Software: pattern player, web page with a design library, GRBL tools
- python3 -m sandtable web: local web page to play designs from a library of 27 built-in patterns, upload .thr or .svg, pause/skip/stop, jog and calibrate. Reconnects by itself when the USB cable comes back. - Plays .thr files and built-in generators with an erase spiral between them, constant ball speed, host-side homing on stock GRBL 1.1 (Uno + CNC shield), FluidNC for the ESP32 board. - Home switch guard: patterns never press the switch, so a press means lost steps and stops the machine at once with an alert. - lineart.py turns SVG line drawings into one continuous path. - Tests against a GRBL simulator. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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"""Built-in pattern generators. Each returns a theta-rho path (theta in radians, continuous;
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rho 0..1) that starts and ends at the centre or the edge, like a .thr file."""
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import math
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TAU = 2 * math.pi
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# ---------------------------------------------------------------- helpers
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def densify_xy(xy, step):
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"""Split straight Cartesian segments so points are at most `step` apart (unit-disc units).
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Needed for shapes made of straight lines: the table moves in theta and rho, so a long
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move between two far-apart points would come out as a curve."""
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out = [xy[0]]
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for (x1, y1), (x2, y2) in zip(xy, xy[1:]):
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n = max(1, int(math.ceil(math.hypot(x2 - x1, y2 - y1) / step)))
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for i in range(1, n + 1):
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t = i / n
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out.append((x1 + (x2 - x1) * t, y1 + (y2 - y1) * t))
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return out
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def _through_centre(xy, near=0.03):
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"""Where a segment passes close to the centre, add the exact centre point, so the arm can
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swing round there (with the ball at rho 0, drawing nothing) instead of a few mm out."""
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out = [xy[0]]
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for (x1, y1), (x2, y2) in zip(xy, xy[1:]):
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dx, dy = x2 - x1, y2 - y1
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L2 = dx * dx + dy * dy
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if L2 > 0:
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t = -(x1 * dx + y1 * dy) / L2
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if 0 < t < 1 and math.hypot(x1 + t * dx, y1 + t * dy) < near:
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out.append((0.0, 0.0))
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out.append((x2, y2))
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return out
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def xy_to_polar(xy):
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"""Cartesian (unit disc) -> continuous theta-rho. At the centre the arm turns in place to the
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next direction before the ball moves out again."""
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pts = []
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prev = None
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at_centre = False
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for x, y in _through_centre(xy):
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r = min(1.0, math.hypot(x, y))
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if r < 1e-6:
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th = prev if prev is not None else 0.0
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at_centre = True
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else:
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a = math.atan2(y, x)
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th = a if prev is None else prev + ((a - prev + math.pi) % TAU - math.pi)
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if at_centre:
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pts.append((th, 0.0)) # turn in place at the centre
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at_centre = False
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pts.append((th, r))
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prev = th
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return pts
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def _normalise(xy):
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m = max(math.hypot(x, y) for x, y in xy) or 1.0
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return [(x / m, y / m) for x, y in xy]
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# ---------------------------------------------------------------- generators
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def spiral(loops=20, direction='out'):
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"""Archimedean spiral between the centre and the edge."""
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n = int(loops * 180)
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pts = [(TAU * loops * i / n, i / n) for i in range(n + 1)]
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if direction == 'in':
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pts = [(th, 1 - r) for th, r in pts]
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return pts
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def rose(petals=5, denominator=1, copies=1, twist_deg=0.0):
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"""Rose curve r = cos(k*theta) with k = petals/denominator, repeated `copies` times,
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each copy turned by `twist_deg`. Starts and ends at the edge."""
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k = petals / denominator
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span = math.pi * denominator if (petals * denominator) % 2 else TAU * denominator
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xy = []
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for c in range(int(copies)):
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rot = math.radians(twist_deg) * c
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n = int(span / math.radians(0.5))
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for i in range(n + 1):
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t = span * i / n
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r = math.cos(k * t)
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xy.append((r * math.cos(t + rot), r * math.sin(t + rot)))
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return xy_to_polar(xy)
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def spirograph(big=96, small=35, pen=0.85):
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"""Hypotrochoid: a pen `pen` (fraction of the small radius) on a wheel of radius `small`
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rolling inside a ring of radius `big`. Starts and ends at the edge."""
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R, r, d = float(big), float(small), float(pen) * float(small)
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g = math.gcd(int(big), int(small)) or 1
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span = TAU * int(small) / g
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n = int(span / math.radians(0.4))
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xy = []
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for i in range(n + 1):
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t = span * i / n
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xy.append(((R - r) * math.cos(t) + d * math.cos((R - r) / r * t),
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(R - r) * math.sin(t) - d * math.sin((R - r) / r * t)))
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return xy_to_polar(_normalise(xy))
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def polygons(sides=6, layers=40, twist_deg=3.0):
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"""Nested regular polygons from the edge to the centre, each turned a little: a twisted star."""
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xy = []
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for L in range(int(layers) + 1):
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rad = 1 - L / layers
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rot = math.radians(twist_deg) * L
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for v in range(int(sides) + 1):
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a = rot + TAU * v / sides
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xy.append((rad * math.cos(a), rad * math.sin(a)))
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xy.append((0.0, 0.0))
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return xy_to_polar(densify_xy(xy, 0.004))
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def ripples(waves=9, amplitude=0.035, loops=17):
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"""A spiral from the edge to the centre with a wave along it: rings of ripples."""
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n = int(loops * 360)
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pts = [(0.0, 1.0)] # start at the edge, where the erase spiral ends
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for i in range(n + 1):
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th = TAU * loops * i / n
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base = (1 - amplitude) * (1 - i / n)
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fade = min(1.0, base / (4 * amplitude)) if amplitude else 0.0 # flatten near the centre
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r = base + amplitude * fade * math.sin(waves * th)
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pts.append((th, max(0.0, min(1.0, r))))
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pts.append((pts[-1][0], 0.0))
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return pts
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def _polar_path(pts, step=0.02):
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"""Join theta-rho corner points with short steps (at most `step` across the sand, unit disc),
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so radial lines stay straight and moves along the rim stay on the rim."""
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out = [pts[0]]
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for (t0, r0), (t1, r1) in zip(pts, pts[1:]):
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n = max(1, int(math.ceil(max(abs(r1 - r0), max(r0, r1) * abs(t1 - t0)) / step)))
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out += [(t0 + (t1 - t0) * i / n, r0 + (r1 - r0) * i / n) for i in range(1, n + 1)]
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return out
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def _start_at_edge(xy):
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"""A closed loop (first point == last) restarted at its outermost point."""
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i0 = max(range(len(xy)), key=lambda i: math.hypot(*xy[i]))
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return xy[i0:] + xy[1:i0 + 1]
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def string_art(points=101, step=40):
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"""Straight chords between `points` pegs round the rim, each chord `step` pegs on, like
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string art. The chords outline a circle in the middle."""
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n, k = int(points), int(step)
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m = n // math.gcd(n, k)
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xy = [(math.cos(TAU * (j * k % n) / n), math.sin(TAU * (j * k % n) / n)) for j in range(m + 1)]
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return xy_to_polar(densify_xy(xy, 0.01))
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def lissajous(a=3, b=2, phase_deg=90.0, copies=1, twist_deg=0.0):
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"""Lissajous figure x = sin(a t + phase), y = sin(b t), stretched to fill the disc. With
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copies, it is drawn again `copies` times, each turned `twist_deg` further, joined along the edge."""
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a, b, ph = int(a), int(b), math.radians(float(phase_deg))
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n = 3000 * max(a, b)
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xy = [(math.sin(a * TAU * i / n + ph), math.sin(b * TAU * i / n)) for i in range(n + 1)]
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base = _start_at_edge(_normalise(xy))
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out, tw = [], math.radians(float(twist_deg))
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for c in range(int(copies)):
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ca, sa = math.cos(tw * c), math.sin(tw * c)
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pol = xy_to_polar([(x * ca - y * sa, x * sa + y * ca) for x, y in base])
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if out:
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k = round((out[-1][0] + tw - pol[0][0]) / TAU) # carry on from where the last copy ended
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pol = [(t + TAU * k, r) for t, r in pol]
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out += _polar_path([out[-1], pol[0]])[1:]
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out += pol if not out else pol[1:]
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return out
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def sunburst(rays=24):
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"""`rays` straight lines through the centre, evenly spaced, joined by short arcs along the
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edge: a starburst."""
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n = int(rays)
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d = math.pi / n
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pts, t = [], 0.0
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for _ in range(n):
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pts += [(t, 1.0), (t, 0.0), (t + math.pi, 0.0), (t + math.pi, 1.0), (t + math.pi + d, 1.0)]
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t += math.pi + d
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return _polar_path(pts)
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def spiral_arms(arms=4, turns=1.0):
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"""A galaxy: `arms` spiral arms, each `turns` turns long, drawn out along one arm and back
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in along the next."""
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n, T = int(arms) // 2 * 2 or 2, float(turns)
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pts = [(0.0, 0.0)]
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for k in range(0, n, 2):
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a, b = TAU * k / n, TAU * (k + 1) / n
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pts += [(a, 0.0), (a + TAU * T, 1.0), (b + TAU * T, 1.0), (b, 0.0)]
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pts.append((TAU, 0.0))
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return _polar_path(pts)
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def test_f():
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"""The letter F, to check that patterns aren't mirrored. Reads normally when the table is right."""
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xy = [(0, 0), (-0.2, 0.1), (-0.2, 0.8), (0.3, 0.8), (-0.2, 0.8), (-0.2, 0.45), (0.15, 0.45),
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(-0.2, 0.45), (-0.2, 0.1), (0, 0)]
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return xy_to_polar(densify_xy(xy, 0.004))
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GENERATORS = {
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'spiral': (spiral, {'loops': 20, 'direction': 'out'}),
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'rose': (rose, {'petals': 5, 'denominator': 1, 'copies': 1, 'twist_deg': 0.0}),
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'spirograph': (spirograph, {'big': 96, 'small': 35, 'pen': 0.85}),
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'polygons': (polygons, {'sides': 6, 'layers': 40, 'twist_deg': 3.0}),
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'ripples': (ripples, {'waves': 9, 'amplitude': 0.035, 'loops': 17}),
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'string_art': (string_art, {'points': 101, 'step': 40}),
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'lissajous': (lissajous, {'a': 3, 'b': 2, 'phase_deg': 90.0, 'copies': 1, 'twist_deg': 0.0}),
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'sunburst': (sunburst, {'rays': 24}),
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'spiral_arms': (spiral_arms, {'arms': 4, 'turns': 1.0}),
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'test_f': (test_f, {}),
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}
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def generate(name, **params):
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if name not in GENERATORS:
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raise KeyError(f'unknown pattern {name!r}; choose from {", ".join(GENERATORS)}')
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fn, defaults = GENERATORS[name]
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args = dict(defaults)
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for k, v in params.items():
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if k not in defaults:
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raise KeyError(f'{name} has no setting {k!r}; settings: {", ".join(defaults) or "none"}')
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args[k] = type(defaults[k])(v) if not isinstance(defaults[k], str) else str(v)
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return fn(**args)
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