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calesthioandHanzo Dev
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11 production pipelines, 47 tools, 124 agent skills. Supports cloud APIs (fal.ai, OpenAI, ElevenLabs, Suno, HeyGen, Runway) and free local providers (diffusers, Piper TTS, WAN 2.1, Hunyuan, CogVideo). Co-authored-by: Hanzo Dev <[email protected]>
104 lines
3.2 KiB
Python
104 lines
3.2 KiB
Python
"""
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Visualization of lozenge (rhombus) tiling patterns.
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Shows how lozenges can tile the plane in a honeycomb-like pattern.
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"""
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from manimlib import *
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import math
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def get_lozenge(side_length=1):
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"""Create a lozenge (rhombus) shape with 60/120 degree angles."""
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verts = [math.sqrt(3) * LEFT, UP, math.sqrt(3) * RIGHT, DOWN]
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result = Polygon(*verts)
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result.scale(side_length / get_norm(verts[0] - verts[1]))
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return result
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class LozengeTiling(InteractiveScene):
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"""
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Demonstrates lozenge tiling of the plane.
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Shows:
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1. A single lozenge with angle labels
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2. How it tiles to create a row
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3. How rows tile to fill the plane
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4. The effect of stretching on the tiling
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"""
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def construct(self):
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# Add Lozenge
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lozenge = get_lozenge()
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lozenge.scale(4)
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lozenge.set_stroke(TEAL)
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arc1 = Arc(-30 * DEGREES, 60 * DEGREES, arc_center=lozenge.get_left(), radius=0.75)
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arc2 = Arc(-150 * DEGREES, 120 * DEGREES, arc_center=lozenge.get_top(), radius=0.5)
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arc1_label = Tex(R"60^\circ")
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arc1_label.next_to(arc1, RIGHT, MED_SMALL_BUFF)
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arc2_label = Tex(R"120^\circ")
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arc2_label.next_to(arc2, DOWN, MED_SMALL_BUFF)
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angle_labels = VGroup(
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arc1, arc1_label,
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arc2, arc2_label,
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)
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angle_labels.set_z_index(1)
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self.play(
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ShowCreation(lozenge, time_span=(1, 2.5)),
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VShowPassingFlash(lozenge.copy().insert_n_curves(20).set_stroke(width=5), time_width=2),
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run_time=3
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)
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self.play(
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Write(arc1_label),
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ShowCreation(arc1),
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)
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self.play(
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Write(arc2_label),
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ShowCreation(arc2),
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)
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self.add(angle_labels)
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self.wait()
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# Tile the plane
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verts = lozenge.get_anchors()[:4]
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v1 = verts[1] - verts[0]
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v2 = verts[-1] - verts[0]
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row = VGroup(lozenge.copy().shift(x * v1) for x in range(-10, 11))
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rows = VGroup(row.copy().shift(y * v2) for y in range(-10, 11))
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tiles = VGroup(*rows.family_members_with_points())
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tiles.sort(lambda p: get_norm(p))
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for mob in row, rows:
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mob.set_fill(GREY, 1)
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mob.set_stroke(WHITE, 2)
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mob.shift(-tiles[0].get_center())
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self.play(
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self.frame.animate.set_height(40),
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lozenge.animate.set_fill(GREY, 1),
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LaggedStart(
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(TransformFromCopy(lozenge, tile, path_arc=30 * DEGREES) for tile in row),
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lag_ratio=1.0 / len(row),
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time_span=(1, 3),
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),
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run_time=4
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)
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self.play(
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LaggedStart(
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(TransformFromCopy(row, row2, path_arc=30 * DEGREES) for row2 in rows),
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lag_ratio=1.0 / len(rows),
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run_time=3,
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),
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)
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self.clear()
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self.add(rows, angle_labels)
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# Squish it
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self.play(FadeOut(angle_labels))
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rows.save_state()
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self.play(rows.animate.stretch(2, 0), run_time=2)
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self.wait()
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self.play(Restore(rows), run_time=2)
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self.play(Write(angle_labels))
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self.wait()
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