from helpers import * from mobject.tex_mobject import TexMobject from mobject import Mobject from mobject.image_mobject import ImageMobject from mobject.vectorized_mobject import * from animation.animation import Animation from animation.transform import * from animation.simple_animations import * from animation.playground import * from animation.continual_animation import * from topics.geometry import * from topics.characters import * from topics.functions import * from topics.fractals import * from topics.number_line import * from topics.combinatorics import * from topics.numerals import * from topics.three_dimensions import * from topics.objects import * from topics.probability import * from topics.complex_numbers import * from scene import Scene from scene.reconfigurable_scene import ReconfigurableScene from scene.zoomed_scene import * from camera import * from mobject.svg_mobject import * from mobject.tex_mobject import * from topics.graph_scene import * # TODO/WARNING: There's a lot of refactoring and cleanup to be done in this code, # (and it will be done, but first I'll figure out what I'm doing with all this...) # -SR class EquationSolver1d(GraphScene, ZoomedScene): CONFIG = { "func" : lambda x : x, "targetX" : 0, "targetY" : 0, "initial_lower_x" : 0, "initial_upper_x" : 10, "num_iterations" : 10, "iteration_at_which_to_start_zoom" : None, "graph_label" : None, "show_target_line" : True } def drawGraph(self): self.setup_axes() self.graph = self.get_graph(self.func) self.add(self.graph) if self.graph_label != None: self.add(self.get_graph_label(self.graph, self.graph_label, x_val = 4, direction = RIGHT)) if self.show_target_line: target_line_object = DashedLine( self.coords_to_point(self.x_min, self.targetY), self.coords_to_point(self.x_max, self.targetY), dashed_segment_length = 0.1) self.add(target_line_object) target_line_label = TexMobject("y = " + str(self.targetY)) target_line_label.next_to(target_line_object.get_left(), UP + RIGHT) self.add(target_line_label) def solveEquation(self): leftBrace, rightBrace = xBraces = TexMobject("||") xBraces.stretch(2, 0) downBrace, upBrace = yBraces = TexMobject("||") yBraces.stretch(2, 0) yBraces.rotate(TAU/4) lowerX = self.initial_lower_x lowerY = self.func(lowerX) upperX = self.initial_upper_x upperY = self.func(upperX) leftBrace.move_to(self.coords_to_point(lowerX, 0)) leftBraceLabel = DecimalNumber(lowerX) leftBraceLabel.next_to(leftBrace, DOWN + LEFT, buff = SMALL_BUFF) leftBraceLabelAnimation = ContinualChangingDecimal(leftBraceLabel, lambda alpha : self.point_to_coords(leftBrace.get_center())[0], tracked_mobject = leftBrace) self.add(leftBraceLabelAnimation) rightBrace.move_to(self.coords_to_point(upperX, 0)) rightBraceLabel = DecimalNumber(upperX) rightBraceLabel.next_to(rightBrace, DOWN + RIGHT, buff = SMALL_BUFF) rightBraceLabelAnimation = ContinualChangingDecimal(rightBraceLabel, lambda alpha : self.point_to_coords(rightBrace.get_center())[0], tracked_mobject = rightBrace) self.add(rightBraceLabelAnimation) downBrace.move_to(self.coords_to_point(0, lowerY)) downBraceLabel = DecimalNumber(lowerY) downBraceLabel.next_to(downBrace, LEFT + DOWN, buff = SMALL_BUFF) downBraceLabelAnimation = ContinualChangingDecimal(downBraceLabel, lambda alpha : self.point_to_coords(downBrace.get_center())[1], tracked_mobject = downBrace) self.add(downBraceLabelAnimation) upBrace.move_to(self.coords_to_point(0, upperY)) upBraceLabel = DecimalNumber(upperY) upBraceLabel.next_to(upBrace, LEFT + UP, buff = SMALL_BUFF) upBraceLabelAnimation = ContinualChangingDecimal(upBraceLabel, lambda alpha : self.point_to_coords(upBrace.get_center())[1], tracked_mobject = upBrace) self.add(upBraceLabelAnimation) lowerDotPoint = self.input_to_graph_point(lowerX, self.graph) lowerDotXPoint = self.coords_to_point(lowerX, 0) lowerDotYPoint = self.coords_to_point(0, self.func(lowerX)) lowerDot = Dot(lowerDotPoint) upperDotPoint = self.input_to_graph_point(upperX, self.graph) upperDot = Dot(upperDotPoint) upperDotXPoint = self.coords_to_point(upperX, 0) upperDotYPoint = self.coords_to_point(0, self.func(upperX)) lowerXLine = Line(lowerDotXPoint, lowerDotPoint, stroke_width = 1, color = YELLOW) upperXLine = Line(upperDotXPoint, upperDotPoint, stroke_width = 1, color = YELLOW) lowerYLine = Line(lowerDotYPoint, lowerDotPoint, stroke_width = 1, color = YELLOW) upperYLine = Line(upperDotYPoint, upperDotPoint, stroke_width = 1, color = YELLOW) self.add(lowerXLine, upperXLine, lowerYLine, upperYLine) self.add(xBraces, yBraces, lowerDot, upperDot) for i in range(self.num_iterations): if i == self.iteration_at_which_to_start_zoom: self.activate_zooming() self.little_rectangle.move_to( self.coords_to_point(self.targetX, self.targetY)) inverseZoomFactor = 1/float(self.zoom_factor) self.play( lowerDot.scale_in_place, inverseZoomFactor, upperDot.scale_in_place, inverseZoomFactor) def makeUpdater(xAtStart): def updater(group, alpha): dot, xBrace, yBrace, xLine, yLine = group newX = interpolate(xAtStart, midX, alpha) newY = self.func(newX) graphPoint = self.input_to_graph_point(newX, self.graph) dot.move_to(graphPoint) xAxisPoint = self.coords_to_point(newX, 0) xBrace.move_to(xAxisPoint) yAxisPoint = self.coords_to_point(0, newY) yBrace.move_to(yAxisPoint) xLine.put_start_and_end_on(xAxisPoint, graphPoint) yLine.put_start_and_end_on(yAxisPoint, graphPoint) return group return updater midX = (lowerX + upperX)/float(2) midY = self.func(midX) midCoords = self.coords_to_point(midX, midY) midColor = RED midXPoint = Dot(self.coords_to_point(midX, 0), color = midColor) self.play( ReplacementTransform(leftBrace.copy(), midXPoint), ReplacementTransform(rightBrace.copy(), midXPoint)) midXLine = Line(self.coords_to_point(midX, 0), midCoords, color = midColor) self.play(ShowCreation(midXLine)) midDot = Dot(midCoords, color = midColor) if(self.iteration_at_which_to_start_zoom != None and i >= self.iteration_at_which_to_start_zoom): midDot.scale_in_place(inverseZoomFactor) self.add(midDot) midYLine = Line(midCoords, self.coords_to_point(0, midY), color = midColor) self.play(ShowCreation(midYLine)) if midY < self.targetY: movingGroup = Group(lowerDot, leftBrace, downBrace, lowerXLine, lowerYLine) self.play( UpdateFromAlphaFunc(movingGroup, makeUpdater(lowerX))) lowerX = midX lowerY = midY else: movingGroup = Group(upperDot, rightBrace, upBrace, upperXLine, upperYLine) self.play( UpdateFromAlphaFunc(movingGroup, makeUpdater(upperX))) upperX = midX upperY = midY self.remove(midXLine, midDot, midYLine) self.wait() def construct(self): self.drawGraph() self.solveEquation() def rev_to_color(alpha): alpha = alpha % 1 colors = ["#FF0000", ORANGE, YELLOW, "#00FF00", "#0000FF", "#FF00FF"] num_colors = len(colors) beta = (alpha % (1.0/num_colors)) * num_colors start_index = int(np.floor(num_colors * alpha)) % num_colors end_index = (start_index + 1) % num_colors return interpolate_color(colors[start_index], colors[end_index], beta) def point_to_rev((x, y)): # Warning: np.arctan2 would happily discontinuously returns the value 0 for (0, 0), due to # design choices in the underlying atan2 library call, but for our purposes, this is # illegitimate, and all winding number calculations must be set up to avoid this if (x, y) == (0, 0): print "Error! Angle of (0, 0) computed!" return None return np.true_divide(np.arctan2(y, x), TAU) # Returns the value with the same fractional component as x, closest to m def resit_near(x, m): frac_diff = (x - m) % 1 if frac_diff > 0.5: frac_diff -= 1 return m + frac_diff # TODO?: Perhaps use modulus of (uniform) continuity instead of num_checkpoints, calculating # latter as needed from former? def make_alpha_winder(func, start, end, num_checkpoints): check_points = [None for i in range(num_checkpoints)] check_points[0] = func(start) step_size = np.true_divide(end - start, num_checkpoints) for i in range(num_checkpoints - 1): check_points[i + 1] = \ resit_near( func(start + (i + 1) * step_size), check_points[i]) def return_func(alpha): index = clamp(0, num_checkpoints - 1, int(alpha * num_checkpoints)) x = interpolate(start, end, alpha) return resit_near(func(x), check_points[index]) return return_func def split_interval((a, b)): mid = (a + b)/2.0 return ((a, mid), (mid, b)) class RectangleData(): def __init__(self, x_interval, y_interval): self.rect = (x_interval, y_interval) def get_top_left(self): return np.array((self.rect[0][0], self.rect[1][1])) def get_top_right(self): return np.array((self.rect[0][1], self.rect[1][1])) def get_bottom_right(self): return np.array((self.rect[0][1], self.rect[1][0])) def get_bottom_left(self): return np.array((self.rect[0][0], self.rect[1][0])) def get_top(self): return (self.get_top_left(), self.get_top_right()) def get_right(self): return (self.get_top_right(), self.get_bottom_right()) def get_bottom(self): return (self.get_bottom_right(), self.get_bottom_left()) def get_left(self): return (self.get_bottom_left(), self.get_top_left()) def splits_on_dim(self, dim): x_interval = self.rect[0] y_interval = self.rect[1] # TODO: Can refactor the following; will do later if dim == 0: return_data = [RectangleData(new_interval, y_interval) for new_interval in split_interval(x_interval)] elif dim == 1: return_data = [RectangleData(x_interval, new_interval) for new_interval in split_interval(y_interval)] else: print "RectangleData.splits_on_dim passed illegitimate dimension!" return tuple(return_data) def split_line_on_dim(self, dim): x_interval = self.rect[0] y_interval = self.rect[1] if dim == 0: sides = (self.get_top(), self.get_bottom()) elif dim == 1: sides = (self.get_left(), self.get_right()) else: print "RectangleData.split_line_on_dim passed illegitimate dimension!" return tuple([mid(x, y) for (x, y) in sides]) def complex_to_pair(c): return (c.real, c.imag) def plane_poly_with_roots(*points): def f((x, y)): return complex_to_pair(np.prod([complex(x, y) - complex(a,b) for (a,b) in points])) return f def plane_func_from_complex_func(f): return lambda (x, y) : complex_to_pair(f(complex(x,y))) def point_func_from_complex_func(f): return lambda (x, y, z): complex_to_R3(f(complex(x, y))) empty_animation = Animation(Mobject(), run_time = 0) def EmptyAnimation(): return empty_animation class WalkerAnimation(Animation): CONFIG = { "walk_func" : None, # Must be initialized to use "remover" : True, "rate_func" : None, "coords_to_point" : None } def __init__(self, walk_func, rev_func, coords_to_point, scale_factor, **kwargs): self.walk_func = walk_func self.rev_func = rev_func self.coords_to_point = coords_to_point self.compound_walker = VGroup() self.compound_walker.walker = PiCreature(color = RED) self.compound_walker.walker.scale(scale_factor) self.compound_walker.arrow = Arrow(ORIGIN, RIGHT) #, buff = 0) self.compound_walker.digest_mobject_attrs() Animation.__init__(self, self.compound_walker, **kwargs) # Perhaps abstract this out into an "Animation updating from original object" class def update_submobject(self, submobject, starting_submobject, alpha): submobject.points = np.array(starting_submobject.points) def update_mobject(self, alpha): Animation.update_mobject(self, alpha) cur_x, cur_y = cur_coords = self.walk_func(alpha) cur_point = self.coords_to_point(cur_x, cur_y) self.mobject.walker.move_to(cur_point) rev = self.rev_func(cur_coords) self.mobject.walker.set_color(rev_to_color(rev)) self.mobject.arrow.set_color(rev_to_color(rev)) self.mobject.arrow.rotate( rev * TAU, about_point = ORIGIN #self.mobject.arrow.get_start() ) def walker_animation_with_display( walk_func, rev_func, coords_to_point, number_update_func = None, scale_factor = 0.35, **kwargs ): walker_anim = WalkerAnimation( walk_func = walk_func, rev_func = rev_func, coords_to_point = coords_to_point, scale_factor = scale_factor, **kwargs) walker = walker_anim.compound_walker.walker if number_update_func != None: display = DecimalNumber(0, include_background_rectangle = True) displaycement = scale_factor * DOWN # How about that pun, eh? display.move_to(walker.get_center() + displaycement) display_anim = ChangingDecimal(display, number_update_func, tracked_mobject = walker_anim.compound_walker.walker, **kwargs) anim_group = AnimationGroup(walker_anim, display_anim) return anim_group else: return walker_anim def LinearWalker( start_coords, end_coords, coords_to_point, rev_func, number_update_func = None, **kwargs ): walk_func = lambda alpha : interpolate(start_coords, end_coords, alpha) return walker_animation_with_display( walk_func = walk_func, coords_to_point = coords_to_point, rev_func = rev_func, number_update_func = number_update_func, **kwargs) class PiWalker(Scene): CONFIG = { "func" : plane_func_from_complex_func(lambda c : c**2), "walk_coords" : [], "step_run_time" : 1 } def construct(self): rev_func = lambda p : point_to_rev(self.func(p)) num_plane = NumberPlane() num_plane.fade() self.add(num_plane) walk_coords = self.walk_coords for i in range(len(walk_coords)): start_x, start_y = start_coords = walk_coords[i] start_point = num_plane.coords_to_point(start_x, start_y) end_x, end_y = end_coords = walk_coords[(i + 1) % len(walk_coords)] end_point = num_plane.coords_to_point(end_x, end_y) self.play( LinearWalker( start_coords = start_coords, end_coords = end_coords, coords_to_point = num_plane.coords_to_point, rev_func = rev_func, remover = (i < len(walk_coords) - 1) ), ShowCreation(Line(start_point, end_point), rate_func = None), run_time = self.step_run_time) # TODO: Allow smooth paths instead of breaking them up into lines, and # use point_from_proportion to get points along the way self.wait() class PiWalkerRect(PiWalker): CONFIG = { "start_x" : -1, "start_y" : 1, "walk_width" : 2, "walk_height" : 2, } def setup(self): TL = np.array((self.start_x, self.start_y)) TR = TL + (self.walk_width, 0) BR = TR + (0, -self.walk_height) BL = BR + (-self.walk_width, 0) self.walk_coords = [TL, TR, BR, BL] PiWalker.setup(self) class PiWalkerCircle(PiWalker): CONFIG = { "radius" : 1, "num_steps" : 100, "step_run_time" : 0.01 } def setup(self): r = self.radius N = self.num_steps self.walk_coords = [r * np.array((np.cos(i * TAU/N), np.sin(i * TAU/N))) for i in range(N)] PiWalker.setup(self) # TODO: Perhaps restructure this to avoid using AnimationGroup, and instead # use lists of animations or lists or other such data, to be merged and processed into parallel # animations later class EquationSolver2d(Scene): CONFIG = { "func" : plane_poly_with_roots((1, 2), (-1, 3)), "initial_lower_x" : -5.1, "initial_upper_x" : 5.1, "initial_lower_y" : -3.1, "initial_upper_y" : 3.1, "num_iterations" : 5, "num_checkpoints" : 10, # 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 } def construct(self): num_plane = NumberPlane() num_plane.fade() self.add(num_plane) rev_func = lambda p : point_to_rev(self.func(p)) clockwise_rev_func = lambda p : -rev_func(p) def Animate2dSolver(cur_depth, rect, dim_to_split): print "Solver at depth: " + str(cur_depth) if cur_depth >= self.num_iterations: return EmptyAnimation() def draw_line_return_wind(start, end, start_wind): 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 thin_line = Line(num_plane.coords_to_point(*start), num_plane.coords_to_point(*end), stroke_width = 2, color = RED) walker_anim = LinearWalker( start_coords = start, end_coords = end, coords_to_point = num_plane.coords_to_point, rev_func = rev_func, number_update_func = rebased_winder, remover = True ) line_draw_anim = AnimationGroup( ShowCreation(thin_line), walker_anim, rate_func = None) anim = line_draw_anim return (anim, rebased_winder(1)) wind_so_far = 0 anim = EmptyAnimation() sides = [ rect.get_top(), rect.get_right(), rect.get_bottom(), rect.get_left() ] for (start, end) in sides: (next_anim, wind_so_far) = draw_line_return_wind(start, end, wind_so_far) anim = Succession(anim, next_anim) total_wind = round(wind_so_far) if total_wind == 0: coords = [ rect.get_top_left(), rect.get_top_right(), rect.get_bottom_right(), rect.get_bottom_left() ] points = [num_plane.coords_to_point(x, y) for (x, y) in coords] # TODO: Maybe use diagonal lines or something to fill in rectangles indicating # their "Nothing here" status? fill_rect = polygonObject = Polygon(*points, fill_opacity = 0.8, color = RED) return Succession(anim, FadeIn(fill_rect)) else: (sub_rect1, sub_rect2) = rect.splits_on_dim(dim_to_split) sub_rects = [sub_rect1, sub_rect2] sub_anims = [ Animate2dSolver( cur_depth = cur_depth + 1, rect = sub_rect, dim_to_split = 1 - dim_to_split ) for sub_rect in sub_rects ] mid_line_coords = rect.split_line_on_dim(dim_to_split) mid_line_points = [num_plane.coords_to_point(x, y) for (x, y) in mid_line_coords] mid_line = DashedLine(*mid_line_points) return Succession(anim, ShowCreation(mid_line), # FadeOut(mid_line), # TODO: Can change timing so this fades out at just the time it would be overdrawn # TODO: Investigate weirdness with changing z buffer order on mid_line vs. rectangle lines AnimationGroup(*sub_anims) ) lower_x = self.initial_lower_x upper_x = self.initial_upper_x lower_y = self.initial_lower_y upper_y = self.initial_upper_y x_interval = (lower_x, upper_x) y_interval = (lower_y, upper_y) rect = RectangleData(x_interval, y_interval) print "Starting to compute anim" anim = Animate2dSolver( cur_depth = 0, rect = rect, dim_to_split = 0, ) print "Done computing anim" self.play(anim) self.wait() # TODO: Perhaps have bullets (pulses) fade out and in at ends of line, instead of jarringly # popping out and in? # # TODO: Perhaps have bullets change color corresponding to a function of their coordinates? # This could involve some merging of functoinality with PiWalker class LinePulser(ContinualAnimation): def __init__(self, line, bullet_template, num_bullets, pulse_time, output_func = None, **kwargs): self.line = line self.num_bullets = num_bullets self.pulse_time = pulse_time self.bullets = [bullet_template.copy() for i in range(num_bullets)] self.output_func = output_func ContinualAnimation.__init__(self, VGroup(line, VGroup(*self.bullets)), **kwargs) def update_mobject(self, dt): alpha = self.external_time % self.pulse_time start = self.line.get_start() end = self.line.get_end() for i in range(self.num_bullets): position = interpolate(start, end, np.true_divide((i + alpha),(self.num_bullets))) self.bullets[i].move_to(position) if self.output_func: position_2d = (position[0], position[1]) rev = point_to_rev(self.output_func(position_2d)) color = rev_to_color(rev) self.bullets[i].set_color(color) class ArrowCircleTest(Scene): def construct(self): circle_radius = 3 circle = Circle(radius = circle_radius, color = WHITE) self.add(circle) base_arrow = Arrow(circle_radius * 0.7 * RIGHT, circle_radius * 1.3 * RIGHT) def rev_rotate(x, revs): x.rotate(revs * TAU, about_point = ORIGIN) x.set_color(rev_to_color(revs)) return x num_arrows = 8 * 3 arrows = [rev_rotate(base_arrow.copy(), (np.true_divide(i, num_arrows))) for i in range(num_arrows)] arrows_vgroup = VGroup(*arrows) self.play(ShowCreation(arrows_vgroup), run_time = 2.5, rate_func = None) self.wait() class FuncRotater(Animation): CONFIG = { "rotate_func" : lambda x : x # Func from alpha to revolutions } # Perhaps abstract this out into an "Animation updating from original object" class def update_submobject(self, submobject, starting_submobject, alpha): submobject.points = np.array(starting_submobject.points) def update_mobject(self, alpha): Animation.update_mobject(self, alpha) angle_revs = self.rotate_func(alpha) # We do a clockwise rotation self.mobject.rotate( -angle_revs * TAU, about_point = ORIGIN ) self.mobject.set_color(rev_to_color(angle_revs)) class TestRotater(Scene): def construct(self): test_line = Line(ORIGIN, RIGHT) self.play(FuncRotater( test_line, rotate_func = lambda x : x % 0.25, run_time = 10)) # TODO: Be careful about clockwise vs. counterclockwise convention throughout! # Make sure this is correct everywhere in resulting video. class OdometerScene(Scene): CONFIG = { "rotate_func" : lambda x : np.sin(x * TAU), "run_time" : 5, "dashed_line_angle" : None, "biased_display_start" : None } def construct(self): radius = 1.3 circle = Circle(center = ORIGIN, radius = radius) self.add(circle) if self.dashed_line_angle: dashed_line = DashedLine(ORIGIN, radius * RIGHT) # Clockwise rotation dashed_line.rotate(-self.dashed_line_angle * TAU, about_point = ORIGIN) self.add(dashed_line) num_display = DecimalNumber(0, include_background_rectangle = True) num_display.move_to(2 * DOWN) display_val_bias = 0 if self.biased_display_start != None: display_val_bias = self.biased_display_start - self.rotate_func(0) display_func = lambda alpha : self.rotate_func(alpha) + display_val_bias base_arrow = Arrow(ORIGIN, RIGHT, buff = 0) self.play( FuncRotater(base_arrow, rotate_func = self.rotate_func), ChangingDecimal(num_display, display_func), run_time = self.run_time, rate_func = None) ############# # Above are mostly general tools; here, we list, in order, finished or near-finished scenes class FirstSqrtScene(EquationSolver1d): CONFIG = { "x_min" : 0, "x_max" : 2.5, "y_min" : 0, "y_max" : 2.5**2, "graph_origin" : 2*DOWN + 5 * LEFT, "x_axis_width" : 12, "zoom_factor" : 3, "zoomed_canvas_center" : 2.25 * UP + 1.75 * LEFT, "func" : lambda x : x**2, "targetX" : np.sqrt(2), "targetY" : 2, "initial_lower_x" : 1, "initial_upper_x" : 2, "num_iterations" : 10, "iteration_at_which_to_start_zoom" : 3, "graph_label" : "y = x^2", "show_target_line" : True, } class SecondSqrtScene(FirstSqrtScene, ReconfigurableScene): # TODO: Don't bother with ReconfigurableScene; just use new config from start # (But can also use this as written, and just cut into middle in Premiere) def setup(self): FirstSqrtScene.setup(self) ReconfigurableScene.setup(self) def construct(self): shiftVal = self.targetY self.drawGraph() newOrigin = self.coords_to_point(0, shiftVal) self.transition_to_alt_config( func = lambda x : x**2 - shiftVal, targetY = 0, graph_label = "y = x^2 - " + str(shiftVal), y_min = self.y_min - shiftVal, y_max = self.y_max - shiftVal, show_target_line = False, graph_origin = newOrigin) self.solveEquation() # TODO: Pi creatures intrigued class ComplexPlaneIs2d(Scene): def construct(self): com_plane = ComplexPlane() self.add(com_plane) # TODO: Add labels to axes, specific complex points self.wait() class NumberLineScene(Scene): def construct(self): num_line = NumberLine() self.add(num_line) # TODO: Add labels, arrows, specific points self.wait() border_color = PURPLE_E inner_color = RED stroke_width = 10 left_point = num_line.number_to_point(-1) right_point = num_line.number_to_point(1) # TODO: Make this line a thin rectangle interval_1d = Line(left_point, right_point, stroke_color = inner_color, stroke_width = stroke_width) rect_1d = Rectangle(stroke_width = 0, fill_opacity = 1, fill_color = inner_color) rect_1d.replace(interval_1d) rect_1d.stretch_to_fit_height(SMALL_BUFF) left_dot = Dot(left_point, stroke_width = stroke_width, color = border_color) right_dot = Dot(right_point, stroke_width = stroke_width, color = border_color) endpoints_1d = VGroup(left_dot, right_dot) full_1d = VGroup(rect_1d, endpoints_1d) self.play(ShowCreation(full_1d)) self.wait() # TODO: Can polish the morphing above; have dots become left and right sides, and # only then fill in the top and bottom num_plane = NumberPlane() random_points = [UP + LEFT, UP + RIGHT, DOWN + RIGHT, DOWN + LEFT] border_2d = Polygon( *random_points, stroke_color = border_color, stroke_width = stroke_width) filling_2d = Polygon( *random_points, fill_color = inner_color, fill_opacity = 0.8, stroke_width = stroke_width) full_2d = VGroup(filling_2d, border_2d) self.play( FadeOut(num_line), FadeIn(num_plane), ReplacementTransform(full_1d, full_2d)) self.wait() initial_2d_func = point_func_from_complex_func(lambda c : np.exp(c)) class Initial2dFuncSceneMorphing(Scene): CONFIG = { "num_needed_anchor_points" : 10, "func" : initial_2d_func, } def setup(self): split_line = DashedLine(SPACE_HEIGHT * UP, SPACE_HEIGHT * DOWN) self.num_plane = NumberPlane(x_radius = SPACE_WIDTH/2) self.num_plane.to_edge(LEFT, buff = 0) self.num_plane.prepare_for_nonlinear_transform() self.add(self.num_plane, split_line) def squash_onto_left(self, object): object.shift(SPACE_WIDTH/2 * LEFT) def squash_onto_right(self, object): object.shift(SPACE_WIDTH/2 * RIGHT) def obj_draw(self, input_object): output_object = input_object.copy() if input_object.get_num_anchor_points() < self.num_needed_anchor_points: input_object.insert_n_anchor_points(self.num_needed_anchor_points) output_object.apply_function(self.func) self.squash_onto_left(input_object) self.squash_onto_right(output_object) self.play( ShowCreation(input_object), ShowCreation(output_object) ) def construct(self): right_plane = self.num_plane.copy() right_plane.center() right_plane.prepare_for_nonlinear_transform() right_plane.apply_function(self.func) right_plane.shift(SPACE_WIDTH/2 * RIGHT) self.right_plane = right_plane crappy_cropper = FullScreenFadeRectangle(fill_opacity = 1) crappy_cropper.stretch_to_fit_width(SPACE_WIDTH) crappy_cropper.to_edge(LEFT, buff = 0) self.play( ReplacementTransform(self.num_plane.copy(), right_plane), FadeIn(crappy_cropper), Animation(self.num_plane), run_time = 3 ) points = [LEFT + DOWN, RIGHT + DOWN, LEFT + UP, RIGHT + UP] for i in range(len(points) - 1): line = Line(points[i], points[i + 1], color = RED) self.obj_draw(line) # Alternative to the above, using MappingCameras, but no morphing animation class Initial2dFuncSceneWithoutMorphing(Scene): def setup(self): left_camera = Camera(**self.camera_config) right_camera = MappingCamera( mapping_func = initial_2d_func, **self.camera_config) split_screen_camera = SplitScreenCamera(left_camera, right_camera, **self.camera_config) self.camera = split_screen_camera def construct(self): num_plane = NumberPlane() num_plane.prepare_for_nonlinear_transform() #num_plane.fade() self.add(num_plane) points = [LEFT + DOWN, RIGHT + DOWN, LEFT + UP, RIGHT + UP] for i in range(len(points) - 1): line = Line(points[i], points[i + 1], color = RED) self.play(ShowCreation(line)) # TODO: Illustrations for introducing domain coloring # TODO: Bunch of Pi walker scenes # TODO: An odometer scene when introducing winding numbers # (Just set up an OdometerScene with function matching the walking of the Pi # creature from previous scene, then place it as a simultaneous inset with Premiere) class LoopSplitScene(Scene): CONFIG = { "output_func" : plane_poly_with_roots((1, 1)) } def PulsedLine(self, start, end, bullet_template, num_bullets = 4, pulse_time = 1, **kwargs): line = Line(start, end, **kwargs) anim = LinePulser( line = line, bullet_template = bullet_template, num_bullets = num_bullets, pulse_time = pulse_time, output_func = self.output_func, **kwargs) return [VGroup(line, *anim.bullets), anim] def construct(self): num_plane = NumberPlane(color = LIGHT_GREY, stroke_width = 1) # We actually don't want to highlight num_plane.axes.set_stroke(color = WHITE, width = 2) num_plane.fade() self.add(num_plane) scale_factor = 2 shift_term = 0 # Original loop tl = scale_factor * (UP + LEFT) + shift_term tm = scale_factor * UP + shift_term tr = scale_factor * (UP + RIGHT) + shift_term mr = scale_factor * RIGHT + shift_term br = scale_factor * (DOWN + RIGHT) + shift_term bm = scale_factor * DOWN + shift_term bl = scale_factor * (DOWN + LEFT) + shift_term lm = scale_factor * LEFT + shift_term loop_color = BLUE default_bullet = PiCreature(color = RED) default_bullet.scale(0.15) modified_bullet = PiCreature(color = PINK) modified_bullet.scale(0.15) def SGroup(*args): return VGroup(*[arg[0] for arg in args]) top_line = self.PulsedLine(tl, tr, default_bullet, color = BLUE) right_line = self.PulsedLine(tr, br, modified_bullet, color = BLUE) bottom_line = self.PulsedLine(br, bl, default_bullet, color = BLUE) left_line = self.PulsedLine(bl, tl, default_bullet, color = BLUE) line_list = [top_line, right_line, bottom_line, left_line] loop = SGroup(*line_list) for line in line_list: self.add(*line) self.wait() # Splits in middle split_line = DashedLine(interpolate(tl, tr, 0.5), interpolate(bl, br, 0.5)) self.play(ShowCreation(split_line)) self.remove(*split_line) mid_line_left = self.PulsedLine(tm, bm, default_bullet, color = loop_color) mid_line_right = self.PulsedLine(bm, tm, modified_bullet, color = loop_color) self.add(*mid_line_left) self.add(*mid_line_right) top_line_left_half = self.PulsedLine(tl, tm, default_bullet, 2, 1, color = loop_color) top_line_right_half = self.PulsedLine(tm, tr, modified_bullet, 2, 1, color = loop_color) bottom_line_left_half = self.PulsedLine(bm, bl, default_bullet, 2, 1, color = loop_color) bottom_line_right_half = self.PulsedLine(br, bm, modified_bullet, 2, 1, color = loop_color) self.remove(*top_line) self.add(*top_line_left_half) self.add(*top_line_right_half) self.remove(*bottom_line) self.add(*bottom_line_left_half) self.add(*bottom_line_right_half) left_open_loop = SGroup(top_line_left_half, left_line, bottom_line_left_half) left_closed_loop = VGroup(left_open_loop, mid_line_left[0]) right_open_loop = SGroup(top_line_right_half, right_line, bottom_line_right_half) right_closed_loop = VGroup(right_open_loop, mid_line_right[0]) # self.play( # ApplyMethod(left_closed_loop.shift, LEFT), # ApplyMethod(right_closed_loop.shift, RIGHT) # ) self.wait() # self.play( # ApplyMethod(left_open_loop.shift, LEFT), # ApplyMethod(right_open_loop.shift, RIGHT) # ) self.wait() mid_lines = SGroup(mid_line_left, mid_line_right) highlight_circle = Circle(color = YELLOW_E) # Perhaps make this a dashed circle? highlight_circle.surround(mid_lines) self.play(Indicate(mid_lines), ShowCreation(highlight_circle, run_time = 0.5)) self.wait() self.play(FadeOut(highlight_circle), FadeOut(mid_lines)) # Because FadeOut didn't remove the continual pulsers, we remove them manually self.remove(mid_line_left[1], mid_line_right[1]) # Brings loop back together; keep in sync with motions which bring loop apart above # self.play( # ApplyMethod(left_open_loop.shift, 2 * RIGHT), # ApplyMethod(right_open_loop.shift, 2 * LEFT) # ) self.wait() # Is there a way to abstract this into a general process to derive a new mapped scene from an old scene? class LoopSplitSceneMapped(LoopSplitScene): 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, # to illustrate relation between degree and large-scale winding number class FundThmAlg(EquationSolver2d): CONFIG = { "func" : plane_poly_with_roots((1, 2), (-1, 1.5), (-1, 1.5)), "num_iterations" : 10, } # TODO: Borsuk-Ulam visuals # Note: May want to do an ordinary square scene, then MappingCamera it into a circle # class BorsukUlamScene(PiWalker): # 3-way scene of "Good enough"-illustrating odometers; to be composed in Premiere left_func = lambda x : x**2 - x + 1 diff_func = lambda x : np.cos(1.4 * (x - 0.1) * (np.log(x + 0.1) - 0.3) * TAU)/2.1 class LeftOdometer(OdometerScene): CONFIG = { "rotate_func" : left_func, "biased_display_start" : 0 } class RightOdometer(OdometerScene): CONFIG = { "rotate_func" : lambda x : left_func(x) + diff_func(x), "biased_display_start" : 0 } class DiffOdometer(OdometerScene): CONFIG = { "rotate_func" : diff_func, "dashed_line_angle" : 0.5, "biased_display_start" : 0 } # TODO: Brouwer's fixed point theorem visuals # class BFTScene(Scene): # TODO: Pi creatures wide-eyed in amazement ################# # TODOs, from easiest to hardest: # Minor fiddling with little things in each animation; placements, colors, timing, text # Initial odometer scene (simple once previous Pi walker scene is decided upon) # Writing new Pi walker scenes by parametrizing general template # ---- # Pi creature emotion stuff # BFT visuals # Borsuk-Ulam visuals # Domain coloring # TODO: Add to camera an option for low-quality background than other rendering, helpful # for previews # FIN