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Three iterations animated
This commit is contained in:
Ben Hambrecht
parent
5a3e672366
commit
77ae163c46
1 changed files with 358 additions and 41 deletions
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@ -1804,34 +1804,37 @@ class IPTScene1(PiCreatureScene):
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class PondScene(ThreeDScene):
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class PondScene(Scene):
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def construct(self):
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BASELINE_YPOS = -1
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BASELINE_YPOS = -2.5
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OBSERVER_POINT = [0,BASELINE_YPOS,0]
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POND0_RADIUS = 1.5
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LAKE0_RADIUS = 1.5
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INDICATOR_RADIUS = 0.6
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TICK_SIZE = 0.5
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LIGHTHOUSE_HEIGHT = 0.2
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SEA_COLOR = BLUE
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SEA_OPACITY = 0.3
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LAKE_COLOR = BLUE
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LAKE_OPACITY = 0.3
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LAKE_STROKE_WIDTH = 5.0
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LAKE_STROKE_COLOR = BLUE
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TEX_SCALE = 0.8
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DOT_COLOR = BLUE
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baseline = VMobject()
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baseline.set_points_as_corners([[-8,BASELINE_YPOS,0],[8,BASELINE_YPOS,0]])
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obs_dot = Dot(OBSERVER_POINT)
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ls0_dot = Dot(OBSERVER_POINT + 2 * POND0_RADIUS * UP)
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obs_dot = Dot(OBSERVER_POINT, fill_color = DOT_COLOR)
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ls0_dot = Dot(OBSERVER_POINT + 2 * LAKE0_RADIUS * UP, fill_color = DOT_COLOR)
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# pond
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pond0 = Circle(radius = POND0_RADIUS,
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# lake
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lake0 = Circle(radius = LAKE0_RADIUS,
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stroke_width = 0,
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fill_color = SEA_COLOR,
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fill_opacity = SEA_OPACITY
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fill_color = LAKE_COLOR,
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fill_opacity = LAKE_OPACITY
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)
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pond0.move_to(OBSERVER_POINT + POND0_RADIUS * UP)
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lake0.move_to(OBSERVER_POINT + LAKE0_RADIUS * UP)
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# Morty and indicator
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morty = Mortimer().scale(0.3)
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@ -1843,27 +1846,35 @@ class PondScene(ThreeDScene):
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)
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indicator.next_to(morty,LEFT)
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self.add(pond0,morty,indicator,obs_dot,ls0_dot)
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# first lighthouse
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ls0 = LightSource()
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ls0.move_source_to(OBSERVER_POINT + LAKE0_RADIUS * 2 * UP)
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self.add(lake0,morty,indicator,obs_dot,ls0_dot, ls0.lighthouse)
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self.wait()
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# shore arcs
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arc_left = Arc(-TAU/2,
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radius = POND0_RADIUS,
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start_angle = -TAU/4
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radius = LAKE0_RADIUS,
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start_angle = -TAU/4,
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stroke_width = LAKE_STROKE_WIDTH,
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stroke_color = LAKE_STROKE_COLOR
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)
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arc_left.move_arc_center_to(OBSERVER_POINT + POND0_RADIUS * UP)
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arc_left.move_arc_center_to(OBSERVER_POINT + LAKE0_RADIUS * UP)
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one_left = TexMobject("1")
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one_left.next_to(arc_left,LEFT)
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arc_right = Arc(TAU/2,
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radius = POND0_RADIUS,
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start_angle = -TAU/4
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radius = LAKE0_RADIUS,
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start_angle = -TAU/4,
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stroke_width = LAKE_STROKE_WIDTH,
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stroke_color = LAKE_STROKE_COLOR
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)
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arc_right.move_arc_center_to(OBSERVER_POINT + POND0_RADIUS * UP)
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arc_right.move_arc_center_to(OBSERVER_POINT + LAKE0_RADIUS * UP)
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one_right = TexMobject("1").scale(TEX_SCALE)
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one_right.next_to(arc_right,RIGHT)
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@ -1875,13 +1886,9 @@ class PondScene(ThreeDScene):
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Write(one_right),
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)
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# first lighthouse
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ls0 = LightSource()
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ls0.move_source_to(OBSERVER_POINT + POND0_RADIUS * 2 * UP)
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self.play(
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SwitchOn(ls0.ambient_light),
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FadeIn(ls0.lighthouse)
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)
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self.play(
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indicator.set_intensity,0.5
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@ -1899,8 +1906,8 @@ class PondScene(ThreeDScene):
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self.play(
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ShowCreation(diameter),
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Write(diameter_text),
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FadeOut(ls0_dot),
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FadeOut(obs_dot)
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FadeOut(obs_dot),
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FadeOut(ls0_dot)
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)
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indicator.reading = TexMobject("{1\over d^2}").scale(TEX_SCALE)
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@ -1942,24 +1949,25 @@ class PondScene(ThreeDScene):
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return np.array([-v[1], v[0], 0])/np.abs(v)
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pond1_radius = 2 * POND0_RADIUS
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pond1 = Circle(radius = pond1_radius,
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stroke_width = 0,
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fill_color = SEA_COLOR,
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fill_opacity = SEA_OPACITY
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lake1_radius = 2 * LAKE0_RADIUS
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lake1 = Circle(radius = lake1_radius,
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stroke_width = LAKE_STROKE_WIDTH,
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fill_color = LAKE_COLOR,
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fill_opacity = LAKE_OPACITY,
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stroke_color = LAKE_STROKE_COLOR
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)
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pond1.move_to(ls0.get_center())
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lake1.move_to(ls0.get_center())
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self.play(
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FadeIn(pond1),
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FadeOut(pond0),
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FadeIn(lake1),
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lake0.set_fill,{"opacity" : 0},
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FadeOut(one_left),
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FadeOut(one_right)
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)
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ls0_loc = ls0.get_source_point()
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ls11_loc = ls0_loc + pond1_radius * LEFT
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ls12_loc = ls0_loc + pond1_radius * RIGHT
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lake_center = ls0_loc = ls0.get_source_point()
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ls11_loc = ls0_loc + lake1_radius * LEFT
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ls12_loc = ls0_loc + lake1_radius * RIGHT
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t11 = Line(ls0_loc, ls11_loc)
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t12 = Line(ls0_loc, ls12_loc)
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@ -1968,12 +1976,12 @@ class PondScene(ThreeDScene):
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ShowCreation(t12),
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)
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hypot11 = Line(ls11_loc,OBSERVER_POINT)
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hypot12 = Line(ls12_loc,OBSERVER_POINT)
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leg11 = Line(OBSERVER_POINT,ls11_loc)
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leg12 = Line(OBSERVER_POINT,ls12_loc)
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self.play(
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ShowCreation(hypot11),
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ShowCreation(hypot12),
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ShowCreation(leg11),
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ShowCreation(leg12),
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)
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@ -1982,10 +1990,301 @@ class PondScene(ThreeDScene):
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ls12 = ls0.copy()
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self.add(ls12)
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self.play(
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ls11.move_source_to,ls11_loc,
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ls12.move_source_to,ls12_loc,
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FadeIn(ls0_dot)
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)
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INDICATOR_WIGGLE_FACTOR = 1.3
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self.play(
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ScaleInPlace(indicator, INDICATOR_WIGGLE_FACTOR, rate_func = wiggle),
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ScaleInPlace(indicator.reading, INDICATOR_WIGGLE_FACTOR, rate_func = wiggle)
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)
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self.play(
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FadeOut(diameter),
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FadeOut(diameter_text)
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)
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def scale_construction_down():
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scaling_args = []
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non_scaling_mobs = [indicator, indicator.reading, morty]
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for mob in self.mobjects:
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if type(mob) == AmbientLight or type(mob) == Lighthouse or mob in non_scaling_mobs:
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continue
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scaling_args.append(mob.scale_about_point)
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scaling_args.append(0.5)
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scaling_args.append(OBSERVER_POINT)
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self.play(*scaling_args)
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scale_construction_down()
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# # # # # # # # # # # # # # #
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# second construction step #
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# # # # # # # # # # # # # # #
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def ls_location_for_angle(angle):
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return lake_center + lake1_radius * np.array([np.cos(angle),np.sin(angle),0])
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self.play(FadeIn(ls0_dot))
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lake2_radius = lake1_radius # not * 2 bc we have rescaled!
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lake2 = Circle(radius = lake2_radius,
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stroke_width = LAKE_STROKE_WIDTH,
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fill_color = LAKE_COLOR,
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fill_opacity = LAKE_OPACITY,
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stroke_color = LAKE_STROKE_COLOR
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)
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lake2.move_to(lake_center)
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self.play(
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FadeIn(lake2),
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FadeOut(lake0),
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FadeOut(ls0_dot),
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lake1.set_fill,{"opacity": 0},
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FadeOut(arc_left),
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FadeOut(arc_right),
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FadeOut(t11),
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FadeOut(t12),
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)
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ls0_dot.move_to(lake_center)
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self.play(FadeIn(ls0_dot))
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ls21_loc = ls_location_for_angle(-3*TAU/8)
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ls22_loc = ls_location_for_angle(TAU/8)
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ls23_loc = ls_location_for_angle(3*TAU/8)
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ls24_loc = ls_location_for_angle(-TAU/8)
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t21 = Line(lake_center, ls21_loc)
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t22 = Line(lake_center, ls22_loc)
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t23 = Line(lake_center, ls23_loc)
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t24 = Line(lake_center, ls24_loc)
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leg21 = Line(OBSERVER_POINT,ls21_loc)
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leg22 = Line(OBSERVER_POINT,ls22_loc)
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leg23 = Line(OBSERVER_POINT,ls23_loc)
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leg24 = Line(OBSERVER_POINT,ls24_loc)
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self.play(
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ShowCreation(t21),
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ShowCreation(t22),
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)
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# place lighthouses at intersection points
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ls21 = ls11
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ls22 = ls11.copy()
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ls23 = ls12
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ls24 = ls12.copy()
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self.play(
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ShowCreation(leg21),
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ShowCreation(leg22),
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)
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self.add(ls21, ls22)
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self.play(
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ls21.move_source_to,ls21_loc,
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ls22.move_source_to,ls22_loc,
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)
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self.play(
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ShowCreation(t23),
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ShowCreation(t24),
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)
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self.play(
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ShowCreation(leg23),
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ShowCreation(leg24),
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)
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self.add(ls23, ls24)
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self.play(
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ls23.move_source_to,ls23_loc,
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ls24.move_source_to,ls24_loc,
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)
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self.play(
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ScaleInPlace(indicator, INDICATOR_WIGGLE_FACTOR, rate_func = wiggle),
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ScaleInPlace(indicator.reading, INDICATOR_WIGGLE_FACTOR, rate_func = wiggle)
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)
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self.play(
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FadeOut(lake1),
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FadeOut(leg11),
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FadeOut(leg12),
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)
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self.play(
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FadeOut(ls0_dot)
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)
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ls0_dot.move_to(lake_center)
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self.play(
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FadeIn(ls0_dot)
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)
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# again scale everything down
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scale_construction_down()
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# # # # # # # # # # # # # #
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# third construction step #
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# # # # # # # # # # # # # #
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lake3_radius = lake2_radius # not * 2 bc we have rescaled!
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lake3 = Circle(radius = lake3_radius,
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stroke_width = LAKE_STROKE_WIDTH,
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fill_color = LAKE_COLOR,
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fill_opacity = LAKE_OPACITY,
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stroke_color = LAKE_STROKE_COLOR
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)
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lake3.move_to(lake_center)
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self.play(
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FadeIn(lake3),
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FadeOut(lake1),
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FadeOut(ls0_dot),
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lake2.set_fill,{"opacity": 0},
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FadeOut(t21),
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FadeOut(t22),
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FadeOut(t23),
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FadeOut(t24),
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)
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ls0_dot.move_to(lake_center)
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self.play(FadeIn(ls0_dot))
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ls31_loc = ls_location_for_angle(-3*TAU/16)
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ls32_loc = ls_location_for_angle(5*TAU/16)
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ls33_loc = ls_location_for_angle(-TAU/16)
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ls34_loc = ls_location_for_angle(7*TAU/16)
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ls35_loc = ls_location_for_angle(TAU/16)
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ls36_loc = ls_location_for_angle(9*TAU/16)
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ls37_loc = ls_location_for_angle(3*TAU/16)
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ls38_loc = ls_location_for_angle(-5*TAU/16)
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t31 = Line(lake_center, ls31_loc)
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t32 = Line(lake_center, ls32_loc)
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t33 = Line(lake_center, ls33_loc)
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t34 = Line(lake_center, ls34_loc)
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t35 = Line(lake_center, ls35_loc)
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t36 = Line(lake_center, ls36_loc)
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t37 = Line(lake_center, ls37_loc)
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t38 = Line(lake_center, ls38_loc)
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leg31 = Line(OBSERVER_POINT,ls31_loc)
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leg32 = Line(OBSERVER_POINT,ls32_loc)
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leg33 = Line(OBSERVER_POINT,ls33_loc)
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leg34 = Line(OBSERVER_POINT,ls34_loc)
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leg35 = Line(OBSERVER_POINT,ls35_loc)
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leg36 = Line(OBSERVER_POINT,ls36_loc)
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leg37 = Line(OBSERVER_POINT,ls37_loc)
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leg38 = Line(OBSERVER_POINT,ls38_loc)
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# place lighthouses at intersection points
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ls31 = ls24
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ls32 = ls24.copy()
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ls33 = ls22
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ls34 = ls22.copy()
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ls35 = ls23
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ls36 = ls23.copy()
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ls37 = ls21
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ls38 = ls21.copy()
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#
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self.play(
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ShowCreation(t31),
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ShowCreation(t32),
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)
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self.play(
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ShowCreation(leg31),
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ShowCreation(leg32),
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)
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self.add(ls31, ls32)
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self.play(
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ls31.move_source_to,ls31_loc,
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ls32.move_source_to,ls32_loc,
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)
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#
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self.play(
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ShowCreation(t33),
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ShowCreation(t34),
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)
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self.play(
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ShowCreation(leg33),
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ShowCreation(leg34),
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)
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self.add(ls33, ls34)
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self.play(
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ls33.move_source_to,ls33_loc,
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ls34.move_source_to,ls34_loc,
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)
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#
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self.play(
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ShowCreation(t35),
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ShowCreation(t36),
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)
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self.play(
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ShowCreation(leg35),
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ShowCreation(leg36),
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)
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self.add(ls35, ls36)
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self.play(
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ls35.move_source_to,ls35_loc,
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ls36.move_source_to,ls36_loc,
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)
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#
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self.play(
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ShowCreation(t37),
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ShowCreation(t38),
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)
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self.play(
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ShowCreation(leg37),
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ShowCreation(leg38),
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)
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self.add(ls37, ls38)
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self.play(
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ls37.move_source_to,ls37_loc,
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ls38.move_source_to,ls38_loc,
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)
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@ -1998,3 +2297,21 @@ class PondScene(ThreeDScene):
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self.play(
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FadeOut(lake1),
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)
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self.play(
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ScaleInPlace(indicator, INDICATOR_WIGGLE_FACTOR, rate_func = wiggle),
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ScaleInPlace(indicator.reading, INDICATOR_WIGGLE_FACTOR, rate_func = wiggle)
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)
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|
|
|||
Loading…
Add table
Reference in a new issue