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Preliminary Lens, Mirror and Glass scenes established
This commit is contained in:
Grant Sanderson
parent
044e0b5c72
commit
601abf18f3
1 changed files with 205 additions and 27 deletions
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@ -49,7 +49,9 @@ class Lens(Arc):
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class PhotonScene(Scene):
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def wavify(self, mobject):
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tangent_vectors = mobject.points[1:]-mobject.points[:-1]
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result = mobject.copy()
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result.ingest_sub_mobjects()
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tangent_vectors = result.points[1:]-result.points[:-1]
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lengths = np.apply_along_axis(
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np.linalg.norm, 1, tangent_vectors
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)
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@ -62,7 +64,6 @@ class PhotonScene(Scene):
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nudge_sizes = 0.1*np.sin(2*np.pi*times)
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thick_nudge_sizes = nudge_sizes.repeat(3).reshape((len(nudge_sizes), 3))
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nudges = thick_nudge_sizes*normal_vectors
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result = mobject.copy()
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result.points[1:] += nudges
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return result
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@ -84,29 +85,12 @@ class SimplePhoton(PhotonScene):
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self.dither()
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class PhotonThroughLens(PhotonScene):
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def construct(self):
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lens = Lens()
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num_paths = 5
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interval_values = np.arange(num_paths)/(num_paths-1.)
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first_contact = [
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lens.point_from_interval(0.4*v+0.55)
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for v in reversed(interval_values)
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]
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second_contact = [
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lens.point_from_interval(0.3*v + 0.1)
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for v in interval_values
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]
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focal_point = 2*RIGHT
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paths = [
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Mobject(
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Line(SPACE_WIDTH*LEFT + fc[1]*UP, fc),
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Line(fc, sc),
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Line(sc, focal_point),
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Line(focal_point, 6*focal_point-5*sc)
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).ingest_sub_mobjects()
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for fc, sc in zip(first_contact, second_contact)
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]
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class MultipathPhotonScene(PhotonScene):
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DEFAULT_CONFIG = {
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"num_paths" : 5
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}
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def run_along_paths(self):
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paths = self.get_paths()
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colors = Color(YELLOW).range_to(WHITE, len(paths))
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for path, color in zip(paths, colors):
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path.highlight(color)
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@ -114,7 +98,6 @@ class PhotonThroughLens(PhotonScene):
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self.photon_run_along_path(path)
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for path in paths
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]
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self.add(lens)
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for photon_run, path in zip(photon_runs, paths):
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self.play(
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photon_run,
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@ -125,7 +108,202 @@ class PhotonThroughLens(PhotonScene):
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)
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self.dither()
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def generate_paths(self):
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raise Exception("Not Implemented")
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class PhotonThroughLens(MultipathPhotonScene):
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def construct(self):
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self.lens = Lens()
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self.add(self.lens)
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self.run_along_paths()
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def get_paths(self):
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interval_values = np.arange(self.num_paths).astype('float')
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interval_values /= (self.num_paths-1.)
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first_contact = [
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self.lens.point_from_proportion(0.4*v+0.55)
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for v in reversed(interval_values)
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]
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second_contact = [
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self.lens.point_from_proportion(0.3*v + 0.1)
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for v in interval_values
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]
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focal_point = 2*RIGHT
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return [
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Mobject(
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Line(SPACE_WIDTH*LEFT + fc[1]*UP, fc),
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Line(fc, sc),
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Line(sc, focal_point),
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Line(focal_point, 6*focal_point-5*sc)
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).ingest_sub_mobjects()
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for fc, sc in zip(first_contact, second_contact)
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]
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class PhotonOffMirror(MultipathPhotonScene):
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def construct(self):
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self.mirror = Line(*SPACE_HEIGHT*np.array([DOWN, UP]))
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self.mirror.highlight(GREY)
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self.add(self.mirror)
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self.run_along_paths()
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def get_paths(self):
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interval_values = np.arange(self.num_paths).astype('float')
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interval_values /= (self.num_paths-1)
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anchor_points = [
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self.mirror.point_from_proportion(0.6*v+0.3)
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for v in interval_values
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]
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start_point = 5*LEFT+3*UP
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end_points = []
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for point in anchor_points:
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vect = start_point-point
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vect[1] *= -1
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end_points.append(point+2*vect)
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return [
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Mobject(
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Line(start_point, anchor_point),
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Line(anchor_point, end_point)
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).ingest_sub_mobjects()
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for anchor_point, end_point in zip(anchor_points, end_points)
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]
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class PhotonsInGlass(MultipathPhotonScene):
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def construct(self):
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glass = Region(lambda x, y : y < 0)
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self.highlight_region(glass, BLUE_E)
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self.run_along_paths()
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def get_paths(self):
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x, y = -3, 3
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start_point = x*RIGHT + y*UP
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angles = np.arange(np.pi/18, np.pi/3, np.pi/18)
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midpoints = y*np.arctan(angles)
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end_points = midpoints + SPACE_HEIGHT*np.arctan(2*angles)
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return [
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Mobject(
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Line(start_point, [midpoint, 0, 0]),
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Line([midpoint, 0, 0], [end_point, -SPACE_HEIGHT, 0])
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).ingest_sub_mobjects()
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for midpoint, end_point in zip(midpoints, end_points)
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]
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class ShowMultiplePathsScene(PhotonScene):
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def construct(self):
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text = TextMobject("Which path minimizes travel time?")
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text.to_edge(UP)
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self.generate_start_and_end_points()
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point_a = Dot(self.start_point)
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point_b = Dot(self.end_point)
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A = TextMobject("A").next_to(point_a, UP)
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B = TextMobject("B").next_to(point_b, DOWN)
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paths = self.get_paths()
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for point, letter in [(point_a, A), (point_b, B)]:
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self.play(
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ShowCreation(point),
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ShimmerIn(letter)
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)
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self.play(ShimmerIn(text))
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curr_path = paths[0].copy()
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curr_path_copy = curr_path.copy().ingest_sub_mobjects()
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self.play(
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self.photon_run_along_path(curr_path),
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ShowCreation(curr_path_copy, rate_func = rush_into)
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)
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self.remove(curr_path_copy)
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for path in paths[1:] + [paths[0]]:
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self.play(Transform(curr_path, path, run_time = 4))
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self.dither()
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def generate_start_and_end_points(self):
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raise Exception("Not Implemented")
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def get_paths(self):
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raise Exception("Not implemented")
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class ShowMultiplePathsThroughLens(ShowMultiplePathsScene):
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def construct(self):
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self.lens = Lens()
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self.add(self.lens)
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ShowMultiplePathsScene.construct(self)
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def generate_start_and_end_points(self):
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self.start_point = 3*LEFT + UP
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self.end_point = 2*RIGHT
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def get_paths(self):
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alphas = [0.2, 0.45, 0.55, 0.8]
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lower_right, upper_right, upper_left, lower_left = map(
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self.lens.point_from_proportion, alphas
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)
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return [
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Mobject(
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Line(self.start_point, a),
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Line(a, b),
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Line(b, self.end_point)
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).highlight(color)
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for (a, b), color in zip(
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[
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(upper_left, upper_right),
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(upper_left, lower_right),
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(lower_left, lower_right),
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(lower_left, upper_right),
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],
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Color(YELLOW).range_to(WHITE, 4)
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)
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]
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class ShowMultiplePathsOffMirror(ShowMultiplePathsScene):
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def construct(self):
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mirror = Line(*SPACE_HEIGHT*np.array([DOWN, UP]))
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mirror.highlight(GREY)
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self.add(mirror)
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ShowMultiplePathsScene.construct(self)
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def generate_start_and_end_points(self):
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self.start_point = 4*LEFT + 2*UP
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self.end_point = 4*LEFT + 2*DOWN
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def get_paths(self):
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return [
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Mobject(
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Line(self.start_point, midpoint),
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Line(midpoint, self.end_point)
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).highlight(color)
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for midpoint, color in zip(
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[2*UP, 2*DOWN],
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Color(YELLOW).range_to(WHITE, 2)
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)
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]
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class ShowMultiplePathsInGlass(ShowMultiplePathsScene):
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def construct(self):
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glass = Region(lambda x, y : y < 0)
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self.highlight_region(glass, BLUE_E)
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ShowMultiplePathsScene.construct(self)
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def generate_start_and_end_points(self):
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self.start_point = 3*LEFT + 2*UP
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self.end_point = 3*RIGHT + 2*DOWN
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def get_paths(self):
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return [
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Mobject(
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Line(self.start_point, midpoint),
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Line(midpoint, self.end_point)
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).highlight(color)
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for midpoint, color in zip(
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[3*LEFT, 3*RIGHT],
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Color(YELLOW).range_to(WHITE, 2)
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)
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]
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