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Merge branch 'master' of github.com:3b1b/manim into lighthouse-grant

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This commit is contained in:
Grant Sanderson 2018-02-26 19:04:09 -08:00
commit ae41269d36
6 changed files with 274 additions and 54 deletions
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281
active_projects/WindingNumber.py
View file

@ -33,6 +33,9 @@ from topics.graph_scene import *
# (and it will be done, but first I'll figure out what I'm doing with all this...)
# -SR
# This turns counterclockwise revs into their color. Beware, we use CCW angles
# in all display code, but generally think in this video's script in terms of
# CW angles
def rev_to_rgba(alpha):
alpha = (0.5 - alpha) % 1 # For convenience, to go CW from red on left instead of CCW from right
# 0 is red, 1/6 is yellow, 1/3 is green, 2/3 is blue
@ -76,7 +79,7 @@ def point_to_rgba(point):
rgba = rev_to_rgba(rev)
base_size = np.sqrt(point[0]**2 + point[1]**2)
rescaled_size = np.sqrt(base_size/(base_size + 1))
return rgba * rescaled_size
return rgba * [rescaled_size, rescaled_size, rescaled_size, 1] # Preserve alpha
positive_color = rev_to_color(0)
negative_color = rev_to_color(0.5)
@ -424,6 +427,12 @@ def plane_func_from_complex_func(f):
def point_func_from_complex_func(f):
return lambda (x, y, z): complex_to_R3(f(complex(x, y)))
def point_func_from_plane_func(f):
def g((x, y, z)):
f_val = f((x, y))
return np.array((f_val[0], f_val[1], 0))
return g
test_map_func = point_func_from_complex_func(lambda c: c**2)
empty_animation = EmptyAnimation()
@ -444,9 +453,10 @@ class WalkerAnimation(Animation):
self.show_arrows = show_arrows
base_walker = Dot().scale(5) # PiCreature().scale(0.8) #
self.compound_walker.walker = base_walker.scale(0.35).set_stroke(BLACK, 1.5) #PiCreature()
self.compound_walker.walker = base_walker.scale(0.35).set_stroke(WHITE, 3) #PiCreature()
if show_arrows:
self.compound_walker.arrow = Arrow(ORIGIN, 0.5 * RIGHT, buff = 0).set_stroke(BLACK, 1.5)
self.compound_walker.arrow = Arrow(ORIGIN, 0.5 * RIGHT, buff = 0)
self.compound_walker.arrow.match_style(self.compound_walker.walker)
self.compound_walker.digest_mobject_attrs()
Animation.__init__(self, self.compound_walker, **kwargs)
@ -528,10 +538,14 @@ class ColorMappedByFuncScene(Scene):
"num_plane" : NumberPlane(),
"show_num_plane" : True,
"show_output" : False, # Not currently implemented; TODO
"show_output" : False
}
def setup(self):
# The composition of input_to_pos and pos_to_color
# is to be equal to func (which turns inputs into colors)
# However, depending on whether we are showing input or output (via a MappingCamera),
# we color the background using either func or the identity map
if self.show_output:
self.input_to_pos_func = self.func
self.pos_to_color_func = lambda p : p
@ -539,10 +553,19 @@ class ColorMappedByFuncScene(Scene):
self.input_to_pos_func = lambda p : p
self.pos_to_color_func = self.func
# func_hash hashes the function at some random points
func_hash_points = [(-0.93, 1), (1, -2.7), (20, 4)]
to_hash = tuple((self.func(p)[0], self.func(p)[1]) for p in func_hash_points)
jitter_val = 0.1
line_coords = np.linspace(-10, 10) + jitter_val
func_hash_points = it.product(line_coords, line_coords)
def mini_hasher(p):
rgba = point_to_rgba(self.pos_to_color_func(p))
if rgba[3] != 1.0:
print "Warning! point_to_rgba assigns fractional alpha", rgba[3]
return tuple(rgba)
to_hash = tuple(mini_hasher(p) for p in func_hash_points)
func_hash = hash(to_hash)
# We hash just based on output image
# Thus, multiple scenes with same output image can re-use it
# without recomputation
full_hash = hash((func_hash, self.camera.pixel_shape))
self.background_image_file = os.path.join(
self.output_directory, "images",
@ -583,11 +606,23 @@ class PureColorMap(ColorMappedByFuncScene):
"show_num_plane" : False
}
class ColorMappedByFuncStill(ColorMappedByFuncScene):
def construct(self):
ColorMappedByFuncScene.construct(self)
self.wait()
# This sets self.background_image_file, but does not display it as the background
class ColorMappedObjectsScene(ColorMappedByFuncScene):
CONFIG = {
"show_num_plane" : False
}
def construct(self):
ColorMappedByFuncScene.construct(self)
# Clearing background
self.camera.background_image = None
self.camera.init_background()
class PiWalker(ColorMappedByFuncScene):
CONFIG = {
"walk_coords" : [],
@ -654,7 +689,7 @@ class PiWalkerCircle(PiWalker):
PiWalker.setup(self)
# TODO: Give drawn lines a bit of buffer, so that the rectangle's corners are filled in
class EquationSolver2d(ColorMappedByFuncScene):
class EquationSolver2d(ColorMappedObjectsScene):
CONFIG = {
"camera_config" : {"use_z_coordinate_for_display_order": True},
"initial_lower_x" : -5.1,
@ -670,17 +705,20 @@ class EquationSolver2d(ColorMappedByFuncScene):
}
def construct(self):
ColorMappedByFuncScene.construct(self)
ColorMappedObjectsScene.construct(self)
num_plane = self.num_plane
self.remove(num_plane)
# Clearing background
self.camera.background_image = None
self.camera.init_background()
rev_func = lambda p : point_to_rev(self.func(p))
clockwise_rev_func = lambda p : -rev_func(p)
base_line = Line(UP, RIGHT, stroke_width = 10 if self.use_fancy_lines else 4, color = RED)
run_time_base = 1
run_time_with_lingering = run_time_base + 0.2
base_rate = lambda t : t
linger_rate = squish_rate_func(lambda t : t, 0,
fdiv(run_time_base, run_time_with_lingering))
def Animate2dSolver(cur_depth, rect, dim_to_split, sides_to_draw = [0, 1, 2, 3]):
print "Solver at depth: " + str(cur_depth)
@ -691,13 +729,10 @@ class EquationSolver2d(ColorMappedByFuncScene):
alpha_winder = make_alpha_winder(clockwise_rev_func, start, end, self.num_checkpoints)
a0 = alpha_winder(0)
rebased_winder = lambda alpha: alpha_winder(alpha) - a0 + start_wind
thick_line = Line(num_plane.coords_to_point(*start), num_plane.coords_to_point(*end),
stroke_width = 10,
color = RED)
colored_line = Line(num_plane.coords_to_point(*start) + IN, num_plane.coords_to_point(*end) + IN)
colored_line.match_style(base_line)
if self.use_fancy_lines:
colored_line = thick_line.color_using_background_image(self.background_image_file)
else:
colored_line = thick_line.set_stroke(width = 4)
colored_line.color_using_background_image(self.background_image_file)
walker_anim = LinearWalker(
start_coords = start,
@ -707,17 +742,20 @@ class EquationSolver2d(ColorMappedByFuncScene):
number_update_func = rebased_winder,
remover = True
)
if should_linger: # Do we need an "and not self.display_in_parallel" here?
rate_func = lingering
run_time = run_time_with_lingering
rate_func = linger_rate
else:
rate_func = None
run_time = run_time_base
rate_func = base_rate
opt_line_anim = ShowCreation(colored_line) if draw_line else empty_animation
line_draw_anim = AnimationGroup(
opt_line_anim,
walker_anim,
run_time = run_time,
rate_func = rate_func)
return (line_draw_anim, rebased_winder(1))
@ -744,7 +782,7 @@ class EquationSolver2d(ColorMappedByFuncScene):
rect.get_bottom_right(),
rect.get_bottom_left()
]
points = np.array([num_plane.coords_to_point(x, y) for (x, y) in coords]) + 2 * IN
points = np.array([num_plane.coords_to_point(x, y) for (x, y) in coords]) + 3 * IN
# TODO: Maybe use diagonal lines or something to fill in rectangles indicating
# their "Nothing here" status?
# Or draw a large X or something
@ -766,7 +804,7 @@ class EquationSolver2d(ColorMappedByFuncScene):
for (sub_rect, side_to_draw) in sub_rect_and_sides
]
mid_line_coords = rect.split_line_on_dim(dim_to_split)
mid_line_points = [num_plane.coords_to_point(x, y) + IN for (x, y) in mid_line_coords]
mid_line_points = [num_plane.coords_to_point(x, y) + 2 * IN for (x, y) in mid_line_coords]
# TODO: Have this match rectangle line style, apart from dashes and thin-ness?
# Though there is also informational value in seeing the dashed line separately from rectangle lines
mid_line = DashedLine(*mid_line_points)
@ -795,11 +833,41 @@ class EquationSolver2d(ColorMappedByFuncScene):
cur_depth = 0,
rect = rect,
dim_to_split = 0,
sides_to_draw = []
)
print "Done computing anim"
self.play(anim)
# Keep timing details here in sync with details above
rect_points = [
rect.get_top_left(),
rect.get_top_right(),
rect.get_bottom_right(),
rect.get_bottom_left(),
]
border = Polygon(*map(lambda x : num_plane.coords_to_point(*x) + IN, rect_points))
border.match_style(base_line)
if self.use_fancy_lines:
border.color_using_background_image(self.background_image_file)
rect_time_without_linger = 4 * run_time_base
rect_time_with_linger = 3 * run_time_base + run_time_with_lingering
def rect_rate(alpha):
time_in = alpha * rect_time_with_linger
if time_in < 3 * run_time_base:
return fdiv(time_in, 4 * run_time_base)
else:
time_in_last_leg = time_in - 3 * run_time_base
alpha_in_last_leg = fdiv(time_in_last_leg, run_time_with_lingering)
return interpolate(0.75, 1, linger_rate(alpha_in_last_leg))
border_anim = ShowCreation(
border,
run_time = rect_time_with_linger,
rate_func = rect_rate
)
self.play(anim, border_anim)
self.wait()
@ -865,10 +933,9 @@ class FuncRotater(Animation):
def update_mobject(self, alpha):
Animation.update_mobject(self, alpha)
angle_revs = self.rotate_func(alpha)
# We do a clockwise rotation
angle_revs = -self.rotate_func(alpha) # Negated so we interpret this clockwise
self.mobject.rotate(
-angle_revs * TAU,
angle_revs * TAU,
about_point = ORIGIN
)
self.mobject.set_color(rev_to_color(angle_revs))
@ -883,8 +950,9 @@ class TestRotater(Scene):
# TODO: Be careful about clockwise vs. counterclockwise convention throughout!
# Make sure this is correct everywhere in resulting video.
class OdometerScene(Scene):
class OdometerScene(ColorMappedObjectsScene):
CONFIG = {
# "func" : lambda p : 100 * p # Full coloring, essentially
"rotate_func" : lambda x : np.sin(x * TAU),
"run_time" : 5,
"dashed_line_angle" : None,
@ -892,8 +960,11 @@ class OdometerScene(Scene):
}
def construct(self):
ColorMappedObjectsScene.construct(self)
radius = 1.3
circle = Circle(center = ORIGIN, radius = radius)
circle.color_using_background_image(self.background_image_file)
self.add(circle)
if self.dashed_line_angle:
@ -902,9 +973,13 @@ class OdometerScene(Scene):
dashed_line.rotate(-self.dashed_line_angle * TAU, about_point = ORIGIN)
self.add(dashed_line)
num_display = DecimalNumber(0, include_background_rectangle = False).set_stroke(1)
num_display = DecimalNumber(0, include_background_rectangle = False)
num_display.move_to(2 * DOWN)
caption = TextMobject("turns clockwise")
caption.next_to(num_display, DOWN)
self.add(caption)
display_val_bias = 0
if self.biased_display_start != None:
display_val_bias = self.biased_display_start - self.rotate_func(0)
@ -961,8 +1036,8 @@ class SecondSqrtScene(FirstSqrtScene):
class RewriteEquation(Scene):
def construct(self):
# Can maybe fitz around with smoothening the transform, so just = goes to - and new stuff
# is added at the right end, while things re-center
# Can maybe use get_center() to perfectly center Groups before and after transform
f_old = TexMobject("f(x)")
f_new = f_old.copy()
equals_old = TexMobject("=")
@ -978,8 +1053,18 @@ class RewriteEquation(Scene):
f_new.next_to(minus_new, LEFT)
equals_new.next_to(g_new, RIGHT)
zero_new.next_to(equals_new, RIGHT)
# where_old = TextMobject("Where does ")
# where_old.next_to(f_old, LEFT)
# where_new = where_old.copy()
# where_new.next_to(f_new, LEFT)
self.add(f_old, equals_old, equals_old_2, g_old)
# qmark_old = TextMobject("?")
# qmark_old.next_to(g_old, RIGHT)
# qmark_new = qmark_old.copy()
# qmark_new.next_to(zero_new, RIGHT)
self.add(f_old, equals_old, equals_old_2, g_old) #, where_old, qmark_old)
self.wait()
self.play(
ReplacementTransform(f_old, f_new),
@ -987,6 +1072,8 @@ class RewriteEquation(Scene):
ReplacementTransform(g_old, g_new),
ReplacementTransform(equals_old_2, minus_new),
ShowCreation(zero_new),
# ReplacementTransform(where_old, where_new),
# ReplacementTransform(qmark_old, qmark_new),
)
self.wait()
@ -1011,12 +1098,18 @@ class SignsExplanation(Scene):
num_line.number_to_point(neg_num),
buff = 0,
color = negative_color)
plus_sign = TexMobject("+", fill_color = positive_color)
minus_sign = TexMobject("-", fill_color = negative_color)
plus_sign.next_to(pos_arrow, UP)
minus_sign.next_to(neg_arrow, UP)
#num_line.add_numbers(pos_num)
self.play(ShowCreation(pos_arrow))
self.play(ShowCreation(pos_arrow), FadeIn(plus_sign))
#num_line.add_numbers(neg_num)
self.play(ShowCreation(neg_arrow))
self.play(ShowCreation(neg_arrow), FadeIn(minus_sign))
class VectorField(Scene):
CONFIG = {
@ -1057,6 +1150,7 @@ class VectorField(Scene):
self.wait()
class HasItsLimitations(Scene):
def construct(self):
num_line = NumberLine()
num_line.add_numbers()
@ -1064,17 +1158,71 @@ class HasItsLimitations(Scene):
self.wait()
base_point = num_line.number_to_point(3) + OUT
dot_color = ORANGE
input_dot = Dot(base_point, color = dot_color)
input_label = TexMobject("Input", fill_color = dot_color)
input_label.next_to(input_dot, UP + LEFT)
input_label.add_background_rectangle()
self.add(input_dot, input_label)
curved_arrow = Arc(0, color = MAROON_E)
curved_arrow.set_bound_angles(np.pi, 0)
curved_arrow.generate_points()
curved_arrow.add_tip()
curved_arrow.move_arc_center_to(base_point + RIGHT)
# Could do something smoother, with arrowhead moving along partial arc?
self.play(ShowCreation(curved_arrow))
output_dot = Dot(base_point + 2 * RIGHT, color = dot_color)
output_label = TexMobject("Output", fill_color = dot_color)
output_label.next_to(output_dot, UP + RIGHT)
output_label.add_background_rectangle()
self.add(output_dot, output_label)
self.wait()
num_plane = NumberPlane()
num_plane.add_coordinates()
self.play(FadeOut(num_line), FadeIn(num_plane))
new_base_point = base_point + 2 * UP
new_input_dot = input_dot.copy().move_to(new_base_point)
new_input_label = input_label.copy().next_to(new_input_dot, UP + LEFT)
new_curved_arrow = Arc(0).match_style(curved_arrow)
new_curved_arrow.set_bound_angles(np.pi * 3/4, 0)
new_curved_arrow.generate_points()
new_curved_arrow.add_tip()
input_diff = input_dot.get_center() - curved_arrow.points[0]
output_diff = output_dot.get_center() - curved_arrow.points[-1]
new_curved_arrow.shift((new_input_dot.get_center() - new_curved_arrow.points[0]) - input_diff)
new_output_dot = output_dot.copy().move_to(new_curved_arrow.points[-1] + output_diff)
new_output_label = output_label.copy().next_to(new_output_dot, UP + RIGHT)
dot_objects = Group(input_dot, input_label, output_dot, output_label, curved_arrow)
new_dot_objects = Group(new_input_dot, new_input_label, new_output_dot, new_output_label, new_curved_arrow)
self.play(
FadeOut(num_line), FadeIn(num_plane),
ReplacementTransform(dot_objects, new_dot_objects),
)
self.wait()
self.add_foreground_mobject(new_dot_objects)
complex_plane = ComplexPlane()
complex_plane.add_coordinates()
# This looks a little wonky and we may wish to do a crossfade in Premiere instead
self.play(FadeOut(num_plane), FadeIn(complex_plane))
self.wait()
class ComplexPlaneIs2d(Scene):
@ -1213,6 +1361,33 @@ class Initial2dFuncSceneWithoutMorphing(Scene):
line = Line(points[i], points[i + 1], color = RED)
self.play(ShowCreation(line))
class DemonstrateColorMapping(ColorMappedObjectsScene):
CONFIG = {
"show_num_plane" : False
}
def construct(self):
ColorMappedObjectsScene.construct(self)
circle = Circle()
circle.color_using_background_image(self.background_image_file)
ray = Line(ORIGIN, 10 * RIGHT)
ray.color_using_background_image(self.background_image_file)
self.play(ShowCreation(circle))
self.play(ShowCreation(ray))
scale_factor = 5
self.play(ApplyMethod(circle.scale, scale_factor))
self.play(ApplyMethod(circle.scale, fdiv(1, scale_factor**2)))
self.play(ApplyMethod(circle.scale, scale_factor))
self.play(Rotating(ray, about_point = ORIGIN))
# TODO: Illustrations for introducing domain coloring
# TODO: Bunch of Pi walker scenes
@ -1362,9 +1537,9 @@ class LoopSplitSceneMapped(LoopSplitScene):
class FundThmAlg(EquationSolver2d):
CONFIG = {
"func" : plane_poly_with_roots((1, 2), (-1, 1.5), (-1, 1.5)),
"num_iterations" : 5,
"num_iterations" : 2,
"display_in_parallel" : True,
"use_fancy_lines" : False,
"use_fancy_lines" : True,
}
# TODO: Borsuk-Ulam visuals
@ -1484,6 +1659,30 @@ class CombineInterval2(Scene):
self.wait()
tiny_loop_func = plane_poly_with_roots((-1, -2), (1, 1), (1, 1))
class TinyLoopInInputPlane(ColorMappedByFuncScene):
CONFIG = {
"func" : tiny_loop_func
}
def construct(self):
ColorMappedByFuncScene.construct(self)
self.wait()
circle = Circle(color = WHITE)
circle.scale(0.5)
circle.move_to(UP + RIGHT)
self.play(ShowCreation(circle))
class TinyLoopInOutputPlane(TinyLoopInInputPlane):
CONFIG = {
"camera_class" : MappingCamera,
"camera_config" : {"mapping_func" : point_func_from_plane_func(tiny_loop_func)},
"show_output" : True,
"show_num_plane" : False,
}
# TODO: Brouwer's fixed point theorem visuals
# class BFTScene(Scene):
@ -1527,7 +1726,7 @@ class MapPiWalkerRect(PiWalkerRect):
CONFIG = {
"camera_class" : MappingCamera,
"camera_config" : {"mapping_func" : rect_to_circle},
"display_output_color_map" : True
"show_output" : True
}
class ShowBack(PiWalkerRect):

15
animation/simple_animations.py
View file

@ -466,21 +466,22 @@ class Succession(Animation):
self.current_alpha = alpha
return
gt_alpha_list = filter(
gt_alpha_iter = it.ifilter(
lambda i : self.critical_alphas[i+1] >= alpha,
range(len(self.critical_alphas)-1)
range(self.num_anims)
)
if gt_alpha_list:
i = gt_alpha_list[0]
else:
i = next(gt_alpha_iter, None)
if i == None:
# In this case, we assume what is happening is that alpha is 1.0,
# but that rounding error is causing us to overshoot the end of
# self.critical_alphas (which is also 1.0)
if not abs(alpha - 1) < 0.001:
warnings.warn(
"Rounding error not near alpha=1 in Succession.update_mobject," + \
"instead alpha = %f"%alpha
)
print self.critical_alphas, alpha
i = len(self.critical_alphas) - 2
#
i = self.num_anims - 1
# At this point, we should have self.critical_alphas[i] <= alpha <= self.critical_alphas[i +1]

9
camera/camera.py
View file

@ -107,7 +107,7 @@ class Camera(object):
def set_pixel_array(self, pixel_array, convert_from_floats = False):
converted_array = self.convert_pixel_array(pixel_array, convert_from_floats)
if not hasattr(self, "pixel_array"): #TODO: And the shapes match?
if not (hasattr(self, "pixel_array") and self.pixel_array.shape == converted_array.shape):
self.pixel_array = converted_array
else:
#Set in place
@ -438,10 +438,15 @@ class Camera(object):
]
out_a = src_a + dst_a*(1.0-src_a)
# When the output alpha is 0 for full transparency,
# we have a choice over what RGB value to use in our
# output representation. We choose 0 here.
out_rgb = fdiv(
src_rgb*src_a[..., None] + \
dst_rgb*dst_a[..., None]*(1.0-src_a[..., None]),
out_a[..., None]
out_a[..., None],
zero_over_zero_value = 0
)
self.pixel_array[..., :3] = out_rgb*self.rgb_max_val

15
helpers.py
View file

@ -694,8 +694,19 @@ class DictAsObject(object):
self.__dict__ = dict
# Just to have a less heavyweight name for this extremely common operation
def fdiv(a, b):
return np.true_divide(a,b)
#
# We may wish to have more fine-grained control over division by zero behavior
# in the future (separate specifiable values for 0/0 and x/0 with x != 0),
# but for now, we just allow the option to handle indeterminate 0/0.
def fdiv(a, b, zero_over_zero_value = None):
if zero_over_zero_value != None:
out = np.full_like(a, zero_over_zero_value)
where = np.logical_or (a != 0, b != 0)
else:
out = None
where = True
return np.true_divide(a, b, out = out, where = where)
def add_extension_if_not_present(file_name, extension):
# This could conceivably be smarter about handling existing differing extensions

4
mobject/tex_mobject.py
View file

@ -41,6 +41,10 @@ class TexMobject(SVGMobject):
}
def __init__(self, *args, **kwargs):
digest_config(self, kwargs, locals())
if "color" in kwargs.keys() and not "fill_color" in kwargs.keys():
self.fill_color = kwargs["color"]
##TODO, Eventually remove this
if len(args) == 1 and isinstance(args[0], list):
self.args = args[0]

4
topics/geometry.py
View file

@ -45,7 +45,7 @@ class Arc(VMobject):
#TODO, do this a better way
p1 = p2 = p3 = p4 = None
start_arrow = end_arrow = None
if at_start:
if at_end:
p1, p2 = self.points[-3:-1]
# self.points[-2:] did overshoot
start_arrow = Arrow(
@ -55,7 +55,7 @@ class Arc(VMobject):
)
self.add(start_arrow.split()[-1]) # just the tip
if at_end:
if at_start:
p4, p3 = self.points[1:3]
# self.points[:2] did overshoot
end_arrow = Arrow(