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This commit is contained in:
Sridhar Ramesh
2018-01-30 18:06:19 -08:00
parent c28b81a230
commit c1dd5f1689
1 changed files with 119 additions and 124 deletions
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243
active_projects/WindingNumber.py
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@@ -201,7 +201,7 @@ class EquationSolver1d(GraphScene, ZoomedScene):
self.solveEquation()
def color_func(alpha):
def rev_to_color(alpha):
alpha = alpha % 1
colors = ["#FF0000", ORANGE, YELLOW, "#00FF00", "#0000FF", "#FF00FF"]
num_colors = len(colors)
@@ -211,119 +211,6 @@ def color_func(alpha):
return interpolate_color(colors[start_index], colors[end_index], beta)
# TODO: Perhaps have bullets (pulses) fade out and in at ends of line, instead of jarringly
# popping out and in?
#
# TODO: Perhaps have bullets change color corresponding to a function of their coordinates?
# This could involve some merging of functoinality with PiWalker
class LinePulser(ContinualAnimation):
def __init__(self, line, bullet_template, num_bullets, pulse_time, output_func = None, **kwargs):
self.line = line
self.num_bullets = num_bullets
self.pulse_time = pulse_time
self.bullets = [bullet_template.copy() for i in range(num_bullets)]
self.output_func = output_func
ContinualAnimation.__init__(self, VGroup(line, VGroup(*self.bullets)), **kwargs)
def update_mobject(self, dt):
alpha = self.external_time % self.pulse_time
start = self.line.get_start()
end = self.line.get_end()
for i in range(self.num_bullets):
position = interpolate(start, end,
np.true_divide((i + alpha),(self.num_bullets)))
self.bullets[i].move_to(position)
if self.output_func:
position_2d = (position[0], position[1])
rev = point_to_rev(self.output_func(position_2d))
color = color_func(rev)
self.bullets[i].set_color(color)
class ArrowCircleTest(Scene):
def construct(self):
circle_radius = 3
circle = Circle(radius = circle_radius, color = WHITE)
self.add(circle)
base_arrow = Arrow(circle_radius * 0.7 * RIGHT, circle_radius * 1.3 * RIGHT)
def rev_rotate(x, revs):
x.rotate(revs * TAU, about_point = ORIGIN)
x.set_color(color_func(revs))
return x
num_arrows = 8 * 3
arrows = [rev_rotate(base_arrow.copy(), (np.true_divide(i, num_arrows))) for i in range(num_arrows)]
arrows_vgroup = VGroup(*arrows)
self.play(ShowCreation(arrows_vgroup), run_time = 2.5, rate_func = None)
self.wait()
class FuncRotater(Animation):
CONFIG = {
"rotate_func" : lambda x : x # Func from alpha to revolutions
}
# Perhaps abstract this out into an "Animation updating from original object" class
def update_submobject(self, submobject, starting_submobject, alpha):
submobject.points = np.array(starting_submobject.points)
def update_mobject(self, alpha):
Animation.update_mobject(self, alpha)
angle_revs = self.rotate_func(alpha)
# We do a clockwise rotation
self.mobject.rotate(
-angle_revs * TAU,
about_point = ORIGIN
)
self.mobject.set_color(color_func(angle_revs))
class TestRotater(Scene):
def construct(self):
test_line = Line(ORIGIN, RIGHT)
self.play(FuncRotater(
test_line,
rotate_func = lambda x : x % 0.25,
run_time = 10))
# TODO: Be careful about clockwise vs. counterclockwise convention throughout!
# Make sure this is correct everywhere in resulting video.
class OdometerScene(Scene):
CONFIG = {
"rotate_func" : lambda x : np.sin(x * TAU),
"run_time" : 5,
"dashed_line_angle" : None,
"biased_display_start" : None
}
def construct(self):
radius = 1.3
circle = Circle(center = ORIGIN, radius = radius)
self.add(circle)
if self.dashed_line_angle:
dashed_line = DashedLine(ORIGIN, radius * RIGHT)
# Clockwise rotation
dashed_line.rotate(-self.dashed_line_angle * TAU, about_point = ORIGIN)
self.add(dashed_line)
num_display = DecimalNumber(0, include_background_rectangle = True)
num_display.move_to(2 * DOWN)
display_val_bias = 0
if self.biased_display_start != None:
display_val_bias = self.biased_display_start - self.rotate_func(0)
display_func = lambda alpha : self.rotate_func(alpha) + display_val_bias
base_arrow = Arrow(ORIGIN, RIGHT, buff = 0)
self.play(
FuncRotater(base_arrow, rotate_func = self.rotate_func),
ChangingDecimal(num_display, display_func),
run_time = self.run_time,
rate_func = None)
def point_to_rev((x, y)):
# Warning: np.arctan2 would happily discontinuously returns the value 0 for (0, 0), due to
# design choices in the underlying atan2 library call, but for our purposes, this is
@@ -463,8 +350,8 @@ class WalkerAnimation(Animation):
cur_point = self.coords_to_point(cur_x, cur_y)
self.mobject.walker.move_to(cur_point)
rev = self.rev_func(cur_coords)
self.mobject.walker.set_color(color_func(rev))
self.mobject.arrow.set_color(color_func(rev))
self.mobject.walker.set_color(rev_to_color(rev))
self.mobject.arrow.set_color(rev_to_color(rev))
self.mobject.arrow.rotate(
rev * TAU,
about_point = ORIGIN #self.mobject.arrow.get_start()
@@ -706,6 +593,119 @@ class EquationSolver2d(Scene):
self.wait()
# TODO: Perhaps have bullets (pulses) fade out and in at ends of line, instead of jarringly
# popping out and in?
#
# TODO: Perhaps have bullets change color corresponding to a function of their coordinates?
# This could involve some merging of functoinality with PiWalker
class LinePulser(ContinualAnimation):
def __init__(self, line, bullet_template, num_bullets, pulse_time, output_func = None, **kwargs):
self.line = line
self.num_bullets = num_bullets
self.pulse_time = pulse_time
self.bullets = [bullet_template.copy() for i in range(num_bullets)]
self.output_func = output_func
ContinualAnimation.__init__(self, VGroup(line, VGroup(*self.bullets)), **kwargs)
def update_mobject(self, dt):
alpha = self.external_time % self.pulse_time
start = self.line.get_start()
end = self.line.get_end()
for i in range(self.num_bullets):
position = interpolate(start, end,
np.true_divide((i + alpha),(self.num_bullets)))
self.bullets[i].move_to(position)
if self.output_func:
position_2d = (position[0], position[1])
rev = point_to_rev(self.output_func(position_2d))
color = rev_to_color(rev)
self.bullets[i].set_color(color)
class ArrowCircleTest(Scene):
def construct(self):
circle_radius = 3
circle = Circle(radius = circle_radius, color = WHITE)
self.add(circle)
base_arrow = Arrow(circle_radius * 0.7 * RIGHT, circle_radius * 1.3 * RIGHT)
def rev_rotate(x, revs):
x.rotate(revs * TAU, about_point = ORIGIN)
x.set_color(rev_to_color(revs))
return x
num_arrows = 8 * 3
arrows = [rev_rotate(base_arrow.copy(), (np.true_divide(i, num_arrows))) for i in range(num_arrows)]
arrows_vgroup = VGroup(*arrows)
self.play(ShowCreation(arrows_vgroup), run_time = 2.5, rate_func = None)
self.wait()
class FuncRotater(Animation):
CONFIG = {
"rotate_func" : lambda x : x # Func from alpha to revolutions
}
# Perhaps abstract this out into an "Animation updating from original object" class
def update_submobject(self, submobject, starting_submobject, alpha):
submobject.points = np.array(starting_submobject.points)
def update_mobject(self, alpha):
Animation.update_mobject(self, alpha)
angle_revs = self.rotate_func(alpha)
# We do a clockwise rotation
self.mobject.rotate(
-angle_revs * TAU,
about_point = ORIGIN
)
self.mobject.set_color(rev_to_color(angle_revs))
class TestRotater(Scene):
def construct(self):
test_line = Line(ORIGIN, RIGHT)
self.play(FuncRotater(
test_line,
rotate_func = lambda x : x % 0.25,
run_time = 10))
# TODO: Be careful about clockwise vs. counterclockwise convention throughout!
# Make sure this is correct everywhere in resulting video.
class OdometerScene(Scene):
CONFIG = {
"rotate_func" : lambda x : np.sin(x * TAU),
"run_time" : 5,
"dashed_line_angle" : None,
"biased_display_start" : None
}
def construct(self):
radius = 1.3
circle = Circle(center = ORIGIN, radius = radius)
self.add(circle)
if self.dashed_line_angle:
dashed_line = DashedLine(ORIGIN, radius * RIGHT)
# Clockwise rotation
dashed_line.rotate(-self.dashed_line_angle * TAU, about_point = ORIGIN)
self.add(dashed_line)
num_display = DecimalNumber(0, include_background_rectangle = True)
num_display.move_to(2 * DOWN)
display_val_bias = 0
if self.biased_display_start != None:
display_val_bias = self.biased_display_start - self.rotate_func(0)
display_func = lambda alpha : self.rotate_func(alpha) + display_val_bias
base_arrow = Arrow(ORIGIN, RIGHT, buff = 0)
self.play(
FuncRotater(base_arrow, rotate_func = self.rotate_func),
ChangingDecimal(num_display, display_func),
run_time = self.run_time,
rate_func = None)
#############
# Above are mostly general tools; here, we list, in order, finished or near-finished scenes
@@ -909,7 +909,6 @@ class LoopSplitScene(Scene):
bullet_template,
num_bullets = 4,
pulse_time = 1,
color_func = None,
**kwargs):
line = Line(start, end, **kwargs)
anim = LinePulser(
@@ -1086,13 +1085,6 @@ class DiffOdometer(OdometerScene):
# Writing new Pi walker scenes by parametrizing general template
# Generalizing Pi walker stuff to make bullets on pulsing lines change colors dynamically according to
# function traced out
# Ask about tracked mobject, which is probably very useful for our animations
# (let's add a ChangingDecimal outputting winding number calculations tracking Pi walkers,
# particularly in EquationSolver2d)
# ----
# Pi creature emotion stuff
@@ -1103,4 +1095,7 @@ class DiffOdometer(OdometerScene):
# Domain coloring
# TODO: Add to camera an option for low-quality background than other rendering, helpful
# for previews
# FIN