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IPTScene in basel2
This commit is contained in:
Grant Sanderson
parent
d7b84b0507
commit
004d3603f2
1 changed files with 388 additions and 4 deletions
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@ -20,6 +20,7 @@ from topics.number_line import *
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from topics.numerals import *
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#from topics.combinatorics import *
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from scene import Scene
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from scene.zoomed_scene import *
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from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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@ -1879,13 +1880,13 @@ class TwoLightSourcesScene(ManipulateLightsourceSetups):
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"radius" : 15,
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"a" : 9,
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"b" : 5,
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"origin_point" : 5*LEFT + 2.5*DOWN
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}
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def construct(self):
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MAX_OPACITY = 0.4
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INDICATOR_RADIUS = 0.6
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OPACITY_FOR_UNIT_INTENSITY = 0.5
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origin_point = 5*LEFT + 2.5*DOWN
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origin_point = self.origin_point
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#Morty
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morty = self.pi_creature
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@ -1951,7 +1952,7 @@ class TwoLightSourcesScene(ManipulateLightsourceSetups):
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identical_lighthouses_words.shift(LEFT)
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identical_lighthouses_arrows = VGroup(*[
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Arrow(
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identical_lighthouses_words.get_bottom(),
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identical_lighthouses_words.get_corner(DOWN+LEFT),
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ls.get_source_point(),
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buff = SMALL_BUFF,
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color = WHITE,
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@ -2053,6 +2054,7 @@ class TwoLightSourcesScene(ManipulateLightsourceSetups):
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)
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)
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self.add(indicator_update_anim)
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self.play(Animation(lsC), run_time = 0) #Why is this needed?
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for point in axes.coords_to_point(5, 2), H:
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self.play(
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lsC.move_source_to, point,
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@ -2143,11 +2145,393 @@ class TwoLightSourcesScene(ManipulateLightsourceSetups):
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self.play(morty.change, "confused")
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self.wait(2)
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class MathologerVideoWrapper(Scene):
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def construct(self):
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title = TextMobject("""
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Mathologer's excellent video on \\\\
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the many Pythagorean theorem cousins
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""")
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# title.scale(0.7)
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title.to_edge(UP)
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logo = ImageMobject("mathologer_logo")
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logo.scale_to_fit_height(1)
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logo.to_corner(UP+LEFT)
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logo.shift(2*SPACE_WIDTH*RIGHT)
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screen = ScreenRectangle(height = 5.5)
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screen.next_to(title, DOWN)
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self.play(
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logo.shift, 2*SPACE_WIDTH*LEFT,
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LaggedStart(FadeIn, title),
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run_time = 2
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)
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self.play(ShowCreation(screen))
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self.wait(5)
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class SimpleIPTProof(Scene):
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def construct(self):
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A = 5*RIGHT
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B = 3*UP
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C = ORIGIN
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#Dumb and inefficient
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alphas = np.linspace(0, 1, 500)
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i = np.argmin(map(
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lambda a : np.linalg.norm(interpolate(A, B, a)),
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alphas
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))
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H = interpolate(A, B, alphas[i])
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triangle = VGroup(
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Line(C, A, color = BLUE),
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Line(C, B, color = RED),
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Line(A, B, color = WHITE),
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Line(C, H, color = GREEN)
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)
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for line, char in zip(triangle, ["a", "b", "c", "h"]):
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label = TexMobject(char)
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label.match_color(line)
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vect = line.get_center() - triangle.get_center()
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vect /= np.linalg.norm(vect)
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label.next_to(line.get_center(), vect)
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triangle.add(label)
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if char == "h":
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label.next_to(line.get_center(), UP+LEFT, SMALL_BUFF)
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triangle.to_corner(UP+LEFT)
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self.add(triangle)
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argument_lines = VGroup(
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TexMobject(
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"\\text{Area} = ",
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"{1 \\over 2}", "a", "b", "=",
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"{1 \\over 2}", "c", "h"
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),
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TexMobject("\\Downarrow"),
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TexMobject("a^2", "b^2", "=", "c^2", "h^2"),
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TexMobject("\\Downarrow"),
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TexMobject(
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"a^2", "b^2", "=",
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"(", "a^2", "+", "b^2", ")", "h^2"
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),
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TexMobject("\\Downarrow"),
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TexMobject(
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"{1 \\over ", "h^2}", "=",
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"{1 \\over ", "b^2}", "+",
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"{1 \\over ", "a^2}",
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),
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)
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argument_lines.arrange_submobjects(DOWN)
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for line in argument_lines:
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line.highlight_by_tex_to_color_map({
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"a" : BLUE,
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"b" : RED,
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"h" : GREEN,
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"Area" : WHITE,
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"Downarrow" : WHITE,
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})
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all_equals = line.get_parts_by_tex("=")
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if all_equals:
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line.alignment_mob = all_equals[-1]
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else:
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line.alignment_mob = line[0]
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line.shift(-line.alignment_mob.get_center()[0]*RIGHT)
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argument_lines.next_to(triangle, RIGHT)
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argument_lines.to_edge(UP)
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prev_line = argument_lines[0]
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self.play(FadeIn(prev_line))
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for arrow, line in zip(argument_lines[1::2], argument_lines[2::2]):
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line.save_state()
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line.shift(
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prev_line.alignment_mob.get_center() - \
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line.alignment_mob.get_center()
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)
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line.fade(1)
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self.play(
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line.restore,
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GrowFromPoint(arrow, arrow.get_top())
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)
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self.wait()
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prev_line = line
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class WeCanHaveMoreFunThanThat(TeacherStudentsScene):
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def construct(self):
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point = VectorizedPoint(SPACE_WIDTH*LEFT/2 + SPACE_HEIGHT*UP/2)
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self.teacher_says(
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"We can have \\\\ more fun than that!",
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target_mode = "hooray"
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)
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self.change_student_modes(*3*["erm"], look_at_arg = point)
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self.wait()
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self.play(
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RemovePiCreatureBubble(
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self.teacher,
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target_mode = "raise_right_hand",
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look_at_arg = point,
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),
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self.get_student_changes(*3*["pondering"], look_at_arg = point)
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)
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self.wait(3)
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class IPTScene(TwoLightSourcesScene, ZoomedScene):
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CONFIG = {
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"max_opacity_ambient" : 0.2,
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"num_levels" : 200,
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}
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def construct(self):
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#Copy pasting from TwoLightSourcesScene....Very bad...
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origin_point = self.origin_point
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self.remove(self.pi_creature)
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#Axes
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axes = Axes(
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x_min = -1, x_max = 10.5,
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y_min = -1, y_max = 6.5,
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)
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axes.shift(origin_point)
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#Important reference points
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A = axes.coords_to_point(self.a, 0)
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B = axes.coords_to_point(0, self.b)
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C = axes.coords_to_point(0, 0)
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xA = A[0]
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yA = A[1]
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xB = B[0]
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yB = B[1]
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xC = C[0]
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yC = C[1]
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# find the coords of the altitude point H
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# as the solution of a certain LSE
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prelim_matrix = np.array([
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[yA - yB, xB - xA],
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[xA - xB, yA - yB]
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]) # sic
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prelim_vector = np.array(
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[xB * yA - xA * yB, xC * (xA - xB) + yC * (yA - yB)]
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)
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H2 = np.linalg.solve(prelim_matrix, prelim_vector)
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H = np.append(H2, 0.)
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#Lightsources
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lsA = LightSource(
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radius = self.radius,
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num_levels = self.num_levels,
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opacity_function = inverse_power_law(2, 1, 1, 1.5),
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max_opacity_ambient = self.max_opacity_ambient,
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)
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lsA.lighthouse.scale(0.5, about_edge = UP)
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lsB = lsA.deepcopy()
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lsA.move_source_to(A)
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lsB.move_source_to(B)
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lsC = lsA.deepcopy()
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lsC.move_source_to(H)
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#Lighthouse labels
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A_label = TextMobject("A")
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A_label.next_to(lsA.lighthouse, RIGHT)
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B_label = TextMobject("B")
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B_label.next_to(lsB.lighthouse, LEFT)
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#Lines
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line_a = Line(C, A)
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line_a.highlight(BLUE)
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line_b = Line(C, B)
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line_b.highlight(RED)
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line_c = Line(A, B)
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line_h = Line(H, C)
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line_h.highlight(GREEN)
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label_a = TexMobject("a")
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label_a.match_color(line_a)
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label_a.next_to(line_a, DOWN, buff = SMALL_BUFF)
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label_b = TexMobject("b")
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label_b.match_color(line_b)
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label_b.next_to(line_b, LEFT, buff = SMALL_BUFF)
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label_h = TexMobject("h")
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label_h.match_color(line_h)
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label_h.next_to(line_h.get_center(), RIGHT, buff = SMALL_BUFF)
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perp_mark = VMobject().set_points_as_corners([
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RIGHT, RIGHT+DOWN, DOWN
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])
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perp_mark.scale(0.25, about_point = ORIGIN)
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perp_mark.rotate(line_c.get_angle() + TAU/4, about_point = ORIGIN)
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perp_mark.shift(H)
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# Mini triangle
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m_hyp_a = Line(H, A)
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m_a = line_a.copy()
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m_hyp_b = Line(H, B)
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m_b = line_b.copy()
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mini_triangle = VGroup(m_a, m_hyp_a, m_b, m_hyp_b)
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mini_triangle.set_stroke(width = 5)
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mini_triangle.generate_target()
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mini_triangle.target.scale(0.1, about_point = origin_point)
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for part, part_target in zip(mini_triangle, mini_triangle.target):
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part.target = part_target
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# Screen label
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screen_word = TextMobject("Screen")
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screen_word.next_to(mini_triangle.target, UP+RIGHT, LARGE_BUFF)
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screen_arrow = Arrow(
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screen_word.get_bottom(),
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mini_triangle.target.get_center(),
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color = WHITE,
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)
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# Setup spotlights
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spotlight_a = VGroup()
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spotlight_a.screen = m_hyp_a
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spotlight_b = VGroup()
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spotlight_b.screen = m_hyp_b
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for spotlight in spotlight_a, spotlight_b:
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spotlight.get_source_point = lsC.get_source_point
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dr = lsC.ambient_light.radius/lsC.ambient_light.num_levels
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def update_spotlight(spotlight):
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spotlight.submobjects = []
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source_point = spotlight.get_source_point()
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c1, c2 = spotlight.screen.get_start(), spotlight.screen.get_end()
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distance = max(
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np.linalg.norm(c1 - source_point),
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np.linalg.norm(c2 - source_point),
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)
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n_parts = np.ceil(distance/dr)
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alphas = np.linspace(0, 1, n_parts+1)
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for a1, a2 in zip(alphas, alphas[1:]):
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spotlight.add(Polygon(
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interpolate(source_point, c1, a1),
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interpolate(source_point, c1, a2),
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interpolate(source_point, c2, a2),
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interpolate(source_point, c2, a1),
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fill_color = YELLOW,
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fill_opacity = 2*lsC.ambient_light.opacity_function(a1*distance),
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stroke_width = 0
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))
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def update_spotlights(spotlights):
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for spotlight in spotlights:
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update_spotlight(spotlight)
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def get_spotlight_triangle(spotlight):
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sp = spotlight.get_source_point()
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c1 = spotlight.screen.get_start()
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c2 = spotlight.screen.get_end()
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return Polygon(
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sp, c1, c2,
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stroke_width = 0,
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fill_color = YELLOW,
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fill_opacity = 0.5,
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)
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spotlights = VGroup(spotlight_a, spotlight_b)
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spotlights_update_anim = ContinualUpdateFromFunc(
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spotlights, update_spotlights
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)
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# Add components
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self.add(
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axes,
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lsA.ambient_light,
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lsB.ambient_light,
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lsC.ambient_light,
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line_c,
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)
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self.add_foreground_mobjects(
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lsA.lighthouse, A_label,
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lsB.lighthouse, B_label,
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lsC.lighthouse, line_h,
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)
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# Show miniature triangle
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self.play(ShowCreation(mini_triangle, submobject_mode = "all_at_once"))
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self.play(
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MoveToTarget(mini_triangle),
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run_time = 2,
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)
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self.add_foreground_mobject(mini_triangle)
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# Show beams of light
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self.play(
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Write(screen_word),
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GrowArrow(screen_arrow),
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)
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self.wait()
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spotlights_update_anim.update(0)
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self.play(
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LaggedStart(FadeIn, spotlight_a),
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LaggedStart(FadeIn, spotlight_b),
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Animation(screen_arrow),
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)
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self.add(spotlights_update_anim)
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self.play(*map(FadeOut, [screen_word, screen_arrow]))
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self.wait()
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# Reshape screen
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m_hyps = [m_hyp_a, m_hyp_b]
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for hyp, line in (m_hyp_a, m_a), (m_hyp_b, m_b):
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hyp.save_state()
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hyp.alt_version = line.copy()
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hyp.alt_version.highlight(WHITE)
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for x in range(2):
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self.play(*[
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Transform(m, m.alt_version)
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for m in m_hyps
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])
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self.wait()
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self.play(*[m.restore for m in m_hyps])
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self.wait()
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# Show spotlight a key point
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def show_key_point(spotlight, new_point):
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screen = spotlight.screen
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update_spotlight_anim = UpdateFromFunc(spotlight, update_spotlight)
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self.play(
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Transform(screen, screen.alt_version),
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update_spotlight_anim,
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)
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triangle = get_spotlight_triangle(spotlight)
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for x in range(3):
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anims = []
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if x > 0:
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anims.append(FadeOut(triangle.copy()))
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anims.append(GrowFromPoint(triangle, H))
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self.play(*anims)
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self.play(FadeOut(triangle))
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self.play(screen.restore, update_spotlight_anim)
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self.wait()
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self.play(
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lsC.move_source_to, new_point,
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Transform(screen, screen.alt_version),
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update_spotlight_anim,
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run_time = 2
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)
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self.wait()
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self.play(
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lsC.move_source_to, H,
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screen.restore,
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update_spotlight_anim,
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run_time = 2
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)
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self.wait()
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self.remove(spotlights_update_anim)
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self.add(spotlight_b)
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self.play(*map(FadeOut, [
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spotlight_a, lsA.ambient_light, lsB.ambient_light
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]))
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show_key_point(spotlight_b, A)
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self.play(
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FadeOut(spotlight_b),
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FadeIn(spotlight_a),
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)
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show_key_point(spotlight_a, B)
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self.wait()
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class IPTScene1(PiCreatureScene):
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class IPTScene1(Scene):
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def construct(self):
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show_detail = True
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