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Merge branch 'master' into eop
This commit is contained in:
Ben Hambrecht
commit
feeb9eca49
3 changed files with 516 additions and 65 deletions
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@ -30,6 +30,8 @@ from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from topics.graph_scene import *
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import time
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import mpmath
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mpmath.mp.dps = 7
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@ -437,7 +439,9 @@ def resit_near(x, m):
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# TODO?: Perhaps use modulus of (uniform) continuity instead of num_checkpoints, calculating
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# latter as needed from former?
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def make_alpha_winder(func, start, end, num_checkpoints):
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#
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# "cheap" argument only used for diagnostic testing right now
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def make_alpha_winder(func, start, end, num_checkpoints, cheap = False):
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check_points = [None for i in range(num_checkpoints)]
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check_points[0] = func(start)
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step_size = fdiv(end - start, num_checkpoints)
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@ -447,9 +451,15 @@ def make_alpha_winder(func, start, end, num_checkpoints):
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func(start + (i + 1) * step_size),
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check_points[i])
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def return_func(alpha):
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if cheap:
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return alpha # A test to see if this func is responsible for slowdown
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index = clamp(0, num_checkpoints - 1, int(alpha * num_checkpoints))
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x = interpolate(start, end, alpha)
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return resit_near(func(x), check_points[index])
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if cheap:
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return check_points[index] # A more principled test that at least returns a reasonable answer
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else:
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return resit_near(func(x), check_points[index])
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return return_func
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# The various inconsistent choices of what datatype to use where are a bit of a mess,
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@ -586,6 +596,7 @@ def walker_animation_with_display(
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show_arrows = True,
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scale_arrows = False,
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num_decimal_points = 1,
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include_background_rectangle = True,
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**kwargs
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):
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@ -601,13 +612,15 @@ def walker_animation_with_display(
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if number_update_func != None:
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display = DecimalNumber(0,
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num_decimal_points = num_decimal_points,
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fill_color = WHITE,
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include_background_rectangle = True)
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display.background_rectangle.fill_opacity = 0.5
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display.background_rectangle.fill_color = GREY
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display.background_rectangle.scale(1.2)
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fill_color = WHITE if include_background_rectangle else BLACK,
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include_background_rectangle = include_background_rectangle)
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if include_background_rectangle:
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display.background_rectangle.fill_opacity = 0.5
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display.background_rectangle.fill_color = GREY
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display.background_rectangle.scale(1.2)
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displaycement = 0.5 * DOWN # How about that pun, eh?
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display.move_to(walker.get_center() + displaycement)
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# display.move_to(walker.get_center() + displaycement)
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display.next_to(walker, DOWN+RIGHT, SMALL_BUFF)
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display_anim = ChangingDecimal(display,
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number_update_func,
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tracked_mobject = walker_anim.compound_walker.walker,
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@ -625,6 +638,7 @@ def LinearWalker(
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number_update_func = None,
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show_arrows = True,
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scale_arrows = False,
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include_background_rectangle = True,
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**kwargs
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):
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walk_func = lambda alpha : interpolate(start_coords, end_coords, alpha)
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@ -635,6 +649,7 @@ def LinearWalker(
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number_update_func = number_update_func,
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show_arrows = show_arrows,
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scale_arrows = scale_arrows,
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include_background_rectangle = include_background_rectangle,
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**kwargs)
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class ColorMappedByFuncScene(Scene):
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@ -747,7 +762,8 @@ class PiWalker(ColorMappedByFuncScene):
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"show_num_plane" : False,
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"draw_lines" : True,
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"num_checkpoints" : 10,
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"num_decimal_points" : 1
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"num_decimal_points" : 1,
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"include_background_rectangle" : False,
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}
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def construct(self):
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@ -803,6 +819,7 @@ class PiWalker(ColorMappedByFuncScene):
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run_time = self.step_run_time,
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walker_stroke_color = WALKER_LIGHT_COLOR if self.color_foreground_not_background else BLACK,
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num_decimal_points = self.num_decimal_points,
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include_background_rectangle = self.include_background_rectangle,
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)
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if self.display_odometer:
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@ -984,6 +1001,18 @@ class EquationSolver2dNode(object):
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bfs_nodes = self.hacky_bfs()
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return Succession(*map(lambda n : n.first_anim, bfs_nodes))
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def play_in_bfs(self, scene, border_anim):
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bfs_nodes = self.hacky_bfs()
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print "Number of nodes: ", len(bfs_nodes)
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if len(bfs_nodes) < 1:
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print "Less than 1 node! Aborting!"
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return
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scene.play(bfs_nodes[0].first_anim, border_anim)
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for node in bfs_nodes[1:]:
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scene.play(node.first_anim)
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class EquationSolver2d(ColorMappedObjectsScene):
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CONFIG = {
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"camera_config" : {"use_z_coordinate_for_display_order": True},
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@ -991,7 +1020,7 @@ class EquationSolver2d(ColorMappedObjectsScene):
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"initial_upper_x" : 5,
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"initial_lower_y" : -3,
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"initial_upper_y" : 3,
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"num_iterations" : 1,
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"num_iterations" : 0,
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"num_checkpoints" : 10,
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# Should really merge this into one enum-style variable
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@ -999,6 +1028,9 @@ class EquationSolver2d(ColorMappedObjectsScene):
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"display_in_bfs" : False,
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"use_fancy_lines" : True,
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"line_color" : WHITE, # Only used for non-fancy lines
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# TODO: Consider adding a "find_all_roots" flag, which could be turned off
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# to only explore one of the two candidate subrectangles when both are viable
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@ -1016,18 +1048,26 @@ class EquationSolver2d(ColorMappedObjectsScene):
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# Used for UhOhScene;
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"manual_wind_override" : None,
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"show_cursor" : False,
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"show_cursor" : True,
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"linger_parameter" : 0.2,
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"linger_parameter" : 0.5,
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"use_separate_plays" : False,
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"use_cheap_winding_numbers" : False, # To use this, make num_checkpoints large
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}
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def construct(self):
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if self.num_iterations == 0:
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print "You forgot to set num_iterations (maybe you meant to subclass something other than EquationSolver2d directly?)"
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return
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ColorMappedObjectsScene.construct(self)
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num_plane = self.num_plane
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clockwise_val_func = lambda p : -point_to_rev(self.func(p))
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base_line = Line(UP, RIGHT, stroke_width = border_stroke_width, color = WHITE)
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base_line = Line(UP, RIGHT, stroke_width = border_stroke_width, color = self.line_color)
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if self.use_fancy_lines:
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base_line.color_using_background_image(self.background_image_file)
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@ -1067,7 +1107,7 @@ class EquationSolver2d(ColorMappedObjectsScene):
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return EquationSolver2dNode(empty_animation)
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def draw_line_return_wind(start, end, start_wind, should_linger = False, draw_line = True):
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alpha_winder = make_alpha_winder(clockwise_val_func, start, end, self.num_checkpoints)
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alpha_winder = make_alpha_winder(clockwise_val_func, start, end, self.num_checkpoints, cheap = self.use_cheap_winding_numbers)
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a0 = alpha_winder(0)
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rebased_winder = lambda alpha: alpha_winder(alpha) - a0 + start_wind
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colored_line = Line(num_plane.coords_to_point(*start) + IN, num_plane.coords_to_point(*end) + IN)
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@ -1122,7 +1162,7 @@ class EquationSolver2d(ColorMappedObjectsScene):
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width = rect.get_width()
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height = rect.get_height()
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cursor.move_to(num_plane.coords_to_point(center_x, center_y))
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cursor.move_to(num_plane.coords_to_point(center_x, center_y) + 10 * IN)
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cursor.scale(min(width, height))
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# Do a quick FadeIn, wait, and quick FadeOut on the cursor, matching rectangle-drawing time
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@ -1134,7 +1174,11 @@ class EquationSolver2d(ColorMappedObjectsScene):
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anim = AnimationGroup(anim, cursor_anim)
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total_wind = head(manual_wind_override) or round(wind_so_far)
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override_wind = head(manual_wind_override)
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if override_wind != None:
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total_wind = override_wind
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else:
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total_wind = round(wind_so_far)
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if total_wind == 0:
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coords = [
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@ -1227,15 +1271,17 @@ class EquationSolver2d(ColorMappedObjectsScene):
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rate_func = rect_rate
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)
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self.play(anim, border_anim)
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print "About to do the big Play; for reference, the current time is ", time.strftime("%H:%M:%S")
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if self.use_separate_plays:
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node.play_in_bfs(self, border_anim)
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else:
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self.play(anim, border_anim)
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print "All done; for reference, the current time is ", time.strftime("%H:%M:%S")
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self.wait()
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# In case we wish to reference these later, as had been done in the
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# WindingNumber_G/SearchSpacePerimeterVsArea scene at one point
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self.node = node
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self.anim = anim
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# TODO: Perhaps have option for bullets (pulses) to fade out and in at ends of line, instead of
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# jarringly popping out and in?
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#
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@ -1248,7 +1294,7 @@ class LinePulser(ContinualAnimation):
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self.pulse_time = pulse_time
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self.bullets = [bullet_template.copy() for i in range(num_bullets)]
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self.output_func = output_func
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ContinualAnimation.__init__(self, VGroup(line, VGroup(*self.bullets)), **kwargs)
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ContinualAnimation.__init__(self, VGroup(*self.bullets), **kwargs)
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def update_mobject(self, dt):
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alpha = self.external_time % self.pulse_time
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@ -1983,7 +2029,9 @@ class LoopSplitScene(ColorMappedObjectsScene):
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def flash_circles(circles):
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self.play(LaggedStart(FadeIn, VGroup(circles)))
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self.play(*map(FadeOut, circles))
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self.wait()
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self.play(FadeOut(VGroup(circles)))
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self.wait()
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self.add(left_square_lines_vmobject, right_square_lines_vmobject)
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self.remove(*midline_lines)
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@ -1997,15 +2045,17 @@ class LoopSplitScene(ColorMappedObjectsScene):
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self.wait()
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flash_circles([indicate_circle(l) for l in left_square_lines])
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self.play(line_fade(faded, 1, right_square_lines_vmobject), *bullet_list_fade(1, 0, left_square_bullets))
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self.wait()
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self.add(*right_square_anims)
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self.play(line_fade(1, faded, left_square_lines_vmobject), *bullet_list_fade(0, 1, right_square_bullets))
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self.wait()
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flash_circles([indicate_circle(l) for l in right_square_lines])
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self.play(line_fade(faded, 1, left_square_lines_vmobject), *bullet_list_fade(1, 0, right_square_bullets))
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self.wait()
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self.play(*bullet_list_fade(0, 1, left_square_bullets + right_square_bullets))
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self.wait()
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outside_circlers = [
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indicate_circle(left_line),
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@ -2017,20 +2067,15 @@ class LoopSplitScene(ColorMappedObjectsScene):
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inner_circle = indicate_circle(midline_lines[0])
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self.play(FadeIn(inner_circle))
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self.wait()
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self.play(FadeOut(inner_circle), line_fade(1, 0, midline_lines_vmobject), *bullet_list_fade(1, 0, midline_bullets))
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self.wait(3)
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# Is there a way to abstract this into a general process to derive a new mapped scene from an old scene?
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class LoopSplitSceneMapped(LoopSplitScene):
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def setup(self):
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left_camera = Camera(**self.camera_config)
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right_camera = MappingCamera(
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mapping_func = lambda (x, y, z) : complex_to_R3(((complex(x,y) + 3)**1.1) - 3),
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**self.camera_config)
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split_screen_camera = SplitScreenCamera(left_camera, right_camera, **self.camera_config)
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self.camera = split_screen_camera
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self.wait()
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# Repeat for effect, goes well with narration
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self.play(FadeIn(inner_circle), line_fade(0, 1, midline_lines_vmobject), *bullet_list_fade(0, 1, midline_bullets))
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self.wait()
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self.play(FadeOut(inner_circle), line_fade(1, 0, midline_lines_vmobject), *bullet_list_fade(1, 0, midline_bullets))
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self.wait()
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# TODO: Perhaps do extra illustration of zooming out and winding around a large circle,
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# to illustrate relation between degree and large-scale winding number
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@ -2038,16 +2083,121 @@ class FundThmAlg(EquationSolver2d):
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CONFIG = {
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"func" : plane_func_by_wind_spec((1, 2), (-1, 1.5), (-1, 1.5)),
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"num_iterations" : 2,
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"use_fancy_lines" : True,
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}
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class SolveX5MinusXMinus1(EquationSolver2d):
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CONFIG = {
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"func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
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"num_iterations" : 5,
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"use_fancy_lines" : True,
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"num_iterations" : 10,
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"show_cursor" : True,
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"display_in_bfs" : True,
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}
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class PureColorMapOfX5Thing(PureColorMap):
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CONFIG = {
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"func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
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}
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class X5ThingWithRightHalfGreyed(SolveX5MinusXMinus1):
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CONFIG = {
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"num_iterations" : 3,
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"manual_wind_override" : (1, None, (1, (0, None, None), (0, None, None)))
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}
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class SolveX5MinusXMinus1_5Iterations(EquationSolver2d):
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CONFIG = {
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"func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
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"num_iterations" : 5,
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"show_cursor" : True,
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"display_in_bfs" : True,
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"manual_wind_override" : (None, None, (None, (0, None, None), (0, None, None)))
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}
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class X5_Monster_Red_Lines(SolveX5MinusXMinus1_5Iterations):
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CONFIG = {
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"use_separate_plays" : True,
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"use_fancy_lines" : False,
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"line_color" : RED,
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}
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class X5_Monster_Green_Lines(X5_Monster_Red_Lines):
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CONFIG = {
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"line_color" : GREEN,
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}
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class X5_Monster_Red_Lines_Long(X5_Monster_Red_Lines):
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CONFIG = {
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"num_iterations" : 6
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}
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class X5_Monster_Green_Lines_Long(X5_Monster_Green_Lines):
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CONFIG = {
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"num_iterations" : 6
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}
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|
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class X5_Monster_Red_Lines_Little_More(X5_Monster_Red_Lines_Long):
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CONFIG = {
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"num_iterations" : 7
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}
|
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|
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class X5_Monster_Green_Lines_Little_More(X5_Monster_Green_Lines_Long):
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CONFIG = {
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"num_iterations" : 7
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}
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|
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class X5_Monster_Red_Lines_No_Numbers(X5_Monster_Red_Lines):
|
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CONFIG = {
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"num_iterations" : 3,
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||||
"show_winding_numbers" : False,
|
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}
|
||||
|
||||
class X5_Monster_Green_Lines_No_Numbers(X5_Monster_Green_Lines):
|
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CONFIG = {
|
||||
"num_iterations" : 3,
|
||||
"show_winding_numbers" : False,
|
||||
}
|
||||
|
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class SolveX5MinusXMinus1_3Iterations(EquationSolver2d):
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CONFIG = {
|
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"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):
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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,
|
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|
||||
# This causes a small slowdown (before rendering, in particular), but not the big one, I think
|
||||
"show_winding_numbers" : True,
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||||
|
||||
# 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)
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||||
# use_z_coordinate = True: 30
|
||||
# show_winding_numbers = True: 10
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# winding AND use_fancy_lines: 10
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||||
# not db AND fancy_lines AND z_coords = true, winding = false: 3. Not 30, but 3. Slow.
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||||
# db AND use_fancy: 3. Slow.
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# fancy AND z_coords: 30. Fast. [Hm, this may have been a mistake; fancy and z_coords is now slow?]
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||||
# 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):
|
||||
CONFIG = {
|
||||
"display_in_parallel" : True
|
||||
|
|
@ -2066,6 +2216,37 @@ class PreviewClip(EquationSolver2d):
|
|||
"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):
|
||||
CONFIG = {
|
||||
"num_iterations" : 3,
|
||||
|
|
@ -2083,6 +2264,11 @@ class LongEquationSolver(EquationSolver2d):
|
|||
"show_cursor" : True,
|
||||
}
|
||||
|
||||
class QuickPreviewUnfancy(LongEquationSolver):
|
||||
CONFIG = {
|
||||
# "use_fancy_lines" : False,
|
||||
}
|
||||
|
||||
# TODO: Borsuk-Ulam visuals
|
||||
# Note: May want to do an ordinary square scene, then MappingCamera it into a circle
|
||||
# class BorsukUlamScene(PiWalker):
|
||||
|
|
@ -2509,18 +2695,6 @@ class ShowBack(PiWalkerRect):
|
|||
"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):
|
||||
CONFIG = {
|
||||
"display_odometer" : True
|
||||
|
|
@ -1928,6 +1928,20 @@ class TinyLoopAroundRed(TinyLoop):
|
|||
"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):
|
||||
CONFIG = {
|
||||
"func" : lambda p : (
|
||||
|
|
@ -2180,7 +2194,11 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
|
|||
CONFIG = {
|
||||
"func" : plane_func_by_wind_spec(
|
||||
(-2, 0, 2), (2, 0, 1)
|
||||
)
|
||||
),
|
||||
"dot_fill_opacity" : 1,
|
||||
"dot_stroke_width" : 1,
|
||||
"include_walkers" : True,
|
||||
"include_question_mark" : True,
|
||||
}
|
||||
def construct(self):
|
||||
ColorMappedObjectsScene.construct(self)
|
||||
|
|
@ -2210,7 +2228,10 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
|
|||
|
||||
#Setup region labels
|
||||
|
||||
for square, tex in (left_square, "x"), (right_square, "y"), (joint_rect, "x+y \\, ?"):
|
||||
sum_tex = "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.move_to(square)
|
||||
|
||||
|
|
@ -2264,7 +2285,7 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
|
|||
path_arc = TAU/6
|
||||
),
|
||||
FadeIn(joint_rect.label[1][1]),
|
||||
FadeIn(joint_rect.label[1][3]),
|
||||
FadeIn(joint_rect.label[1][3:]),
|
||||
FadeOut(right_square.label[0]),
|
||||
Transform(
|
||||
right_square.label[1], joint_rect.label[1][2],
|
||||
|
|
@ -2313,9 +2334,12 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
|
|||
|
||||
#Setup dot, arrow and label
|
||||
dot = self.dot = Dot(radius = 0.1)
|
||||
dot.set_stroke(WHITE, 1)
|
||||
dot.set_stroke(WHITE, self.dot_stroke_width)
|
||||
update_dot_color = ContinualUpdateFromFunc(
|
||||
dot, lambda d : d.set_fill(get_output_color())
|
||||
dot, lambda d : d.set_fill(
|
||||
get_output_color(),
|
||||
self.dot_fill_opacity
|
||||
)
|
||||
)
|
||||
|
||||
label = DecimalNumber(0, num_decimal_points = 1)
|
||||
|
|
@ -2326,7 +2350,7 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
|
|||
|
||||
arrow_length = 0.75
|
||||
arrow = Vector(arrow_length*RIGHT)
|
||||
arrow.set_stroke(WHITE, 1)
|
||||
arrow.set_stroke(WHITE, self.dot_stroke_width)
|
||||
def arrow_update_func(arrow):
|
||||
arrow.set_fill(get_output_color(), 1)
|
||||
arrow.rotate(-TAU*get_output_rev() - arrow.get_angle())
|
||||
|
|
@ -2335,7 +2359,8 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
|
|||
return arrow
|
||||
update_arrow = ContinualUpdateFromFunc(arrow, arrow_update_func)
|
||||
|
||||
self.add(update_arrow, update_dot_color, label_upadte)
|
||||
if self.include_walkers:
|
||||
self.add(update_arrow, update_dot_color, label_upadte)
|
||||
return dot
|
||||
|
||||
def position_dot(self, point):
|
||||
|
|
@ -2343,6 +2368,17 @@ class TransitionFromPathsToBoundaries(ColorMappedObjectsScene):
|
|||
self.start_rev = self.get_output_rev()
|
||||
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):
|
||||
def construct(self):
|
||||
zero_point = 2*LEFT
|
||||
|
|
@ -2621,9 +2657,7 @@ class PolynomialTerms(MonomialTerm):
|
|||
|
||||
class SearchSpacePerimeterVsArea(EquationSolver2d):
|
||||
CONFIG = {
|
||||
"func" : plane_func_by_wind_spec(
|
||||
(-3, -1.3, 2), (0.1, 0.2, 1), (2.8, -2, 1)
|
||||
),
|
||||
"func" : example_plane_func,
|
||||
"num_iterations" : 15,
|
||||
"display_in_parallel" : False,
|
||||
"use_fancy_lines" : True,
|
||||
|
|
@ -2686,6 +2720,223 @@ class SearchSpacePerimeterVsArea(EquationSolver2d):
|
|||
self.play(FadeOut(full_rect))
|
||||
self.wait()
|
||||
|
||||
class ShowPolynomialFinalState(SolveX5MinusXMinus1):
|
||||
CONFIG = {
|
||||
"num_iterations" : 15,
|
||||
}
|
||||
def construct(self):
|
||||
self.force_skipping()
|
||||
SolveX5MinusXMinus1.construct(self)
|
||||
self.revert_to_original_skipping_status()
|
||||
|
||||
class PiCreatureInAwe(Scene):
|
||||
def construct(self):
|
||||
randy = Randolph()
|
||||
|
||||
|
||||
self.play(randy.change, "awe")
|
||||
self.play(Blink(randy))
|
||||
self.play(randy.look, UP, run_time = 2)
|
||||
self.play(
|
||||
randy.look, RIGHT,
|
||||
run_time = 4,
|
||||
rate_func = there_and_back,
|
||||
path_arc = -TAU/4
|
||||
)
|
||||
self.wait()
|
||||
|
||||
class ShowComplexFunction(Scene):
|
||||
def construct(self):
|
||||
plane = ComplexPlane()
|
||||
plane.add_coordinates()
|
||||
four_i = plane.coordinate_labels[-1]
|
||||
plane.coordinate_labels.remove(four_i)
|
||||
plane.remove(four_i)
|
||||
|
||||
title = TextMobject("Complex Plane")
|
||||
title.to_edge(UP, buff = MED_SMALL_BUFF)
|
||||
rect = BackgroundRectangle(title, fill_opacity = 1, buff = MED_SMALL_BUFF)
|
||||
|
||||
x = complex(1, 0.4)
|
||||
f = lambda x : x**5 - x - 1
|
||||
|
||||
x_point = plane.number_to_point(x)
|
||||
fx_point = plane.number_to_point(f(x))
|
||||
|
||||
x_dot = Dot(x_point)
|
||||
fx_dot = Dot(fx_point, color = YELLOW)
|
||||
arrow = Arrow(
|
||||
x_point, fx_point,
|
||||
use_rectangular_stem = False,
|
||||
path_arc = TAU/3,
|
||||
color = YELLOW
|
||||
)
|
||||
arrow.pointwise_become_partial(arrow, 0, 0.95)
|
||||
|
||||
x_label = TexMobject("x = %d+%.1fi"%(x.real, x.imag))
|
||||
x_label.next_to(x_dot, RIGHT)
|
||||
x_label.add_background_rectangle()
|
||||
|
||||
fx_label = TexMobject("f(x) = x^5 - x - 1")
|
||||
fx_label.next_to(fx_dot, DOWN, SMALL_BUFF)
|
||||
fx_label.highlight(YELLOW)
|
||||
fx_label.add_background_rectangle()
|
||||
fx_label.generate_target()
|
||||
fx_label.target.move_to(title)
|
||||
fx_label.target[1].highlight(WHITE)
|
||||
|
||||
self.play(
|
||||
Write(plane),
|
||||
FadeIn(rect),
|
||||
LaggedStart(FadeIn, title)
|
||||
)
|
||||
self.play(*map(FadeIn, [x_dot, x_label]))
|
||||
self.wait()
|
||||
self.play(
|
||||
ReplacementTransform(x_dot.copy(), fx_dot, path_arc = arrow.path_arc),
|
||||
ShowCreation(arrow, rate_func = squish_rate_func(smooth, 0.2, 1))
|
||||
)
|
||||
self.play(FadeIn(fx_label))
|
||||
self.wait(2)
|
||||
self.play(
|
||||
MoveToTarget(fx_label),
|
||||
*map(FadeOut, [title, x_dot, x_label, arrow, fx_dot])
|
||||
)
|
||||
self.play(FadeOut(plane.coordinate_labels))
|
||||
self.wait()
|
||||
|
||||
class WindingNumbersInInputOutputContext(PathContainingZero):
|
||||
CONFIG = {
|
||||
"in_loop_center_coords" : (-2, -1),
|
||||
"run_time" : 10,
|
||||
}
|
||||
def construct(self):
|
||||
self.remove(self.pi_creature)
|
||||
self.setup_planes()
|
||||
|
||||
in_loop = Circle()
|
||||
in_loop.flip(RIGHT)
|
||||
# in_loop = Square(side_length = 2)
|
||||
in_loop.insert_n_anchor_points(100)
|
||||
in_loop.move_to(self.input_plane.coords_to_point(
|
||||
*self.in_loop_center_coords
|
||||
))
|
||||
in_loop.match_background_image_file(self.input_coloring)
|
||||
|
||||
out_loop = in_loop.copy()
|
||||
out_loop.match_background_image_file(self.output_coloring)
|
||||
update_out_loop = ContinualUpdateFromFunc(
|
||||
out_loop,
|
||||
lambda m : m.set_points(in_loop.points).apply_function(self.point_function)
|
||||
)
|
||||
# self.add(update_out_loop)
|
||||
|
||||
in_dot = Dot(radius = 0.04)
|
||||
update_in_dot = ContinualUpdateFromFunc(
|
||||
in_dot, lambda d : d.move_to(in_loop.point_from_proportion(1))
|
||||
)
|
||||
self.add(update_in_dot)
|
||||
|
||||
out_arrow = Arrow(LEFT, RIGHT)
|
||||
update_out_arrow = ContinualUpdateFromFunc(
|
||||
out_arrow,
|
||||
lambda a : a.put_start_and_end_on(
|
||||
self.output_plane.coords_to_point(0, 0),
|
||||
out_loop.point_from_proportion(1)
|
||||
)
|
||||
)
|
||||
update_out_arrow_color = ContinualUpdateFromFunc(
|
||||
out_arrow,
|
||||
lambda a : a.highlight(rev_to_color(a.get_angle()/TAU))
|
||||
)
|
||||
self.add(update_out_arrow, update_out_arrow_color)
|
||||
|
||||
words = TextMobject(
|
||||
"How many times does \\\\ the output wind around?"
|
||||
)
|
||||
label = self.output_plane.label
|
||||
words.move_to(label, UP)
|
||||
self.output_plane.remove(label)
|
||||
self.add(words)
|
||||
|
||||
decimal = DecimalNumber(0)
|
||||
decimal.next_to(self.output_plane.get_corner(UP+RIGHT), DOWN+LEFT)
|
||||
|
||||
|
||||
self.play(
|
||||
ShowCreation(in_loop),
|
||||
ShowCreation(out_loop),
|
||||
ChangeDecimalToValue(decimal, 2),
|
||||
Animation(in_dot),
|
||||
run_time = self.run_time,
|
||||
rate_func = bezier([0, 0, 1, 1])
|
||||
)
|
||||
|
||||
class SolveX5SkipToEnd(SolveX5MinusXMinus1):
|
||||
CONFIG = {
|
||||
"num_iterations" : 4,
|
||||
}
|
||||
def construct(self):
|
||||
self.force_skipping()
|
||||
SolveX5MinusXMinus1.construct(self)
|
||||
self.revert_to_original_skipping_status()
|
||||
|
||||
mobjects = VGroup(*self.get_mobjects())
|
||||
lines = VGroup()
|
||||
rects = VGroup()
|
||||
for mob in mobjects:
|
||||
if mob.background_image_file is not None:
|
||||
mob.set_stroke(width = 2)
|
||||
lines.add(mob)
|
||||
elif isinstance(mob, Polygon):
|
||||
rects.add(mob)
|
||||
else:
|
||||
self.remove(mob)
|
||||
|
||||
self.clear()
|
||||
self.add(lines, rects)
|
||||
|
||||
class ZeroFoundOnBoundary(Scene):
|
||||
def construct(self):
|
||||
arrow = Vector(DOWN+LEFT, color = WHITE)
|
||||
words = TextMobject("Found zero on boundary!")
|
||||
words.next_to(arrow.get_start(), UP)
|
||||
words.shift(1.5*RIGHT)
|
||||
|
||||
point = VectorizedPoint()
|
||||
point.next_to(arrow, DOWN+LEFT)
|
||||
|
||||
self.play(Flash(point))
|
||||
self.play(
|
||||
GrowArrow(arrow),
|
||||
Write(words),
|
||||
)
|
||||
self.wait()
|
||||
|
||||
class AllOfTheVideos(Scene):
|
||||
CONFIG = {
|
||||
"camera_config" : {
|
||||
"background_alpha" : 255,
|
||||
}
|
||||
}
|
||||
def construct(self):
|
||||
thumbnail_dir = os.path.join(MEDIA_DIR, "3b1b_videos/Winding/OldThumbnails")
|
||||
n = 4
|
||||
images = Group(*[
|
||||
ImageMobject(os.path.join(thumbnail_dir, file))
|
||||
for file in os.listdir(thumbnail_dir)[:n**2]
|
||||
])
|
||||
for image in images:
|
||||
rect = SurroundingRectangle(image, buff = 0)
|
||||
rect.set_stroke(WHITE, 1)
|
||||
image.add(rect)
|
||||
images.arrange_submobjects_in_grid(n, n, buff = 0)
|
||||
images.scale_to_fit_height(2*SPACE_HEIGHT)
|
||||
random.shuffle(images.submobjects)
|
||||
|
||||
self.play(LaggedStart(FadeIn, images, run_time = 4))
|
||||
self.wait()
|
||||
|
||||
class EndingCredits(Scene):
|
||||
def construct(self):
|
||||
text = TextMobject(
|
||||
|
|
@ -2999,8 +3250,33 @@ class EndScreen(PatreonEndScreen, PiCreatureScene):
|
|||
self.play(morty.change, mode)
|
||||
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)
|
||||
|
||||
|
||||
|
||||
|
|
@ -216,6 +216,7 @@ class ComplexPlane(NumberPlane):
|
|||
num_mob.scale_to_fit_height(self.written_coordinate_height)
|
||||
num_mob.next_to(point, DOWN+LEFT, SMALL_BUFF)
|
||||
result.add(num_mob)
|
||||
self.coordinate_labels = result
|
||||
return result
|
||||
|
||||
def add_coordinates(self, *numbers):
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue