def construct(self):
words, s = TextMobject(["Pseudo-Hilbert Curve", "s"]).split()
pre_words = TextMobject("Order 1")
pre_words.next_to(words, LEFT, buff = 0.5)
s.next_to(words, RIGHT, buff = 0.05, aligned_edge = DOWN)
cluster = Mobject(pre_words, words, s)
cluster.center()
cluster.scale(0.7)
cluster.to_edge(UP, buff = 0.3)
cluster.highlight(GREEN)
grid1 = Grid(1, 1)
grid2 = Grid(2, 2)
curve = HilbertCurve(order = 1)
self.add(words, s)
self.dither()
self.play(Transform(
s, pre_words,
path_func = path_along_arc(-np.pi/3)
))
self.dither()
self.play(ShowCreation(grid1))
self.dither()
self.play(ShowCreation(grid2))
self.dither()
kwargs = {
"run_time" : 5,
"rate_func" : None
}
self.play(ShowCreation(curve, **kwargs))
self.dither()
def get_triangles(self):
triangle = Polygon(LEFT / np.sqrt(3),
UP,
RIGHT / np.sqrt(3),
color=GREEN)
triangles = Mobject(triangle.copy().scale(0.5).shift(LEFT), triangle,
triangle.copy().scale(0.3).shift(0.5 * UP + RIGHT))
triangles.center()
return triangles
def construct(self, order):
start_color, end_color = RED, GREEN
curve = HilbertCurve(order = order)
line = Line(5*LEFT, 5*RIGHT)
for mob in curve, line:
mob.gradient_highlight(start_color, end_color)
freq_line = get_freq_line()
freq_line.replace(line, stretch = True)
unit = 6./(2**order) #sidelength of pixel
up = unit*UP
right = unit*RIGHT
lower_left = 3*(LEFT+DOWN)
squares = Mobject(*[
Square(
side_length = unit,
color = WHITE
).shift(x*right+y*up)
for x, y in it.product(range(2**order), range(2**order))
])
squares.center()
targets = Mobject()
for square in squares.submobjects:
center = square.get_center()
distances = np.apply_along_axis(
lambda p : np.linalg.norm(p-center),
1,
curve.points
)
index_along_curve = np.argmin(distances)
fraction_along_curve = index_along_curve/float(curve.get_num_points())
target = square.copy().center().scale(0.8/(2**order))
line_index = int(fraction_along_curve*line.get_num_points())
target.shift(line.points[line_index])
targets.add(target)
self.add(squares)
self.play(ShowCreation(
curve,
run_time = 5,
rate_func = None
))
self.dither()
self.play(
Transform(curve, line),
Transform(squares, targets),
run_time = 3
)
self.dither()
self.play(ShowCreation(freq_line))
self.dither()
def get_triangles(self):
triangle = Polygon(
LEFT/np.sqrt(3),
UP,
RIGHT/np.sqrt(3),
color = GREEN
)
triangles = Mobject(
triangle.copy().scale(0.5).shift(LEFT),
triangle,
triangle.copy().scale(0.3).shift(0.5*UP+RIGHT)
)
triangles.center()
return triangles