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https://github.com/3b1b/manim.git
synced 2025-08-01 17:29:06 +08:00
Further ShowEqualAngleSlices progress
This commit is contained in:
Grant Sanderson
@ -2597,18 +2597,7 @@ class IntroduceShapeOfVelocities(AskAboutEllipses, MovingCameraScene):
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for alpha in alphas
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])
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moving_vector = self.get_velocity_vector(0)
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def update_moving_vector(vector):
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new_vector = self.get_velocity_vector(
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self.orbit.proportion,
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# scalar=4.0,
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)
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Transform(vector, new_vector).update(1)
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moving_vector_animation = ContinualUpdateFromFunc(
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moving_vector, update_moving_vector
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)
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moving_vector, moving_vector_animation = self.get_velocity_vector_and_update()
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self.play(LaggedStart(
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ShowCreation, vectors,
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@ -2725,6 +2714,20 @@ class IntroduceShapeOfVelocities(AskAboutEllipses, MovingCameraScene):
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)
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return vector
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def get_velocity_vector_and_update(self):
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moving_vector = self.get_velocity_vector(0)
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def update_moving_vector(vector):
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new_vector = self.get_velocity_vector(
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self.orbit.proportion,
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)
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Transform(vector, new_vector).update(1)
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moving_vector_animation = ContinualUpdateFromFunc(
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moving_vector, update_moving_vector
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)
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return moving_vector, moving_vector_animation
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class AskWhy(TeacherStudentsScene):
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def construct(self):
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@ -2752,6 +2755,7 @@ class ShowEqualAngleSlices(IntroduceShapeOfVelocities):
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CONFIG = {
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"animate_sun": False,
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"theta": 30 * DEGREES,
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# "theta": 15 * DEGREES,
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}
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def construct(self):
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@ -2761,7 +2765,6 @@ class ShowEqualAngleSlices(IntroduceShapeOfVelocities):
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self.ask_about_time_per_slice()
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self.areas_are_proportional_to_radius_squared()
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self.show_inverse_square_law()
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self.show_change_in_velocity()
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self.directly_compare_velocity_vectors()
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self.show_equal_angle_changes()
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@ -2906,7 +2909,7 @@ class ShowEqualAngleSlices(IntroduceShapeOfVelocities):
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angle = angle % TAU
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angle_degrees = angle * (360 / TAU)
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P_label = TexMobject(
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"P_{%d^\\circ}" % int(np.round(angle_degrees, -1))
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"P_{%d^\\circ}" % int(np.round(angle_degrees))
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)
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P_label.next_to(
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dot, line.get_unit_vector(),
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@ -2945,13 +2948,11 @@ class ShowEqualAngleSlices(IntroduceShapeOfVelocities):
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def ask_about_time_per_slice(self):
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wedge1 = self.wedges[0]
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wedge2 = self.wedges[6]
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wedge2 = self.wedges[len(self.wedges) / 2]
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arc1 = self.arcs[0]
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arc2 = self.arcs[6]
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arc2 = self.arcs[len(self.arcs) / 2]
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comet = self.comet
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frame = self.camera_frame
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words1 = TextMobject(
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"Time spent \\\\ traversing \\\\ this slice?"
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)
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@ -2962,12 +2963,12 @@ class ShowEqualAngleSlices(IntroduceShapeOfVelocities):
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arrow1 = Arrow(
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words1.get_bottom(),
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wedge1.get_center() + 0.5 * DOWN,
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wedge1.get_center() + wedge1.get_height() * DOWN / 2,
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color=WHITE,
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)
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arrow2 = Arrow(
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words2.get_right(),
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wedge2.get_center() + 0.5 * UL,
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wedge2.get_center() + wedge2.get_height() * UL / 4,
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color=WHITE
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)
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@ -2991,17 +2992,243 @@ class ShowEqualAngleSlices(IntroduceShapeOfVelocities):
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self.play(MoveAlongPath(comet, arc2, rate_func=None, run_time=3))
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self.wait()
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self.area_questions = VGroup(words1, words2)
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self.area_question_arrows = VGroup(arrow1, arrow2)
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self.highlighted_wedges = VGroup(wedge1, wedge2)
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def areas_are_proportional_to_radius_squared(self):
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pass
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wedges = self.highlighted_wedges
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wedge = wedges[1]
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frame = self.camera_frame
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ellipse = self.ellipse
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sun_center = self.sun.get_center()
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line = self.lines[len(self.lines) / 2]
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thick_line = line.copy().set_stroke(PINK, 4)
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radius_word = TextMobject("Radius")
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radius_word.next_to(thick_line, UP, SMALL_BUFF)
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radius_word.match_color(thick_line)
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arc = self.arcs[len(self.arcs) / 2]
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thick_arc = arc.copy().set_stroke(RED, 4)
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scaling_group = VGroup(
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wedge, thick_line, radius_word, thick_arc
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)
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expression = TextMobject(
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"Time", "$\\propto$",
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"Area", "$\\propto$", "$(\\text{Radius})^2$"
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)
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expression.next_to(ellipse, UP, LARGE_BUFF)
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prop_to_brace = Brace(expression[1], DOWN, buff=SMALL_BUFF)
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prop_to_words = TextMobject("(proportional to)")
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prop_to_words.scale(0.7)
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prop_to_words.next_to(prop_to_brace, DOWN, SMALL_BUFF)
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VGroup(prop_to_words, prop_to_brace).set_color(GREEN)
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self.play(
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Write(expression[:3]),
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frame.shift, 0.5 * UP,
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FadeInFromDown(prop_to_words),
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GrowFromCenter(prop_to_brace),
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)
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self.wait(2)
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self.play(
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ShowCreation(thick_line),
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FadeInFromDown(radius_word)
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)
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self.wait()
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self.play(ShowCreationThenDestruction(thick_arc))
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self.play(ShowCreation(thick_arc))
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self.wait()
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self.play(Write(expression[3:]))
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self.play(
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scaling_group.scale, 0.5,
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{"about_point": sun_center},
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Animation(self.area_question_arrows),
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Animation(self.dots),
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Animation(self.comet),
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rate_func=there_and_back,
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run_time=4,
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)
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self.wait()
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expression.add(prop_to_brace, prop_to_words)
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self.proportionality_expression = expression
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def show_inverse_square_law(self):
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pass
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prop_exp = self.proportionality_expression
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comet = self.comet
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frame = self.camera_frame
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ellipse = self.ellipse
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orbit = self.orbit
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next_line = self.lines[(len(self.lines) / 2) + 1]
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def show_change_in_velocity(self):
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pass
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arc = self.arcs[len(self.arcs) / 2]
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force_expression = TexMobject(
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"ma", "=", "\\text{Force}",
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"\\propto", "\\frac{1}{(\\text{Radius})^2}"
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)
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force_expression.next_to(ellipse, LEFT, MED_LARGE_BUFF)
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force_expression.align_to(prop_exp, UP)
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force_expression.set_color_by_tex("Force", YELLOW)
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acceleration_expression = TexMobject(
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"a", "=", "{\\Delta v",
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"\\over", "\\Delta t}",
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"\\propto", "{1 \\over (\\text{Radius})^2}"
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)
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acceleration_expression.next_to(
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force_expression, DOWN, buff=0.75,
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aligned_edge=LEFT
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)
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delta_v_expression = TexMobject(
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"\\Delta v}", "\\propto",
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"{\\Delta t", "\\over", "(\\text{Radius})^2}"
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)
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delta_v_expression.next_to(
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acceleration_expression, DOWN, buff=0.75,
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aligned_edge=LEFT
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)
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delta_t_numerator = delta_v_expression.get_part_by_tex(
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"\\Delta t"
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)
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moving_R_squared = prop_exp.get_part_by_tex("Radius").copy()
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moving_R_squared.generate_target()
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moving_R_squared.target.move_to(delta_t_numerator, DOWN)
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moving_R_squared.target.set_color(GREEN)
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randy = Randolph()
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randy.next_to(force_expression, DOWN, LARGE_BUFF)
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force_vector, force_vector_update = self.get_force_arrow_and_update(
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comet, scale_factor=3,
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)
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moving_vector, moving_vector_animation = self.get_velocity_vector_and_update()
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self.play(
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FadeOut(self.area_questions),
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FadeOut(self.area_question_arrows),
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FadeInFromDown(force_expression),
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frame.shift, 2 * LEFT,
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)
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self.remove(*self.area_questions)
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self.play(
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randy.change, "confused", force_expression,
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VFadeIn(randy)
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)
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self.wait(2)
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self.play(
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randy.change, "pondering", force_expression[0],
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ShowPassingFlashAround(force_expression[:2]),
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)
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self.play(Blink(randy))
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self.play(
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FadeInFromDown(acceleration_expression),
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randy.change, "hooray", force_expression,
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randy.shift, 2 * DOWN,
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)
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self.wait(2)
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self.play(Blink(randy))
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self.play(randy.change, "thinking")
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self.wait()
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self.play(
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comet.move_to, arc.points[0],
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path_arc=90 * DEGREES
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)
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force_vector_update.update(0)
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self.play(
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Blink(randy),
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GrowArrow(force_vector)
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)
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self.add(force_vector_update)
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self.add_foreground_mobjects(comet)
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# Slightly hacky orbit treatment here...
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orbit.proportion = 0.5
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moving_vector_animation.update(0)
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start_velocity_vector = moving_vector.copy()
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self.play(
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GrowArrow(start_velocity_vector),
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randy.look_at, moving_vector
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)
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self.add(moving_vector_animation)
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self.add(orbit)
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while orbit.proportion < next_line.prop:
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self.wait(self.frame_duration)
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self.remove(orbit)
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self.add_foreground_mobjects(comet)
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self.wait(2)
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self.play(
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randy.change, "pondering", force_expression,
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randy.shift, 2 * DOWN,
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FadeInFromDown(delta_v_expression)
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)
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self.play(Blink(randy))
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self.wait(2)
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self.play(
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delta_t_numerator.scale, 1.5, {"about_edge": DOWN},
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delta_t_numerator.set_color, YELLOW
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)
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self.play(CircleThenFadeAround(prop_exp[:-2]))
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self.play(
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FadeOut(delta_t_numerator),
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MoveToTarget(moving_R_squared),
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randy.change, "happy", delta_v_expression
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)
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self.wait()
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self.play(FadeOut(randy))
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self.start_velocity_vector = start_velocity_vector
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self.end_velocity_vector = moving_vector.copy()
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self.moving_vector = moving_vector
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self.force_expressions = VGroup(
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force_expression,
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acceleration_expression,
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delta_v_expression,
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)
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def directly_compare_velocity_vectors(self):
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pass
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ellipse = self.ellipse
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lines = self.lines
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expressions = self.force_expressions
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vectors = VGroup(*[
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self.get_velocity_vector(line.prop)
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for line in lines
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])
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root_point = ellipse.get_left() + 3 * LEFT + DOWN
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root_dot = Dot(root_point)
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for vector in vectors:
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vector.target = Arrow(
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*vector.get_start_and_end(),
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color=vector.get_color(),
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buff=0
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)
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vector.target.scale(2)
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vector.target.shift(
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root_point - vector.target.get_start()
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)
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vector.target.add_to_back(
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vector.target.copy().set_stroke(BLACK, 5)
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)
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self.play(LaggedStart(GrowArrow, vectors))
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self.play(
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LaggedStart(MoveToTarget, vectors),
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GrowFromCenter(root_dot),
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expressions.scale, 0.5, {"about_edge": UL}
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)
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def show_equal_angle_changes(self):
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pass
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class ShowMoreFinelyChoppedOrbit(ShowEqualAngleSlices):
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def construct(self):
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pass
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