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migurski/inscribe-hatch.py

Created January 5, 2025 02:26
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inscribe-hatch.py
#!/usr/bin/env python3
import itertools
import typing
import math
import cairo
import shapely.affinity
import shapely.geometry
DISTANCE_CUTOFF = 2 # max jump length to bridge with a curve
OUTLINE_DISTANCE = .5 # ideally half the line width
INSET_DISTANCE = .9 # distance from outside edge to begin hatching
HATCH_OVERLAP = .3 # amount to overlap hatch lines to account for slop; 0 = no overlap
CURVE_JOIN_DISTANCE = .25
BACK_AND_FORTH = True
class Segment (typing.NamedTuple):
'''
'''
row: int
x1: float
y1: float
x2: float
y2: float
def distance(self, other):
''' Distance from self end to other beginning
'''
return math.hypot(self.x2 - other.x1, self.y2 - other.y1)
class Fragment (typing.NamedTuple):
'''
'''
p1: int
p2: int
p: int
class MultiPath (typing.NamedTuple):
'''
'''
points: shapely.geometry.MultiPoint
fragments: typing.List[typing.List[Fragment]]
def get_hatch_segment_xs(xmin, xmax):
'''
'''
if not BACK_AND_FORTH:
# All parallel lines point in the same direction and ends do not connect
return itertools.cycle([(xmax, xmin)])
return itertools.cycle([(xmin, xmax), (xmax, xmin)])
def fill_hatch_segments(polygon):
'''
'''
assert polygon.type == 'Polygon'
xmin, y, xmax, ymax = polygon.bounds
rows, xs = itertools.count(), get_hatch_segment_xs(xmin, xmax)
segments = []
for (row, (x1, x2)) in zip(rows, xs):
line = shapely.geometry.LineString([(x1, y), (x2, y)])
if y > ymax:
break
elif not line.intersects(polygon):
continue
else:
y += 1
scan = line.intersection(polygon)
segments.extend([
Segment(
row,
part.coords[0][0],
part.coords[0][1],
part.coords[-1][0],
part.coords[-1][1],
)
for part in getattr(scan, 'geoms', [scan])
if part.type == 'LineString'
])
return segments
def fill_hatch_sequences(polygon):
'''
'''
assert polygon.type == 'Polygon'
distance_cutoff = DISTANCE_CUTOFF if BACK_AND_FORTH else 0
segments = fill_hatch_segments(polygon)
sequences = []
while segments:
segment = segments.pop(0)
sequence = [(segment.x1, segment.y1), (segment.x2, segment.y2)]
while True:
others = [
(i, other)
for (i, other) in enumerate(segments)
if abs(other.row - segment.row) == 1
and segment.distance(other) < distance_cutoff
]
if not others:
sequences.append(sequence)
break
others.sort(key=lambda o: segment.distance(o[1]))
segment = segments.pop(others[0][0])
prior_length = abs(sequence[-1][-2] - sequence[-2][-2])
follow_length = abs(segment.x2 - segment.x1)
prior_diff = min(CURVE_JOIN_DISTANCE, prior_length)
follow_diff = min(CURVE_JOIN_DISTANCE, follow_length)
if segment.row % 2 == 0:
# pointing right
prior_diff, follow_diff = -prior_diff, -follow_diff
sequence[-1] = tuple(
list(sequence[-1][:-2]) + [sequence[-1][-2] - prior_diff, sequence[-1][-1]]
)
x3 = segment.x1 - follow_diff
y3 = segment.y1
x1, y1 = sequence[-1][-2] + 2*prior_diff, sequence[-1][-1]
x2, y2 = x3 + 2*follow_diff, y3
sequence.extend([
(x1, y1, x2, y2, x3, y3),
(segment.x2, segment.y2),
])
return sequences
def inscribed_hatch_multipath(polygon, scale, angle=None):
'''
'''
assert polygon.type == 'Polygon'
# Add a bit of overlap to the hatched lines when the Axidraw is sloppy
_scale = scale / (1.0 + HATCH_OVERLAP)
# Track the best option of the angle deltas we try
_count, multipath = math.inf, None
# Try several candidate angle deltas?
angles = [angle] if angle is not None else (0, 26, 52, 77, 103, 129, 154)
for _angle in angles:
transformed_polygon = shapely.affinity.rotate(
shapely.affinity.scale(polygon, 1/_scale, 1/_scale, origin=(0, 0)),
_angle,
origin=(0, 0),
)
transformed_multipath = native_hatch_multipath(transformed_polygon)
untransformed_points = shapely.affinity.scale(
shapely.affinity.rotate(transformed_multipath.points, -_angle, origin=(0, 0)),
_scale,
_scale,
origin=(0, 0),
)
if len(transformed_multipath.fragments) < _count:
# Choose a new, better multipath candidate
_count = len(transformed_multipath.fragments)
multipath = MultiPath(untransformed_points, transformed_multipath.fragments)
if _count <= 3:
# Eh, good enough
break
return multipath
def native_hatch_multipath(polygon):
'''
'''
assert polygon.type == 'Polygon'
points, fragments = [], []
outline = polygon.buffer(-OUTLINE_DISTANCE).boundary
for line in getattr(outline, 'geoms', [outline]):
if line.type == 'LineString' and True:
fragments.append([
Fragment(None, None, i)
for i in range(len(points), len(points) + len(line.coords))
])
points.extend(line.coords)
inset_multipolygon = polygon.buffer(-INSET_DISTANCE)
if inset_multipolygon.type not in ('Polygon', 'MultiPolygon') or inset_multipolygon.area == 0:
return MultiPath(shapely.geometry.MultiPoint(points), fragments)
for inset_polygon in getattr(inset_multipolygon, 'geoms', [inset_multipolygon]):
for sequence in fill_hatch_sequences(inset_polygon):
head, tail = sequence[0], sequence[1:]
assert len(head) == 2
fragments.append([Fragment(None, None, len(points))])
points.append(head[-2:])
for part in tail:
assert len(part) in (2, 6)
if len(part) == 2:
fragments[-1].append(Fragment(None, None, len(points)))
points.append(part)
else:
fragments[-1].append(Fragment(len(points), len(points)+1, len(points)+2))
points.extend([part[:2], part[2:4], part[4:6]])
return MultiPath(shapely.geometry.MultiPoint(points), fragments)
def draw_shapely_line_geom(ctx, geom):
if getattr(geom, 'geoms', False):
parts = [part for part in geom.geoms]
else:
parts = [geom]
for part in parts:
try:
coords = part.coords
except NotImplementedError:
continue
if not coords:
continue
ctx.move_to(*coords[0])
for coord in coords[1:]:
ctx.line_to(*coord)
def draw_multipath_strokes(ctx, multipath):
'''
'''
for fragments in multipath.fragments:
head, tail = fragments[0], fragments[1:]
p = multipath.points.geoms[head.p]
ctx.move_to(p.x, p.y)
for fragment in tail:
if fragment.p1 is None and fragment.p2 is None:
p = multipath.points.geoms[fragment.p]
ctx.line_to(p.x, p.y)
else:
p1 = multipath.points.geoms[fragment.p1]
p2 = multipath.points.geoms[fragment.p2]
p = multipath.points.geoms[fragment.p]
ctx.curve_to(p1.x, p1.y, p2.x, p2.y, p.x, p.y)
ctx.stroke()
def calculate_hatch_angle(shape):
'''
'''
rectangle = shape.minimum_rotated_rectangle.exterior
(x1, y1), (x2, y2), (x3, y3) = rectangle.coords[:3]
if math.hypot(x3 - x2, y3 - y2) < math.hypot(x2 - x1, y2 - y1):
return 180 * math.atan2(y2 - y3, x3 - x2) / math.pi
else:
return 180 * math.atan2(y1 - y2, x2 - x1) / math.pi
if __name__ == '__main__':
font_svg = __import__('font-svg')
color_cube = __import__('color-cube')
FONT = font_svg.load_font('fonts/EMSReadability.svg')
with cairo.SVGSurface('out.svg', 8.5*72, 5.5*72) as surface:
context = cairo.Context(surface)
hotdog1 = shapely.geometry.LineString([(72, 72), (144, 144)]).buffer(36, 5)
draw_multipath_strokes(
context,
inscribed_hatch_multipath(hotdog1, 9, None),
)
hotdog2 = shapely.geometry.LineString([(216, 72), (252, 144)]).buffer(36, 5)
draw_multipath_strokes(
context,
inscribed_hatch_multipath(hotdog2, 6, None),
)
hotdog3 = shapely.geometry.LineString([(288, 72), (360, 108)]).buffer(36, 5)
draw_multipath_strokes(
context,
inscribed_hatch_multipath(hotdog3, 3, None),
)
context.stroke()
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out.svg
<?xml version="1.0" encoding="UTF-8"?>
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<g id="surface1">
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