mirror of
https://github.com/3b1b/manim.git
synced 2025-08-21 05:44:04 +00:00
Setup position on ShowCommutativeDiagram
This commit is contained in:
Grant Sanderson
parent
e922f4980f
commit
f5d3742ff8
1 changed files with 209 additions and 15 deletions
|
|
@ -659,6 +659,7 @@ class FourierMachineScene(Scene):
|
|||
"y_max" : 2,
|
||||
"y_axis_config" : {"unit_size" : 0.8},
|
||||
},
|
||||
"time_label_t" : 3.4,
|
||||
"circle_plane_config" : {
|
||||
"x_radius" : 2.5,
|
||||
"y_radius" : 2.5,
|
||||
|
|
@ -709,7 +710,10 @@ class FourierMachineScene(Scene):
|
|||
labels = VGroup(time_label, intensity_label)
|
||||
for label in labels:
|
||||
label.scale(self.text_scale_val)
|
||||
time_label.next_to(time_axes.coords_to_point(3.5,0), DOWN)
|
||||
time_label.next_to(
|
||||
time_axes.coords_to_point(self.time_label_t,0),
|
||||
DOWN
|
||||
)
|
||||
intensity_label.next_to(time_axes.y_axis.get_top(), RIGHT)
|
||||
time_axes.labels = labels
|
||||
time_axes.add(labels)
|
||||
|
|
@ -1524,6 +1528,7 @@ class ShowLowerFrequency(DrawFrequencyPlot):
|
|||
v_lines = self.get_v_lines_indicating_periods(freq)
|
||||
self.v_lines_indicating_periods = v_lines
|
||||
wps_label = self.get_winding_frequency_label()
|
||||
ChangeDecimalToValue(wps_label[0], freq).update(1)
|
||||
wps_label.add_to_back(BackgroundRectangle(wps_label))
|
||||
wps_label.move_to(self.circle_plane, UP)
|
||||
|
||||
|
|
@ -1616,6 +1621,8 @@ class ShowLinearity(DrawFrequencyPlot):
|
|||
"high_freq_color": YELLOW,
|
||||
"low_freq_color": PINK,
|
||||
"sum_color": GREEN,
|
||||
"low_freq" : 2.0,
|
||||
"high_freq" : 3.0,
|
||||
}
|
||||
def construct(self):
|
||||
self.remove(self.pi_creature)
|
||||
|
|
@ -1624,15 +1631,17 @@ class ShowLinearity(DrawFrequencyPlot):
|
|||
self.point_out_two_spikes()
|
||||
|
||||
def show_sum_of_signals(self):
|
||||
low_freq, high_freq = 2.0, 3.0
|
||||
low_freq, high_freq = self.low_freq, self.high_freq
|
||||
axes = self.get_time_axes()
|
||||
axes_copy = axes.copy()
|
||||
low_freq_graph = self.get_cosine_wave(
|
||||
freq = low_freq, scale_val = 0.5,
|
||||
)
|
||||
high_freq_graph = self.get_cosine_wave(
|
||||
freq = high_freq, scale_val = 0.5,
|
||||
low_freq_graph, high_freq_graph = [
|
||||
self.get_cosine_wave(
|
||||
freq = freq,
|
||||
scale_val = 0.5,
|
||||
shift_val = 0.55,
|
||||
)
|
||||
for freq in low_freq, high_freq
|
||||
]
|
||||
sum_graph = self.get_time_graph(
|
||||
lambda t : sum([
|
||||
low_freq_graph.underlying_function(t),
|
||||
|
|
@ -1659,7 +1668,7 @@ class ShowLinearity(DrawFrequencyPlot):
|
|||
graph.highlight(color)
|
||||
label.highlight(color)
|
||||
sum_label[0].match_color(low_freq_graph)
|
||||
sum_label[2].match_color(highlight_freq_graph)
|
||||
sum_label[2].match_color(high_freq_graph)
|
||||
|
||||
self.add(axes, low_freq_graph)
|
||||
self.play(
|
||||
|
|
@ -1674,19 +1683,204 @@ class ShowLinearity(DrawFrequencyPlot):
|
|||
ReplacementTransform(axes_copy, axes),
|
||||
ReplacementTransform(high_freq_graph, sum_graph),
|
||||
ReplacementTransform(low_freq_graph, sum_graph),
|
||||
ReplacementTransform(
|
||||
VGroup(low_freq_label, high_freq_label),
|
||||
sum_label
|
||||
)
|
||||
|
||||
)
|
||||
self.wait()
|
||||
self.graph = graph
|
||||
|
||||
def show_winding_with_sum_graph(self):
|
||||
pass
|
||||
graph = self.graph
|
||||
circle_plane = self.get_circle_plane()
|
||||
frequency_axes = self.get_frequency_axes()
|
||||
pol_graph = self.get_polarized_mobject(graph, freq = 0.0)
|
||||
|
||||
wps_label = self.get_winding_frequency_label()
|
||||
ChangeDecimalToValue(wps_label[0], 0.0).update(1)
|
||||
wps_label.add_to_back(BackgroundRectangle(wps_label))
|
||||
wps_label.move_to(circle_plane, UP)
|
||||
|
||||
v_lines = self.get_v_lines_indicating_periods(0.001)
|
||||
self.v_lines_indicating_periods = v_lines
|
||||
|
||||
dot = Dot(
|
||||
self.get_pol_graph_center_of_mass(),
|
||||
color = self.center_of_mass_color
|
||||
)
|
||||
self.center_of_mass_dot = dot
|
||||
self.generate_center_of_mass_dot_update_anim()
|
||||
|
||||
fourier_graph = self.get_fourier_transform_graph(graph)
|
||||
fourier_graph_update = self.get_fouier_graph_drawing_update_anim(
|
||||
fourier_graph
|
||||
)
|
||||
x_coord_label = TextMobject(
|
||||
"x-coordinate of center of mass"
|
||||
)
|
||||
x_coord_label.scale(self.text_scale_val)
|
||||
x_coord_label.next_to(
|
||||
self.frequency_axes.input_to_graph_point(
|
||||
self.signal_frequency, fourier_graph
|
||||
), UP
|
||||
)
|
||||
x_coord_label.highlight(self.center_of_mass_color)
|
||||
almost_fourier_label = TextMobject(
|
||||
"``Almost-Fourier transform''"
|
||||
)
|
||||
|
||||
self.generate_fourier_dot_transform(fourier_graph)
|
||||
|
||||
self.play(LaggedStart(
|
||||
FadeIn, VGroup(
|
||||
circle_plane, wps_label,
|
||||
frequency_axes, x_coord_label,
|
||||
),
|
||||
run_time = 1,
|
||||
))
|
||||
self.play(
|
||||
ReplacementTransform(graph.copy(), pol_graph),
|
||||
GrowFromCenter(dot)
|
||||
)
|
||||
freqs = [
|
||||
self.low_freq, self.high_freq,
|
||||
self.frequency_axes.x_max
|
||||
]
|
||||
for freq in freqs:
|
||||
self.change_frequency(
|
||||
freq,
|
||||
added_anims = [fourier_graph_update],
|
||||
run_time = 8,
|
||||
rate_func = bezier([0, 0, 1, 1]),
|
||||
)
|
||||
|
||||
def point_out_two_spikes(self):
|
||||
pass
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
class ShowCommutativeDiagram(ShowLinearity):
|
||||
CONFIG = {
|
||||
"time_axes_config" : {
|
||||
"x_max" : 1.9,
|
||||
"y_max" : 2.0,
|
||||
"y_min" : -2.0,
|
||||
"y_axis_config" : {
|
||||
"unit_size" : 0.5,
|
||||
},
|
||||
"x_axis_config" : {
|
||||
"numbers_to_show" : [1],
|
||||
}
|
||||
},
|
||||
"time_label_t" : 1.5,
|
||||
"frequency_axes_config" : {
|
||||
"x_min" : 0.0,
|
||||
"x_max" : 4.0,
|
||||
"y_min" : -0.1,
|
||||
"y_max" : 0.5,
|
||||
"y_axis_config" : {
|
||||
"unit_size" : 1.5,
|
||||
"tick_frequency" : 0.5,
|
||||
},
|
||||
}
|
||||
}
|
||||
def construct(self):
|
||||
self.remove(self.pi_creature)
|
||||
|
||||
#Setup axes
|
||||
time_axes = self.get_time_axes()
|
||||
time_axes.scale(0.8)
|
||||
ta_group = VGroup(
|
||||
time_axes, time_axes.deepcopy(), time_axes.deepcopy(),
|
||||
)
|
||||
ta_group.arrange_submobjects(DOWN, buff = MED_LARGE_BUFF)
|
||||
ta_group.to_corner(UP+LEFT, buff = MED_SMALL_BUFF)
|
||||
|
||||
freq_axes = Axes(**self.frequency_axes_config)
|
||||
freq_axes.highlight(TEAL)
|
||||
freq_label = TextMobject("Frequency")
|
||||
freq_label.scale(self.text_scale_val)
|
||||
freq_label.next_to(freq_axes.x_axis, DOWN, SMALL_BUFF, RIGHT)
|
||||
freq_axes.add(freq_label)
|
||||
freq_axes.scale(0.8)
|
||||
fa_group = VGroup(
|
||||
freq_axes, freq_axes.deepcopy(), freq_axes.deepcopy()
|
||||
)
|
||||
VGroup(ta_group[1], fa_group[1]).shift(MED_LARGE_BUFF*UP)
|
||||
for ta, fa in zip(ta_group, fa_group):
|
||||
if ta is not ta_group[0]:
|
||||
ta.remove(ta.labels)
|
||||
fa.remove(fa[-1])
|
||||
fa.next_to(
|
||||
ta.x_axis.main_line, RIGHT,
|
||||
submobject_to_align = fa.x_axis.main_line
|
||||
)
|
||||
fa.to_edge(RIGHT)
|
||||
|
||||
## Add graphs
|
||||
funcs = [
|
||||
lambda t : np.cos(2*TAU*t),
|
||||
lambda t : np.cos(3*TAU*t),
|
||||
]
|
||||
funcs.append(lambda t : funcs[0](t)+funcs[1](t))
|
||||
colors = [
|
||||
self.low_freq_color,
|
||||
self.high_freq_color,
|
||||
self.sum_color,
|
||||
]
|
||||
labels = [
|
||||
TextMobject("2 Hz"),
|
||||
TextMobject("3 Hz"),
|
||||
# TextMobject("2 Hz", "+", "3 Hz"),
|
||||
VectorizedPoint()
|
||||
]
|
||||
for func, color, label, ta, fa in zip(funcs, colors, labels, ta_group, fa_group):
|
||||
time_graph = ta.get_graph(func)
|
||||
time_graph.highlight(color)
|
||||
label.highlight(color)
|
||||
label.scale(0.75)
|
||||
label.next_to(time_graph, UP, SMALL_BUFF)
|
||||
fourier = self.get_fourier_transform(
|
||||
func, ta.x_min, 4*ta.x_max
|
||||
)
|
||||
fourier_graph = fa.get_graph(fourier)
|
||||
fourier_graph.highlight(self.center_of_mass_color)
|
||||
|
||||
arrow = Arrow(
|
||||
ta.x_axis.main_line, fa.x_axis.main_line,
|
||||
color = WHITE,
|
||||
buff = MED_LARGE_BUFF,
|
||||
)
|
||||
words = TextMobject("Almost-Fourier \\\\ transform")
|
||||
words.scale(0.6)
|
||||
words.next_to(arrow, UP)
|
||||
arrow.words = words
|
||||
self.add(arrow, words)
|
||||
|
||||
ta.graph = time_graph
|
||||
ta.graph_label = label
|
||||
ta.arrow = arrow
|
||||
ta.add(time_graph, label)
|
||||
fa.graph = fourier_graph
|
||||
fa.add(fourier_graph)
|
||||
# labels[-1][0].match_color(labels[0])
|
||||
# labels[-1][2].match_color(labels[1])
|
||||
|
||||
|
||||
#Add arrows
|
||||
sum_arrows = VGroup()
|
||||
for group in ta_group, fa_group:
|
||||
arrow = Arrow(
|
||||
group[1].graph, group[2].graph,
|
||||
color = WHITE,
|
||||
buff = SMALL_BUFF
|
||||
)
|
||||
arrow.scale(0.8, about_edge = UP)
|
||||
arrow.words = TextMobject("Sum").scale(0.75)
|
||||
arrow.words.next_to(arrow, RIGHT, buff = MED_SMALL_BUFF)
|
||||
sum_arrows.add(arrow)
|
||||
self.add(arrow, arrow.words)
|
||||
|
||||
self.add(ta_group, fa_group)
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue