import numpy as np import itertools as it from helpers import * from mobject.tex_mobject import TexMobject, TextMobject, Brace from mobject import Mobject from mobject.image_mobject import \ MobjectFromRegion, ImageMobject, MobjectFromPixelArray from topics.three_dimensions import Stars from animation import Animation from animation.transform import \ Transform, CounterclockwiseTransform, ApplyPointwiseFunction,\ FadeIn, FadeOut, GrowFromCenter, ApplyFunction, ApplyMethod, \ ShimmerIn from animation.simple_animations import \ ShowCreation, Homotopy, PhaseFlow, ApplyToCenters, DelayByOrder, \ ShowPassingFlash from animation.playground import TurnInsideOut, Vibrate from topics.geometry import \ Line, Circle, Square, Grid, Rectangle, Arrow, Dot, Point, \ Arc, FilledRectangle from topics.characters import Randolph, Mathematician from topics.functions import ParametricFunction, FunctionGraph from topics.number_line import NumberPlane from region import Region, region_from_polygon_vertices from scene import Scene from brachistochrone.curves import Cycloid class Lens(Arc): DEFAULT_CONFIG = { "radius" : 2, "angle" : np.pi/2, "color" : BLUE_B, } def __init__(self, **kwargs): digest_config(self, kwargs) Arc.__init__(self, self.angle, **kwargs) def generate_points(self): Arc.generate_points(self) self.rotate(-np.pi/4) self.shift(-self.get_left()) self.add_points(self.copy().rotate(np.pi).points) class PhotonScene(Scene): def wavify(self, mobject): result = mobject.copy() result.ingest_sub_mobjects() tangent_vectors = result.points[1:]-result.points[:-1] lengths = np.apply_along_axis( np.linalg.norm, 1, tangent_vectors ) thick_lengths = lengths.repeat(3).reshape((len(lengths), 3)) unit_tangent_vectors = tangent_vectors/thick_lengths rot_matrix = np.transpose(rotation_matrix(np.pi/2, OUT)) normal_vectors = np.dot(unit_tangent_vectors, rot_matrix) # total_length = np.sum(lengths) times = np.cumsum(lengths) nudge_sizes = 0.1*np.sin(2*np.pi*times) thick_nudge_sizes = nudge_sizes.repeat(3).reshape((len(nudge_sizes), 3)) nudges = thick_nudge_sizes*normal_vectors result.points[1:] += nudges return result def photon_run_along_path(self, path, color = YELLOW, **kwargs): photon = self.wavify(path) photon.highlight(color) return ShowPassingFlash(photon, **kwargs) class SimplePhoton(PhotonScene): def construct(self): text = TextMobject("Light") text.to_edge(UP) self.play(ShimmerIn(text)) self.play(self.photon_run_along_path( Cycloid(), rate_func = None )) self.dither() class MultipathPhotonScene(PhotonScene): DEFAULT_CONFIG = { "num_paths" : 5 } def run_along_paths(self): paths = self.get_paths() colors = Color(YELLOW).range_to(WHITE, len(paths)) for path, color in zip(paths, colors): path.highlight(color) photon_runs = [ self.photon_run_along_path(path) for path in paths ] for photon_run, path in zip(photon_runs, paths): self.play( photon_run, ShowCreation( path, rate_func = lambda t : 0.9*smooth(t) ) ) self.dither() def generate_paths(self): raise Exception("Not Implemented") class PhotonThroughLens(MultipathPhotonScene): def construct(self): self.lens = Lens() self.add(self.lens) self.run_along_paths() def get_paths(self): interval_values = np.arange(self.num_paths).astype('float') interval_values /= (self.num_paths-1.) first_contact = [ self.lens.point_from_proportion(0.4*v+0.55) for v in reversed(interval_values) ] second_contact = [ self.lens.point_from_proportion(0.3*v + 0.1) for v in interval_values ] focal_point = 2*RIGHT return [ Mobject( Line(SPACE_WIDTH*LEFT + fc[1]*UP, fc), Line(fc, sc), Line(sc, focal_point), Line(focal_point, 6*focal_point-5*sc) ).ingest_sub_mobjects() for fc, sc in zip(first_contact, second_contact) ] class PhotonOffMirror(MultipathPhotonScene): def construct(self): self.mirror = Line(*SPACE_HEIGHT*np.array([DOWN, UP])) self.mirror.highlight(GREY) self.add(self.mirror) self.run_along_paths() def get_paths(self): interval_values = np.arange(self.num_paths).astype('float') interval_values /= (self.num_paths-1) anchor_points = [ self.mirror.point_from_proportion(0.6*v+0.3) for v in interval_values ] start_point = 5*LEFT+3*UP end_points = [] for point in anchor_points: vect = start_point-point vect[1] *= -1 end_points.append(point+2*vect) return [ Mobject( Line(start_point, anchor_point), Line(anchor_point, end_point) ).ingest_sub_mobjects() for anchor_point, end_point in zip(anchor_points, end_points) ] class PhotonsInGlass(MultipathPhotonScene): def construct(self): glass = Region(lambda x, y : y < 0) self.highlight_region(glass, BLUE_E) self.run_along_paths() def get_paths(self): x, y = -3, 3 start_point = x*RIGHT + y*UP angles = np.arange(np.pi/18, np.pi/3, np.pi/18) midpoints = y*np.arctan(angles) end_points = midpoints + SPACE_HEIGHT*np.arctan(2*angles) return [ Mobject( Line(start_point, [midpoint, 0, 0]), Line([midpoint, 0, 0], [end_point, -SPACE_HEIGHT, 0]) ).ingest_sub_mobjects() for midpoint, end_point in zip(midpoints, end_points) ] class ShowMultiplePathsScene(PhotonScene): def construct(self): text = TextMobject("Which path minimizes travel time?") text.to_edge(UP) self.generate_start_and_end_points() point_a = Dot(self.start_point) point_b = Dot(self.end_point) A = TextMobject("A").next_to(point_a, UP) B = TextMobject("B").next_to(point_b, DOWN) paths = self.get_paths() for point, letter in [(point_a, A), (point_b, B)]: self.play( ShowCreation(point), ShimmerIn(letter) ) self.play(ShimmerIn(text)) curr_path = paths[0].copy() curr_path_copy = curr_path.copy().ingest_sub_mobjects() self.play( self.photon_run_along_path(curr_path), ShowCreation(curr_path_copy, rate_func = rush_into) ) self.remove(curr_path_copy) for path in paths[1:] + [paths[0]]: self.play(Transform(curr_path, path, run_time = 4)) self.dither() def generate_start_and_end_points(self): raise Exception("Not Implemented") def get_paths(self): raise Exception("Not implemented") class ShowMultiplePathsThroughLens(ShowMultiplePathsScene): def construct(self): self.lens = Lens() self.add(self.lens) ShowMultiplePathsScene.construct(self) def generate_start_and_end_points(self): self.start_point = 3*LEFT + UP self.end_point = 2*RIGHT def get_paths(self): alphas = [0.2, 0.45, 0.55, 0.8] lower_right, upper_right, upper_left, lower_left = map( self.lens.point_from_proportion, alphas ) return [ Mobject( Line(self.start_point, a), Line(a, b), Line(b, self.end_point) ).highlight(color) for (a, b), color in zip( [ (upper_left, upper_right), (upper_left, lower_right), (lower_left, lower_right), (lower_left, upper_right), ], Color(YELLOW).range_to(WHITE, 4) ) ] class ShowMultiplePathsOffMirror(ShowMultiplePathsScene): def construct(self): mirror = Line(*SPACE_HEIGHT*np.array([DOWN, UP])) mirror.highlight(GREY) self.add(mirror) ShowMultiplePathsScene.construct(self) def generate_start_and_end_points(self): self.start_point = 4*LEFT + 2*UP self.end_point = 4*LEFT + 2*DOWN def get_paths(self): return [ Mobject( Line(self.start_point, midpoint), Line(midpoint, self.end_point) ).highlight(color) for midpoint, color in zip( [2*UP, 2*DOWN], Color(YELLOW).range_to(WHITE, 2) ) ] class ShowMultiplePathsInGlass(ShowMultiplePathsScene): def construct(self): glass = Region(lambda x, y : y < 0) self.highlight_region(glass, BLUE_E) ShowMultiplePathsScene.construct(self) def generate_start_and_end_points(self): self.start_point = 3*LEFT + 2*UP self.end_point = 3*RIGHT + 2*DOWN def get_paths(self): return [ Mobject( Line(self.start_point, midpoint), Line(midpoint, self.end_point) ).highlight(color) for midpoint, color in zip( [3*LEFT, 3*RIGHT], Color(YELLOW).range_to(WHITE, 2) ) ]