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revert to earlier version

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This commit is contained in:
Ben Hambrecht 2018-04-03 20:16:31 +02:00
parent 9e1216397a
commit 646e1856e8
3 changed files with 173 additions and 297 deletions
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278
old_projects/WindingNumber.py → active_projects/WindingNumber.py
View file

@ -1,7 +1,5 @@
from big_ol_pile_of_manim_imports import * from big_ol_pile_of_manim_imports import *
import time
import mpmath import mpmath
mpmath.mp.dps = 7 mpmath.mp.dps = 7
@ -409,9 +407,7 @@ def resit_near(x, m):
# TODO?: Perhaps use modulus of (uniform) continuity instead of num_checkpoints, calculating # TODO?: Perhaps use modulus of (uniform) continuity instead of num_checkpoints, calculating
# latter as needed from former? # latter as needed from former?
# def make_alpha_winder(func, start, end, num_checkpoints):
# "cheap" argument only used for diagnostic testing right now
def make_alpha_winder(func, start, end, num_checkpoints, cheap = False):
check_points = [None for i in range(num_checkpoints)] check_points = [None for i in range(num_checkpoints)]
check_points[0] = func(start) check_points[0] = func(start)
step_size = fdiv(end - start, num_checkpoints) step_size = fdiv(end - start, num_checkpoints)
@ -421,15 +417,9 @@ def make_alpha_winder(func, start, end, num_checkpoints, cheap = False):
func(start + (i + 1) * step_size), func(start + (i + 1) * step_size),
check_points[i]) check_points[i])
def return_func(alpha): def return_func(alpha):
if cheap:
return alpha # A test to see if this func is responsible for slowdown
index = clamp(0, num_checkpoints - 1, int(alpha * num_checkpoints)) index = clamp(0, num_checkpoints - 1, int(alpha * num_checkpoints))
x = interpolate(start, end, alpha) x = interpolate(start, end, alpha)
if cheap: return resit_near(func(x), check_points[index])
return check_points[index] # A more principled test that at least returns a reasonable answer
else:
return resit_near(func(x), check_points[index])
return return_func return return_func
# The various inconsistent choices of what datatype to use where are a bit of a mess, # The various inconsistent choices of what datatype to use where are a bit of a mess,
@ -566,7 +556,6 @@ def walker_animation_with_display(
show_arrows = True, show_arrows = True,
scale_arrows = False, scale_arrows = False,
num_decimal_points = 1, num_decimal_points = 1,
include_background_rectangle = True,
**kwargs **kwargs
): ):
@ -582,15 +571,13 @@ def walker_animation_with_display(
if number_update_func != None: if number_update_func != None:
display = DecimalNumber(0, display = DecimalNumber(0,
num_decimal_points = num_decimal_points, num_decimal_points = num_decimal_points,
fill_color = WHITE if include_background_rectangle else BLACK, fill_color = WHITE,
include_background_rectangle = include_background_rectangle) include_background_rectangle = True)
if include_background_rectangle: display.background_rectangle.fill_opacity = 0.5
display.background_rectangle.fill_opacity = 0.5 display.background_rectangle.fill_color = GREY
display.background_rectangle.fill_color = GREY display.background_rectangle.scale(1.2)
display.background_rectangle.scale(1.2)
displaycement = 0.5 * DOWN # How about that pun, eh? displaycement = 0.5 * DOWN # How about that pun, eh?
# display.move_to(walker.get_center() + displaycement) display.move_to(walker.get_center() + displaycement)
display.next_to(walker, DOWN+RIGHT, SMALL_BUFF)
display_anim = ChangingDecimal(display, display_anim = ChangingDecimal(display,
number_update_func, number_update_func,
tracked_mobject = walker_anim.compound_walker.walker, tracked_mobject = walker_anim.compound_walker.walker,
@ -608,7 +595,6 @@ def LinearWalker(
number_update_func = None, number_update_func = None,
show_arrows = True, show_arrows = True,
scale_arrows = False, scale_arrows = False,
include_background_rectangle = True,
**kwargs **kwargs
): ):
walk_func = lambda alpha : interpolate(start_coords, end_coords, alpha) walk_func = lambda alpha : interpolate(start_coords, end_coords, alpha)
@ -619,7 +605,6 @@ def LinearWalker(
number_update_func = number_update_func, number_update_func = number_update_func,
show_arrows = show_arrows, show_arrows = show_arrows,
scale_arrows = scale_arrows, scale_arrows = scale_arrows,
include_background_rectangle = include_background_rectangle,
**kwargs) **kwargs)
class ColorMappedByFuncScene(Scene): class ColorMappedByFuncScene(Scene):
@ -732,8 +717,7 @@ class PiWalker(ColorMappedByFuncScene):
"show_num_plane" : False, "show_num_plane" : False,
"draw_lines" : True, "draw_lines" : True,
"num_checkpoints" : 10, "num_checkpoints" : 10,
"num_decimal_points" : 1, "num_decimal_points" : 1
"include_background_rectangle" : False,
} }
def construct(self): def construct(self):
@ -789,7 +773,6 @@ class PiWalker(ColorMappedByFuncScene):
run_time = self.step_run_time, run_time = self.step_run_time,
walker_stroke_color = WALKER_LIGHT_COLOR if self.color_foreground_not_background else BLACK, walker_stroke_color = WALKER_LIGHT_COLOR if self.color_foreground_not_background else BLACK,
num_decimal_points = self.num_decimal_points, num_decimal_points = self.num_decimal_points,
include_background_rectangle = self.include_background_rectangle,
) )
if self.display_odometer: if self.display_odometer:
@ -971,18 +954,6 @@ class EquationSolver2dNode(object):
bfs_nodes = self.hacky_bfs() bfs_nodes = self.hacky_bfs()
return Succession(*map(lambda n : n.first_anim, bfs_nodes)) return Succession(*map(lambda n : n.first_anim, bfs_nodes))
def play_in_bfs(self, scene, border_anim):
bfs_nodes = self.hacky_bfs()
print "Number of nodes: ", len(bfs_nodes)
if len(bfs_nodes) < 1:
print "Less than 1 node! Aborting!"
return
scene.play(bfs_nodes[0].first_anim, border_anim)
for node in bfs_nodes[1:]:
scene.play(node.first_anim)
class EquationSolver2d(ColorMappedObjectsScene): class EquationSolver2d(ColorMappedObjectsScene):
CONFIG = { CONFIG = {
"camera_config" : {"use_z_coordinate_for_display_order": True}, "camera_config" : {"use_z_coordinate_for_display_order": True},
@ -990,7 +961,7 @@ class EquationSolver2d(ColorMappedObjectsScene):
"initial_upper_x" : 5, "initial_upper_x" : 5,
"initial_lower_y" : -3, "initial_lower_y" : -3,
"initial_upper_y" : 3, "initial_upper_y" : 3,
"num_iterations" : 0, "num_iterations" : 1,
"num_checkpoints" : 10, "num_checkpoints" : 10,
# Should really merge this into one enum-style variable # Should really merge this into one enum-style variable
@ -998,9 +969,6 @@ class EquationSolver2d(ColorMappedObjectsScene):
"display_in_bfs" : False, "display_in_bfs" : False,
"use_fancy_lines" : True, "use_fancy_lines" : True,
"line_color" : WHITE, # Only used for non-fancy lines
# TODO: Consider adding a "find_all_roots" flag, which could be turned off # TODO: Consider adding a "find_all_roots" flag, which could be turned off
# to only explore one of the two candidate subrectangles when both are viable # to only explore one of the two candidate subrectangles when both are viable
@ -1018,26 +986,18 @@ class EquationSolver2d(ColorMappedObjectsScene):
# Used for UhOhScene; # Used for UhOhScene;
"manual_wind_override" : None, "manual_wind_override" : None,
"show_cursor" : True, "show_cursor" : False,
"linger_parameter" : 0.5, "linger_parameter" : 0.2,
"use_separate_plays" : False,
"use_cheap_winding_numbers" : False, # To use this, make num_checkpoints large
} }
def construct(self): def construct(self):
if self.num_iterations == 0:
print "You forgot to set num_iterations (maybe you meant to subclass something other than EquationSolver2d directly?)"
return
ColorMappedObjectsScene.construct(self) ColorMappedObjectsScene.construct(self)
num_plane = self.num_plane num_plane = self.num_plane
clockwise_val_func = lambda p : -point_to_rev(self.func(p)) clockwise_val_func = lambda p : -point_to_rev(self.func(p))
base_line = Line(UP, RIGHT, stroke_width = border_stroke_width, color = self.line_color) base_line = Line(UP, RIGHT, stroke_width = border_stroke_width, color = WHITE)
if self.use_fancy_lines: if self.use_fancy_lines:
base_line.color_using_background_image(self.background_image_file) base_line.color_using_background_image(self.background_image_file)
@ -1077,7 +1037,7 @@ class EquationSolver2d(ColorMappedObjectsScene):
return EquationSolver2dNode(empty_animation) return EquationSolver2dNode(empty_animation)
def draw_line_return_wind(start, end, start_wind, should_linger = False, draw_line = True): def draw_line_return_wind(start, end, start_wind, should_linger = False, draw_line = True):
alpha_winder = make_alpha_winder(clockwise_val_func, start, end, self.num_checkpoints, cheap = self.use_cheap_winding_numbers) alpha_winder = make_alpha_winder(clockwise_val_func, start, end, self.num_checkpoints)
a0 = alpha_winder(0) a0 = alpha_winder(0)
rebased_winder = lambda alpha: alpha_winder(alpha) - a0 + start_wind rebased_winder = lambda alpha: alpha_winder(alpha) - a0 + start_wind
colored_line = Line(num_plane.coords_to_point(*start) + IN, num_plane.coords_to_point(*end) + IN) colored_line = Line(num_plane.coords_to_point(*start) + IN, num_plane.coords_to_point(*end) + IN)
@ -1132,7 +1092,7 @@ class EquationSolver2d(ColorMappedObjectsScene):
width = rect.get_width() width = rect.get_width()
height = rect.get_height() height = rect.get_height()
cursor.move_to(num_plane.coords_to_point(center_x, center_y) + 10 * IN) cursor.move_to(num_plane.coords_to_point(center_x, center_y))
cursor.scale(min(width, height)) cursor.scale(min(width, height))
# Do a quick FadeIn, wait, and quick FadeOut on the cursor, matching rectangle-drawing time # Do a quick FadeIn, wait, and quick FadeOut on the cursor, matching rectangle-drawing time
@ -1144,11 +1104,7 @@ class EquationSolver2d(ColorMappedObjectsScene):
anim = AnimationGroup(anim, cursor_anim) anim = AnimationGroup(anim, cursor_anim)
override_wind = head(manual_wind_override) total_wind = head(manual_wind_override) or round(wind_so_far)
if override_wind != None:
total_wind = override_wind
else:
total_wind = round(wind_so_far)
if total_wind == 0: if total_wind == 0:
coords = [ coords = [
@ -1241,17 +1197,15 @@ class EquationSolver2d(ColorMappedObjectsScene):
rate_func = rect_rate rate_func = rect_rate
) )
print "About to do the big Play; for reference, the current time is ", time.strftime("%H:%M:%S") self.play(anim, border_anim)
if self.use_separate_plays:
node.play_in_bfs(self, border_anim)
else:
self.play(anim, border_anim)
print "All done; for reference, the current time is ", time.strftime("%H:%M:%S")
self.wait() self.wait()
# In case we wish to reference these later, as had been done in the
# WindingNumber_G/SearchSpacePerimeterVsArea scene at one point
self.node = node
self.anim = anim
# TODO: Perhaps have option for bullets (pulses) to fade out and in at ends of line, instead of # TODO: Perhaps have option for bullets (pulses) to fade out and in at ends of line, instead of
# jarringly popping out and in? # jarringly popping out and in?
# #
@ -1264,7 +1218,7 @@ class LinePulser(ContinualAnimation):
self.pulse_time = pulse_time self.pulse_time = pulse_time
self.bullets = [bullet_template.copy() for i in range(num_bullets)] self.bullets = [bullet_template.copy() for i in range(num_bullets)]
self.output_func = output_func self.output_func = output_func
ContinualAnimation.__init__(self, VGroup(*self.bullets), **kwargs) ContinualAnimation.__init__(self, VGroup(line, VGroup(*self.bullets)), **kwargs)
def update_mobject(self, dt): def update_mobject(self, dt):
alpha = self.external_time % self.pulse_time alpha = self.external_time % self.pulse_time
@ -1999,9 +1953,7 @@ class LoopSplitScene(ColorMappedObjectsScene):
def flash_circles(circles): def flash_circles(circles):
self.play(LaggedStart(FadeIn, VGroup(circles))) self.play(LaggedStart(FadeIn, VGroup(circles)))
self.wait() self.play(*map(FadeOut, circles))
self.play(FadeOut(VGroup(circles)))
self.wait()
self.add(left_square_lines_vmobject, right_square_lines_vmobject) self.add(left_square_lines_vmobject, right_square_lines_vmobject)
self.remove(*midline_lines) self.remove(*midline_lines)
@ -2015,17 +1967,15 @@ class LoopSplitScene(ColorMappedObjectsScene):
self.wait() self.wait()
flash_circles([indicate_circle(l) for l in left_square_lines]) flash_circles([indicate_circle(l) for l in left_square_lines])
self.play(line_fade(faded, 1, right_square_lines_vmobject), *bullet_list_fade(1, 0, left_square_bullets)) self.play(line_fade(faded, 1, right_square_lines_vmobject), *bullet_list_fade(1, 0, left_square_bullets))
self.wait()
self.add(*right_square_anims) self.add(*right_square_anims)
self.play(line_fade(1, faded, left_square_lines_vmobject), *bullet_list_fade(0, 1, right_square_bullets)) self.play(line_fade(1, faded, left_square_lines_vmobject), *bullet_list_fade(0, 1, right_square_bullets))
self.wait() self.wait()
flash_circles([indicate_circle(l) for l in right_square_lines]) flash_circles([indicate_circle(l) for l in right_square_lines])
self.play(line_fade(faded, 1, left_square_lines_vmobject), *bullet_list_fade(1, 0, right_square_bullets)) self.play(line_fade(faded, 1, left_square_lines_vmobject), *bullet_list_fade(1, 0, right_square_bullets))
self.wait()
self.play(*bullet_list_fade(0, 1, left_square_bullets + right_square_bullets))
self.wait() self.wait()
self.play(*bullet_list_fade(0, 1, left_square_bullets + right_square_bullets))
outside_circlers = [ outside_circlers = [
indicate_circle(left_line), indicate_circle(left_line),
@ -2037,15 +1987,20 @@ class LoopSplitScene(ColorMappedObjectsScene):
inner_circle = indicate_circle(midline_lines[0]) inner_circle = indicate_circle(midline_lines[0])
self.play(FadeIn(inner_circle)) self.play(FadeIn(inner_circle))
self.wait()
self.play(FadeOut(inner_circle), line_fade(1, 0, midline_lines_vmobject), *bullet_list_fade(1, 0, midline_bullets)) self.play(FadeOut(inner_circle), line_fade(1, 0, midline_lines_vmobject), *bullet_list_fade(1, 0, midline_bullets))
self.wait()
self.wait(3)
# Repeat for effect, goes well with narration
self.play(FadeIn(inner_circle), line_fade(0, 1, midline_lines_vmobject), *bullet_list_fade(0, 1, midline_bullets)) # Is there a way to abstract this into a general process to derive a new mapped scene from an old scene?
self.wait() class LoopSplitSceneMapped(LoopSplitScene):
self.play(FadeOut(inner_circle), line_fade(1, 0, midline_lines_vmobject), *bullet_list_fade(1, 0, midline_bullets))
self.wait() def setup(self):
left_camera = Camera(**self.camera_config)
right_camera = MappingCamera(
mapping_func = lambda (x, y, z) : complex_to_R3(((complex(x,y) + 3)**1.1) - 3),
**self.camera_config)
split_screen_camera = SplitScreenCamera(left_camera, right_camera, **self.camera_config)
self.camera = split_screen_camera
# TODO: Perhaps do extra illustration of zooming out and winding around a large circle, # TODO: Perhaps do extra illustration of zooming out and winding around a large circle,
# to illustrate relation between degree and large-scale winding number # to illustrate relation between degree and large-scale winding number
@ -2053,121 +2008,16 @@ class FundThmAlg(EquationSolver2d):
CONFIG = { CONFIG = {
"func" : plane_func_by_wind_spec((1, 2), (-1, 1.5), (-1, 1.5)), "func" : plane_func_by_wind_spec((1, 2), (-1, 1.5), (-1, 1.5)),
"num_iterations" : 2, "num_iterations" : 2,
"use_fancy_lines" : True,
} }
class SolveX5MinusXMinus1(EquationSolver2d): class SolveX5MinusXMinus1(EquationSolver2d):
CONFIG = {
"func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
"num_iterations" : 10,
"show_cursor" : True,
"display_in_bfs" : True,
}
class PureColorMapOfX5Thing(PureColorMap):
CONFIG = {
"func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
}
class X5ThingWithRightHalfGreyed(SolveX5MinusXMinus1):
CONFIG = {
"num_iterations" : 3,
"manual_wind_override" : (1, None, (1, (0, None, None), (0, None, None)))
}
class SolveX5MinusXMinus1_5Iterations(EquationSolver2d):
CONFIG = { CONFIG = {
"func" : plane_func_from_complex_func(lambda c : c**5 - c - 1), "func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
"num_iterations" : 5, "num_iterations" : 5,
"show_cursor" : True, "use_fancy_lines" : True,
"display_in_bfs" : True,
"manual_wind_override" : (None, None, (None, (0, None, None), (0, None, None)))
} }
class X5_Monster_Red_Lines(SolveX5MinusXMinus1_5Iterations):
CONFIG = {
"use_separate_plays" : True,
"use_fancy_lines" : False,
"line_color" : RED,
}
class X5_Monster_Green_Lines(X5_Monster_Red_Lines):
CONFIG = {
"line_color" : GREEN,
}
class X5_Monster_Red_Lines_Long(X5_Monster_Red_Lines):
CONFIG = {
"num_iterations" : 6
}
class X5_Monster_Green_Lines_Long(X5_Monster_Green_Lines):
CONFIG = {
"num_iterations" : 6
}
class X5_Monster_Red_Lines_Little_More(X5_Monster_Red_Lines_Long):
CONFIG = {
"num_iterations" : 7
}
class X5_Monster_Green_Lines_Little_More(X5_Monster_Green_Lines_Long):
CONFIG = {
"num_iterations" : 7
}
class X5_Monster_Red_Lines_No_Numbers(X5_Monster_Red_Lines):
CONFIG = {
"num_iterations" : 3,
"show_winding_numbers" : False,
}
class X5_Monster_Green_Lines_No_Numbers(X5_Monster_Green_Lines):
CONFIG = {
"num_iterations" : 3,
"show_winding_numbers" : False,
}
class SolveX5MinusXMinus1_3Iterations(EquationSolver2d):
CONFIG = {
"func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
"num_iterations" : 3,
"show_cursor" : True,
"display_in_bfs" : True,
}
class Diagnostic(SolveX5MinusXMinus1_3Iterations):
CONFIG = {
# I think the combination of these two makes things slow
"use_separate_plays" : not False, # This one isn't important to set any particular way, so let's leave it like this
"use_fancy_lines" : True,
# This causes a small slowdown (before rendering, in particular), but not the big one, I think
"show_winding_numbers" : True,
# This doesn't significantly matter for rendering time, I think
"camera_config" : {"use_z_coordinate_for_display_order" : True}
}
# All above flags False (meaning not db = False): just under 30 it/s
# not db = True: 30
# use_fancy_lines = True: 30 at first (if scene.play(bfs_nodes[0].first_anim, border_anim is off), but then drops to 3 (or drops right away if that simultaneous play is on)
# use_z_coordinate = True: 30
# show_winding_numbers = True: 10
# winding AND use_fancy_lines: 10
# not db AND fancy_lines AND z_coords = true, winding = false: 3. Not 30, but 3. Slow.
# db AND use_fancy: 3. Slow.
# fancy AND z_coords: 30. Fast. [Hm, this may have been a mistake; fancy and z_coords is now slow?]
# fancy, winding, AND z_coords, but not (not db): 10
# not db, winding, AND z_coords, but not fancy: 10
# class DiagnosticB(Diagnostic):
# CONFIG = {
# "num_iterations" : 3,
# #"num_checkpoints" : 100,
# #"show_winding_numbers" : False,
# #"use_cheap_winding_numbers" : True,
# }
class SolveX5MinusXMinus1Parallel(SolveX5MinusXMinus1): class SolveX5MinusXMinus1Parallel(SolveX5MinusXMinus1):
CONFIG = { CONFIG = {
"display_in_parallel" : True "display_in_parallel" : True
@ -2186,37 +2036,6 @@ class PreviewClip(EquationSolver2d):
"use_fancy_lines" : True, "use_fancy_lines" : True,
} }
class ParallelClip(EquationSolver2d):
CONFIG = {
"func" : plane_func_by_wind_spec(
(-3, -1.3, 2), (0.1, 0.2, 1), (2.8, -2, 1)
),
"num_iterations" : 5,
"display_in_parallel" : True,
}
class EquationSolver2dMatchBreakdown(EquationSolver2d):
CONFIG = {
"func" : plane_func_by_wind_spec(
(-2, 0.3, 2), (2, -0.2, 1) # Not an exact match, because our breakdown function has a zero along midlines...
),
"num_iterations" : 5,
"display_in_parallel" : True,
"show_cursor" : True
}
class EquationSolver2dMatchBreakdown_parallel(EquationSolver2dMatchBreakdown):
CONFIG = {
"display_in_parallel" : True,
"display_in_bfs" : False,
}
class EquationSolver2dMatchBreakdown_bfs(EquationSolver2dMatchBreakdown):
CONFIG = {
"display_in_parallel" : False,
"display_in_bfs" : True,
}
class QuickPreview(PreviewClip): class QuickPreview(PreviewClip):
CONFIG = { CONFIG = {
"num_iterations" : 3, "num_iterations" : 3,
@ -2234,11 +2053,6 @@ class LongEquationSolver(EquationSolver2d):
"show_cursor" : True, "show_cursor" : True,
} }
class QuickPreviewUnfancy(LongEquationSolver):
CONFIG = {
# "use_fancy_lines" : False,
}
# TODO: Borsuk-Ulam visuals # TODO: Borsuk-Ulam visuals
# Note: May want to do an ordinary square scene, then MappingCamera it into a circle # Note: May want to do an ordinary square scene, then MappingCamera it into a circle
# class BorsukUlamScene(PiWalker): # class BorsukUlamScene(PiWalker):
@ -2665,6 +2479,18 @@ class ShowBack(PiWalkerRect):
"func" : plane_func_by_wind_spec((1, 2), (-1, 1.5), (-1, 1.5)) "func" : plane_func_by_wind_spec((1, 2), (-1, 1.5), (-1, 1.5))
} }
class Diagnostic(Scene):
def construct(self):
testList = map(lambda n : (n, rev_to_rgba(n)), [0, 0.1, 0.2, 0.3, 0.4])
print "Here you go:", testList
self.wait()
class DiagnosticColorMap(PureColorMap):
CONFIG = {
"func" : lambda (x, y) : (25 * x, 25 * y),
"show_num_plane" : False,
}
class PiWalkerOdometerTest(PiWalkerExamplePlaneFunc): class PiWalkerOdometerTest(PiWalkerExamplePlaneFunc):
CONFIG = { CONFIG = {
"display_odometer" : True "display_odometer" : True

86
old_projects/WindingNumber_G.py → active_projects/WindingNumber_G.py
View file

@ -1896,20 +1896,6 @@ class TinyLoopAroundRed(TinyLoop):
"target_coords" : (-1, 1), "target_coords" : (-1, 1),
} }
class ConfusedPiCreature(PiCreatureScene):
def construct(self):
morty = self.pi_creature
morty.set_color(YELLOW_E)
morty.flip()
morty.center()
self.play(morty.change, "awe", DOWN+3*RIGHT)
self.wait(2)
self.play(morty.change, "confused")
self.wait(2)
self.play(morty.change, "pondering")
self.wait(2)
class FailureOfComposition(ColorMappedObjectsScene): class FailureOfComposition(ColorMappedObjectsScene):
CONFIG = { CONFIG = {
"func" : lambda p : ( "func" : lambda p : (
@ -2162,11 +2148,7 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
CONFIG = { CONFIG = {
"func" : plane_func_by_wind_spec( "func" : plane_func_by_wind_spec(
(-2, 0, 2), (2, 0, 1) (-2, 0, 2), (2, 0, 1)
), )
"dot_fill_opacity" : 1,
"dot_stroke_width" : 1,
"include_walkers" : True,
"include_question_mark" : True,
} }
def construct(self): def construct(self):
ColorMappedObjectsScene.construct(self) ColorMappedObjectsScene.construct(self)
@ -2196,10 +2178,7 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
#Setup region labels #Setup region labels
sum_tex = "x+y" for square, tex in (left_square, "x"), (right_square, "y"), (joint_rect, "x+y \\, ?"):
if self.include_question_mark:
sum_tex += "\\, ?"
for square, tex in (left_square, "x"), (right_square, "y"), (joint_rect, sum_tex):
square.label = TextMobject("Winding = ", "$%s$"%tex) square.label = TextMobject("Winding = ", "$%s$"%tex)
square.label.move_to(square) square.label.move_to(square)
@ -2253,7 +2232,7 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
path_arc = TAU/6 path_arc = TAU/6
), ),
FadeIn(joint_rect.label[1][1]), FadeIn(joint_rect.label[1][1]),
FadeIn(joint_rect.label[1][3:]), FadeIn(joint_rect.label[1][3]),
FadeOut(right_square.label[0]), FadeOut(right_square.label[0]),
Transform( Transform(
right_square.label[1], joint_rect.label[1][2], right_square.label[1], joint_rect.label[1][2],
@ -2302,12 +2281,9 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
#Setup dot, arrow and label #Setup dot, arrow and label
dot = self.dot = Dot(radius = 0.1) dot = self.dot = Dot(radius = 0.1)
dot.set_stroke(WHITE, self.dot_stroke_width) dot.set_stroke(WHITE, 1)
update_dot_color = ContinualUpdateFromFunc( update_dot_color = ContinualUpdateFromFunc(
dot, lambda d : d.set_fill( dot, lambda d : d.set_fill(get_output_color())
get_output_color(),
self.dot_fill_opacity
)
) )
label = DecimalNumber(0, num_decimal_points = 1) label = DecimalNumber(0, num_decimal_points = 1)
@ -2318,7 +2294,7 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
arrow_length = 0.75 arrow_length = 0.75
arrow = Vector(arrow_length*RIGHT) arrow = Vector(arrow_length*RIGHT)
arrow.set_stroke(WHITE, self.dot_stroke_width) arrow.set_stroke(WHITE, 1)
def arrow_update_func(arrow): def arrow_update_func(arrow):
arrow.set_fill(get_output_color(), 1) arrow.set_fill(get_output_color(), 1)
arrow.rotate(-TAU*get_output_rev() - arrow.get_angle()) arrow.rotate(-TAU*get_output_rev() - arrow.get_angle())
@ -2327,8 +2303,7 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
return arrow return arrow
update_arrow = ContinualUpdateFromFunc(arrow, arrow_update_func) update_arrow = ContinualUpdateFromFunc(arrow, arrow_update_func)
if self.include_walkers: self.add(update_arrow, update_dot_color, label_upadte)
self.add(update_arrow, update_dot_color, label_upadte)
return dot return dot
def position_dot(self, point): def position_dot(self, point):
@ -2336,17 +2311,6 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
self.start_rev = self.get_output_rev() self.start_rev = self.get_output_rev()
self.curr_winding = 0 self.curr_winding = 0
class TransitionFromPathsToBoundariesArrowless(TransitionFromPathsToBoundaries):
CONFIG = {
"func" : plane_func_by_wind_spec(
(-2, 0, 2), (2, 0, 1)
),
"dot_fill_opacity" : 0,
"dot_stroke_width" : 0,
"include_walkers" : False,
"include_question_mark" : False,
}
class BreakDownLoopWithNonzeroWinding(TransitionFromPathsToBoundaries): class BreakDownLoopWithNonzeroWinding(TransitionFromPathsToBoundaries):
def construct(self): def construct(self):
zero_point = 2*LEFT zero_point = 2*LEFT
@ -2625,7 +2589,9 @@ class PolynomialTerms(MonomialTerm):
class SearchSpacePerimeterVsArea(EquationSolver2d): class SearchSpacePerimeterVsArea(EquationSolver2d):
CONFIG = { CONFIG = {
"func" : example_plane_func, "func" : plane_func_by_wind_spec(
(-3, -1.3, 2), (0.1, 0.2, 1), (2.8, -2, 1)
),
"num_iterations" : 15, "num_iterations" : 15,
"display_in_parallel" : False, "display_in_parallel" : False,
"use_fancy_lines" : True, "use_fancy_lines" : True,
@ -2688,6 +2654,7 @@ class SearchSpacePerimeterVsArea(EquationSolver2d):
self.play(FadeOut(full_rect)) self.play(FadeOut(full_rect))
self.wait() self.wait()
<<<<<<< HEAD:old_projects/WindingNumber_G.py
class ShowPolynomialFinalState(SolveX5MinusXMinus1): class ShowPolynomialFinalState(SolveX5MinusXMinus1):
CONFIG = { CONFIG = {
"num_iterations" : 15, "num_iterations" : 15,
@ -2905,6 +2872,8 @@ class AllOfTheVideos(Scene):
self.play(LaggedStart(FadeIn, images, run_time = 4)) self.play(LaggedStart(FadeIn, images, run_time = 4))
self.wait() self.wait()
=======
>>>>>>> parent of feeb9ec... Merge branch 'master' into eop:active_projects/WindingNumber_G.py
class EndingCredits(Scene): class EndingCredits(Scene):
def construct(self): def construct(self):
text = TextMobject( text = TextMobject(
@ -3218,33 +3187,8 @@ class EndScreen(PatreonEndScreen, PiCreatureScene):
self.play(morty.change, mode) self.play(morty.change, mode)
self.wait(2) self.wait(2)
class Thumbnail(SearchSpacePerimeterVsArea):
CONFIG = {
"num_iterations" : 18,
"func" : plane_func_by_wind_spec(
(-3, -1.3, 2), (0.1, 0.2, 1), (2.8, -2, 1)
),
}
def construct(self):
self.force_skipping()
EquationSolver2d.construct(self)
self.revert_to_original_skipping_status()
mobjects = VGroup(*self.get_mobjects())
lines = VGroup()
rects = VGroup()
get_length = lambda mob : max(mob.get_width(), mob.get_height())
for mob in mobjects:
if mob.background_image_file is not None:
mob.set_stroke(width = 4*np.sqrt(get_length(mob)))
lines.add(mob)
elif isinstance(mob, Polygon):
rects.add(mob)
else:
self.remove(mob)
self.clear()
self.add(lines)

106
once_useful_constructs/complex_transformation_scene.py
View file

@ -156,6 +156,112 @@ class ComplexTransformationScene(Scene):
*added_anims *added_anims
) )
<<<<<<< HEAD:once_useful_constructs/complex_transformation_scene.py
=======
##### Unsure about what comes under here...
def complex_string(complex_num):
return filter(lambda c : c not in "()", str(complex_num))
class ComplexPlane(NumberPlane):
CONFIG = {
"color" : BLUE,
"unit_size" : 1,
"line_frequency" : 1,
"faded_line_frequency" : 0.5,
}
def __init__(self, **kwargs):
digest_config(self, kwargs)
kwargs.update({
"x_unit_size" : self.unit_size,
"y_unit_size" : self.unit_size,
"x_line_frequency" : self.line_frequency,
"x_faded_line_frequency" : self.faded_line_frequency,
"y_line_frequency" : self.line_frequency,
"y_faded_line_frequency" : self.faded_line_frequency,
})
NumberPlane.__init__(self, **kwargs)
def number_to_point(self, number):
number = complex(number)
return self.coords_to_point(number.real, number.imag)
def point_to_number(self, point):
x, y = self.point_to_coords(point)
return complex(x, y)
def get_coordinate_labels(self, *numbers):
# TODO: Should merge this with the code from NumberPlane.get_coordinate_labels
result = VGroup()
nudge = 0.1*(DOWN+RIGHT)
if len(numbers) == 0:
numbers = range(-int(self.x_radius), int(self.x_radius)+1)
numbers += [
complex(0, y)
for y in range(-int(self.y_radius), int(self.y_radius)+1)
]
for number in numbers:
if number == complex(0, 0):
continue
point = self.number_to_point(number)
num_str = str(number).replace("j", "i")
if num_str.startswith("0"):
num_str = "0"
elif num_str in ["1i", "-1i"]:
num_str = num_str.replace("1", "")
num_mob = TexMobject(num_str)
num_mob.add_background_rectangle()
num_mob.scale_to_fit_height(self.written_coordinate_height)
num_mob.next_to(point, DOWN+LEFT, SMALL_BUFF)
result.add(num_mob)
return result
def add_coordinates(self, *numbers):
self.add(*self.get_coordinate_labels(*numbers))
return self
def add_spider_web(self, circle_freq = 1, angle_freq = np.pi/6):
# This code no longer works because it has this reference to self.fade_factor
# which is never initialized. Shall we delete this little-used function entirely?
self.fade(self.fade_factor)
config = {
"color" : self.color,
"density" : self.density,
}
for radius in np.arange(circle_freq, SPACE_WIDTH, circle_freq):
self.add(Circle(radius = radius, **config))
for angle in np.arange(0, 2*np.pi, angle_freq):
end_point = np.cos(angle)*RIGHT + np.sin(angle)*UP
end_point *= SPACE_WIDTH
self.add(Line(ORIGIN, end_point, **config))
return self
class ComplexFunction(ApplyPointwiseFunction):
def __init__(self, function, mobject = ComplexPlane, **kwargs):
if "path_func" not in kwargs:
self.path_func = path_along_arc(
np.log(function(complex(1))).imag
)
ApplyPointwiseFunction.__init__(
self,
lambda (x, y, z) : complex_to_R3(function(complex(x, y))),
instantiate(mobject),
**kwargs
)
class ComplexHomotopy(Homotopy):
def __init__(self, complex_homotopy, mobject = ComplexPlane, **kwargs):
"""
Complex Hootopy a function Cx[0, 1] to C
"""
def homotopy(event):
x, y, z, t = event
c = complex_homotopy((complex(x, y), t))
return (c.real, c.imag, z)
Homotopy.__init__(self, homotopy, mobject, *args, **kwargs)
>>>>>>> parent of feeb9ec... Merge branch 'master' into eop:topics/complex_numbers.py