
avg_side_length = (abs(ab_vec) + abs(bc_vec) + abs(ca_vec)) / 3
5761
pyr_h = avg_side_length * pyr_height_weight
5862
pyr_pt = LineSegment3(center_pt, normal, pyr_h).p2
59-
60-
63+
6164
triangles.extend([[new_a, pyr_pt, new_c], [new_b, pyr_pt, new_a], [new_c, pyr_pt, new_b]])
62-
65+
6366
return triangles
64-
6567

66-
def kochify(seg, height_ratio=0.33, left_loc= 0.33, midpoint_loc=0.5, right_loc= 0.66):
68+
69+
def kochify(seg, height_ratio=0.33, left_loc=0.33, midpoint_loc=0.5, right_loc=0.66):
6770
a, b = seg.p1, seg.p2
6871
l = affine_combination(a, b, left_loc)
6972
c = affine_combination(a, b, midpoint_loc)
7073
r = affine_combination(a, b, right_loc)
71-
# The point of the new triangle will be height_ratio * abs(seg) long,
74+
# The point of the new triangle will be height_ratio * abs(seg) long,
7275
# and run perpendicular to seg, through c.
7376
perp = seg.v.cross().normalized()
74-
75-
c_height = height_ratio* abs(seg)
77+
78+
c_height = height_ratio * abs(seg)
7679
perp_pt = LineSegment2(c, perp, -c_height).p2
77-
80+
7881
# For the moment, assume perp_pt is on the right side of seg.
7982
# Will confirm this later if needed
80-
return [ LineSegment2(a, l),
81-
LineSegment2(l, perp_pt),
82-
LineSegment2(perp_pt, r),
83-
LineSegment2(r, b)]
83+
return [LineSegment2(a, l),
84+
LineSegment2(l, perp_pt),
85+
LineSegment2(perp_pt, r),
86+
LineSegment2(r, b)]
87+
8488

8589
def main_3d(out_dir):
8690
gens = 4
87-
91+
8892
# Parameters
8993
ab_weight = 0.5
9094
bc_weight = 0.5
@@ -94,113 +98,112 @@ def main_3d(out_dir):
9498
pyr_c_weight = ONE_THIRD
9599
pyr_height_weight = ONE_THIRD
96100
pyr_height_weight = ONE_THIRD
97-
# pyr_height_weight = .25
98-
101+
# pyr_height_weight = .25
102+
99103
all_polys = union()
100-
104+
101105
# setup
102106
ax, ay, az = 100, -100, 100
103-
bx, by, bz = 100, 100,-100
107+
bx, by, bz = 100, 100, -100
104108
cx, cy, cz = -100, 100, 100
105109
dx, dy, dz = -100, -100, -100
106-
generations = [ [[ Point3(ax, ay, az), Point3(bx, by, bz), Point3(cx, cy, cz)],
107-
[ Point3(bx, by, bz), Point3(ax, ay, az), Point3(dx, dy, dz)],
108-
[ Point3(ax, ay, az), Point3(cx, cy, cz), Point3(dx, dy, dz)],
109-
[ Point3(cx, cy, cz), Point3(bx, by, bz), Point3(dx, dy, dz)],
110-
]
110+
generations = [[[Point3(ax, ay, az), Point3(bx, by, bz), Point3(cx, cy, cz)],
111+
[Point3(bx, by, bz), Point3(ax, ay, az), Point3(dx, dy, dz)],
112+
[Point3(ax, ay, az), Point3(cx, cy, cz), Point3(dx, dy, dz)],
113+
[Point3(cx, cy, cz), Point3(bx, by, bz), Point3(dx, dy, dz)],
111114
]
112-
115+
]
116+
113117
# Recursively generate snowflake segments
114118
for g in range(1, gens):
115-
generations.append([])
116-
for a, b, c in generations[g-1]:
117-
new_tris = kochify_3d(a, b, c,
118-
ab_weight, bc_weight, ca_weight,
119-
pyr_a_weight, pyr_b_weight,pyr_c_weight,
120-
pyr_height_weight)
119+
generations.append([])
120+
for a, b, c in generations[g - 1]:
121+
new_tris = kochify_3d(a, b, c,
122+
ab_weight, bc_weight, ca_weight,
123+
pyr_a_weight, pyr_b_weight, pyr_c_weight,
124+
pyr_height_weight)
121125
# new_tris = kochify_3d( a, b, c)
122126
generations[g].extend(new_tris)
123-
127+
124128
# Put all generations into SCAD
125129
orig_length = abs(generations[0][0][1] - generations[0][0][0])
126130
for g, a_gen in enumerate(generations):
127131
# Move each generation up in y so it doesn't overlap the others
128-
h = orig_length *1.5 * g
129-
132+
h = orig_length * 1.5 * g
133+
130134
# Build the points and triangles arrays that SCAD needs
131135
faces = []
132136
points = []
133-
for a,b,c in a_gen:
134-
points.extend([ [a.x, a.y, a.z], [b.x, b.y, b.z], [c.x, c.y, c.z]])
137+
for a, b, c in a_gen:
138+
points.extend([[a.x, a.y, a.z], [b.x, b.y, b.z], [c.x, c.y, c.z]])
135139
t = len(points)
136-
faces.append([t-3, t-2, t-1])
137-
140+
faces.append([t - 3, t - 2, t - 1])
141+
138142
# Do the SCAD
139143
edges = [list(range(len(points)))]
140144
all_polys.add(up(h)(
141-
polyhedron(points=points, faces=faces)
142-
)
145+
polyhedron(points=points, faces=faces)
146+
)
143147
)
144-
148+
145149
file_out = os.path.join(out_dir, 'koch_3d.scad')
146150
cur_file = __file__
147-
print("%(cur_file)s: SCAD file written to: %(file_out)s"%vars())
148-
scad_render_to_file(all_polys, file_out, include_orig_code=True)
151+
print("%(cur_file)s: SCAD file written to: %(file_out)s" % vars())
152+
scad_render_to_file(all_polys, file_out, include_orig_code=True)
153+
149154

150155
def main(out_dir):
151156
# Parameters
152157
midpoint_weight = 0.5
153158
height_ratio = 0.25
154159
left_loc = ONE_THIRD
155160
midpoint_loc = 0.5
156-
right_loc = 2*ONE_THIRD
161+
right_loc = 2 * ONE_THIRD
157162
gens = 5
158-
159-
# Results
163+
164+
# Results
160165
all_polys = union()
161-
166+
162167
# setup
163168
ax, ay = 0, 0
164169
bx, by = 100, 0
165170
cx, cy = 50, 86.6
166-
base_seg1 = LineSegment2( Point2(ax, ay), Point2(cx, cy))
167-
base_seg2 = LineSegment2( Point2(cx, cy), Point2(bx, by))
168-
base_seg3 = LineSegment2( Point2(bx, by), Point2(ax, ay))
171+
base_seg1 = LineSegment2(Point2(ax, ay), Point2(cx, cy))
172+
base_seg2 = LineSegment2(Point2(cx, cy), Point2(bx, by))
173+
base_seg3 = LineSegment2(Point2(bx, by), Point2(ax, ay))
169174
generations = [[base_seg1, base_seg2, base_seg3]]
170-
171-
175+
172176
# Recursively generate snowflake segments
173177
for g in range(1, gens):
174-
generations.append([])
175-
for seg in generations[g-1]:
178+
generations.append([])
179+
for seg in generations[g - 1]:
176180
generations[g].extend(kochify(seg, height_ratio, left_loc, midpoint_loc, right_loc))
177181
# generations[g].extend(kochify(seg))
178-
182+
179183
# # Put all generations into SCAD
180184
orig_length = abs(generations[0][0])
181185
for g, a_gen in enumerate(generations):
182-
points = [s.p1 for s in a_gen ]
186+
points = [s.p1 for s in a_gen]
183187
# points.append(a_gen[-1].p2) # add the last point
184-
188+
185189
rect_offset = 10
186-
190+
187191
# Just use arrays for points so SCAD understands
188192
points = [[p.x, p.y] for p in points]
189-
193+
190194
# Move each generation up in y so it doesn't overlap the others
191-
h = orig_length *1.5 * g
192-
195+
h = orig_length * 1.5 * g
196+
193197
# Do the SCAD
194198
edges = [list(range(len(points)))]
195-
all_polys.add(forward(h)(polygon(points=points, paths=edges )))
196-
197-
file_out = os.path.join(out_dir,'koch.scad')
198-
cur_file = __file__
199-
print("%(cur_file)s: SCAD file written to: %(file_out)s "%vars())
200-
scad_render_to_file(all_polys, file_out, include_orig_code=True )
199+
all_polys.add(forward(h)(polygon(points=points, paths=edges)))
200+
201+
file_out = os.path.join(out_dir, 'koch.scad')
202+
cur_file = __file__
203+
print("%(cur_file)s: SCAD file written to: %(file_out)s " % vars())
204+
scad_render_to_file(all_polys, file_out, include_orig_code=True)
201205

202206
if __name__ == '__main__':
203207
out_dir = sys.argv[1] if len(sys.argv) > 1 else os.curdir
204208
main_3d(out_dir)
205209
main(out_dir)
206-

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