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Merge pull request #95 from 3b1b/fourier-work

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Fourier work
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Grant Sanderson 2018-01-28 16:27:53 -08:00 • committed by GitHub
commit 994749cead
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3 changed files with 45 additions and 33 deletions
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64
active_projects/fourier.py
View file

@ -4190,15 +4190,11 @@ class FourierEndScreen(PatreonEndScreen):
class Thumbnail(Scene):
def construct(self):
title = TextMobject("Fourier\\\\", "Visualized")
title[1].highlight(YELLOW)
title[1].set_stroke(RED, 1)
title.highlight(YELLOW)
title.set_stroke(RED, 1)
title.set_stroke(RED, 2)
title.scale(2.5)
title.add_background_rectangle()
# title.to_edge(UP)
# self.add(title)
def func(t):
return np.cos(2*TAU*t) + np.cos(3*TAU*t) + np.cos(5*t)
fourier = get_fourier_transform(func, -5, 5)
@ -4206,36 +4202,40 @@ class Thumbnail(Scene):
graph = FunctionGraph(func, x_min = -5, x_max = 5)
graph.highlight(BLUE)
fourier_graph = FunctionGraph(fourier, x_min = 0, x_max = 6)
fourier_graph.highlight(RED_C)
fourier_graph.highlight(YELLOW)
for g in graph, fourier_graph:
g.stretch_to_fit_height(2)
g.stretch_to_fit_width(10)
g.set_stroke(width = 8)
arrow = Vector(
2.5*DOWN,
rectangular_stem_width = 0.2,
tip_length = 0.5,
color = WHITE
)
q_mark = TextMobject("?").scale(2)
q_mark.highlight(YELLOW)
q_mark.set_stroke(RED, 1)
arrows = VGroup(*it.chain(*zip(
[q_mark.copy() for x in range(5)],
[arrow.copy() for x in range(5)]
)))
# arrows.submobjects.pop()
# arrows.arrange_submobjects(RIGHT, buff = MED_LARGE_BUFF)
group = VGroup(graph, title, fourier_graph)
arrows = VGroup(*[arrow.copy() for x in range(2)])
arrows.arrange_submobjects(RIGHT, buff = 6*LARGE_BUFF)
# group = VGroup(graph, arrows, fourier_graph)
group.arrange_submobjects(DOWN)
# group.next_to(title, DOWN, MED_LARGE_BUFF)
arrows.move_to(title)
title.shift(MED_SMALL_BUFF*UP)
graph.shift(SMALL_BUFF*UP)
self.add(arrows, group)
pol_graphs = VGroup()
for f in np.linspace(1.98, 2.02, 7):
pol_graph = ParametricFunction(
lambda t : complex_to_R3(
(2+np.cos(2*TAU*t)+np.cos(3*TAU*t))*np.exp(-complex(0, TAU*f*t))
),
t_min = -5,
t_max = 5,
num_graph_points = 200,
)
pol_graph.match_color(graph)
pol_graph.scale_to_fit_height(2)
pol_graphs.add(pol_graph)
pol_graphs.arrange_submobjects(RIGHT, buff = LARGE_BUFF)
pol_graphs.gradient_highlight(BLUE_C, YELLOW)
pol_graphs.match_width(graph)
pol_graphs.set_stroke(width = 2)
self.clear()
title.center().to_edge(UP)
pol_graphs.scale_to_fit_width(2*SPACE_WIDTH - 1)
pol_graphs.center()
title.move_to(pol_graphs)
title.shift(SMALL_BUFF*LEFT)
graph.next_to(title, UP)
fourier_graph.next_to(title, DOWN)
self.add(pol_graphs, title, graph, fourier_graph)

3
mobject/vectorized_mobject.py
View file

@ -353,7 +353,8 @@ class VMobject(Mobject):
for index in range(num_curves):
curr_bezier_points = self.points[3*index:3*index+4]
num_inter_curves = sum(index_allocation == index)
alphas = np.arange(0, num_inter_curves+1)/float(num_inter_curves)
alphas = np.linspace(0, 1, num_inter_curves+1)
# alphas = np.arange(0, num_inter_curves+1)/float(num_inter_curves)
for a, b in zip(alphas, alphas[1:]):
new_points = partial_bezier_points(
curr_bezier_points, a, b

11
topics/geometry.py
View file

@ -333,6 +333,17 @@ class Line(VMobject):
self.shift(new_start - self.get_start())
return self
def insert_n_anchor_points(self, n):
if not self.path_arc:
n_anchors = self.get_num_anchor_points()
new_num_points = 3*(n_anchors + n)+1
self.points = np.array([
self.point_from_proportion(alpha)
for alpha in np.linspace(0, 1, new_num_points)
])
else:
VMobject.insert_n_anchor_points(self, n)
class DashedLine(Line):
CONFIG = {
"dashed_segment_length" : 0.05