def generate_discrete_path(self):
points = self.cycloid.points
tops = list(self.layer_tops)
tops.append(tops[-1]-self.layer_thickness)
indices = [
np.argmin(np.abs(points[:, 1]-top))
for top in tops
]
self.bend_points = points[indices[1:-1]]
self.path_angles = []
self.discrete_path = Mobject1D(
color = YELLOW,
density = 3*DEFAULT_POINT_DENSITY_1D
)
for start, end in zip(indices, indices[1:]):
start_point, end_point = points[start], points[end]
self.discrete_path.add_line(
start_point, end_point
)
self.path_angles.append(
angle_of_vector(start_point-end_point)-np.pi/2
)
self.discrete_path.add_line(
points[end], SPACE_WIDTH*RIGHT+(self.layer_tops[-1]-1)*UP
)
def construct(self):
curve = HilbertCurve(order=1)
grid = Grid(2, 2, stroke_width=1)
self.add(grid, curve)
for order in range(2, 6):
self.dither()
new_grid = Grid(2**order, 2**order, stroke_width=1)
self.play(ShowCreation(new_grid), Animation(curve))
self.remove(grid)
grid = new_grid
self.play(Transform(curve, HilbertCurve(order=order)))
square = Square(side_length=6, color=WHITE)
square.corner = Mobject1D()
square.corner.add_line(3 * DOWN, ORIGIN)
square.corner.add_line(ORIGIN, 3 * RIGHT)
square.digest_mobject_attrs()
square.scale(2**(-5))
square.corner.highlight(
Color(rgb=curve.rgbs[curve.get_num_points() / 3]))
square.shift(
grid.get_corner(UP+LEFT)-\
square.get_corner(UP+LEFT)
)
self.dither()
self.play(FadeOut(grid), FadeOut(curve), FadeIn(square))
self.play(ApplyMethod(square.replace, grid))
self.dither()
def generate_discrete_path(self):
points = self.cycloid.points
tops = [mob.get_top()[1] for mob in self.layers]
tops.append(tops[-1] - self.layers[0].get_height())
indices = [np.argmin(np.abs(points[:, 1] - top)) for top in tops]
self.bend_points = points[indices[1:-1]]
self.path_angles = []
self.discrete_path = Mobject1D(color=WHITE,
density=3 * DEFAULT_POINT_DENSITY_1D)
for start, end in zip(indices, indices[1:]):
start_point, end_point = points[start], points[end]
self.discrete_path.add_line(start_point, end_point)
self.path_angles.append(
angle_of_vector(start_point - end_point) - np.pi / 2)
self.discrete_path.add_line(
points[end], SPACE_WIDTH * RIGHT + (tops[-1] - 0.5) * UP)
