def show_car_movement(self, *added_anims, **kwargs):
distance = np.linalg.norm(self.car.get_center() -
self.start_car_copy.get_center())
if distance > 1:
self.play(FadeOut(self.car))
self.car.move_to(self.line.get_left())
self.play(FadeIn(self.car))
kwargs["run_time"] = kwargs.get("run_time", self.car_run_time)
self.play(MoveCar(self.car, self.line.get_right(), **kwargs),
*added_anims)
def show_functions(self):
def get_deriv(n):
return lambda x : derivative(
s_scene.graph.underlying_function, x, n
)
s_scene = TrajectoryGraphScene()
v_scene = TrajectoryGraphScene(
func = get_deriv(1),
color = GREEN,
y_max = 4,
y_axis_label = "v",
)
a_scene = TrajectoryGraphScene(
func = get_deriv(2),
color = MAROON_B,
y_axis_label = "a",
y_min = -2,
y_max = 2,
)
j_scene = TrajectoryGraphScene(
func = get_deriv(3),
color = PINK,
y_axis_label = "j",
y_min = -2,
y_max = 2,
)
s_graph, v_graph, a_graph, j_graph = graphs = [
VGroup(*scene.get_top_level_mobjects())
for scene in (s_scene, v_scene, a_scene, j_scene)
]
for i, graph in enumerate(graphs):
graph.set_height(FRAME_Y_RADIUS)
graph.to_corner(UP+LEFT)
graph.shift(i*DOWN/2.0)
s_words = TexMobject(
"s(t)", "\\Leftrightarrow", "\\text{Displacement}"
)
s_words.set_color_by_tex("s(t)", s_scene.graph.get_color())
v_words = TexMobject(
"\\frac{ds}{dt}(t)", "\\Leftrightarrow",
"\\text{Velocity}"
)
v_words.set_color_by_tex("ds", v_scene.graph.get_color())
j_words = TexMobject(
"\\frac{d^3 s}{dt^3}(t)", "\\Leftrightarrow",
"\\text{Jerk}"
)
j_words.set_color_by_tex("d^3", j_scene.graph.get_color())
self.a_words.generate_target()
words_group = VGroup(s_words, v_words, self.a_words.target, j_words)
words_group.arrange_submobjects(
DOWN,
buff = MED_LARGE_BUFF,
aligned_edge = LEFT
)
words_group.to_corner(UP+RIGHT)
j_graph.scale(0.3).next_to(j_words, LEFT)
positive_rect = Rectangle()
positive_rect.set_stroke(width = 0)
positive_rect.set_fill(GREEN, 0.5)
positive_rect.replace(
Line(
a_scene.coords_to_point(0, -1),
a_scene.coords_to_point(5, 1),
),
stretch = True
)
negative_rect = Rectangle()
negative_rect.set_stroke(width = 0)
negative_rect.set_fill(RED, 0.5)
negative_rect.replace(
Line(
a_scene.coords_to_point(5, 1),
a_scene.coords_to_point(10, -1),
),
stretch = True
)
self.show_car_movement(
MoveToTarget(self.a_words),
FadeIn(s_words),
FadeIn(s_graph),
)
self.play(
s_graph.scale, 0.3,
s_graph.next_to, s_words, LEFT
)
self.play(*list(map(FadeIn, [v_graph, v_words])) )
self.wait(2)
self.play(
v_graph.scale, 0.3,
v_graph.next_to, v_words, LEFT
)
self.wait(2)
self.play(
Indicate(self.a_words),
FadeIn(a_graph),
)
self.wait()
self.play(FadeIn(positive_rect))
for x in range(2):
self.show_car_movement(
run_time = 3,
rate_func = lambda t : smooth(t/2.0)
)
self.wait()
self.play(FadeIn(negative_rect))
self.wait()
self.play(MoveCar(
self.car, self.line.get_end(),
run_time = 3,
rate_func = lambda t : 2*smooth((t+1)/2.0) - 1
))
self.wait()
self.play(
a_graph.scale, 0.3,
a_graph.next_to, self.a_words, LEFT,
*list(map(FadeOut, [positive_rect, negative_rect]))
)
self.play(
FadeOut(self.car),
FadeIn(j_words),
FadeIn(j_graph),
self.line.scale, 0.5, self.line.get_left(),
self.line.shift, LEFT,
)
self.car.scale(0.5)
self.car.move_to(self.line.get_start())
self.play(FadeIn(self.car))
self.show_car_movement()
self.wait(2)
