mirror of
https://github.com/3b1b/manim.git
synced 2025-09-01 00:48:45 +00:00
Just before rewrite of chapter 11
This commit is contained in:
Grant Sanderson
parent
f3ca337ee4
commit
2a1e834036
1 changed files with 238 additions and 5 deletions
|
|
@ -872,7 +872,6 @@ class AddTwoFunctions(FunctionGraphScene):
|
|||
FadeIn(rect),
|
||||
Animation(prefix),
|
||||
Transform(fg_group, suffix),
|
||||
run_time = 2
|
||||
)
|
||||
self.remove(prefix, fg_group)
|
||||
self.add(sum_def)
|
||||
|
|
@ -949,20 +948,254 @@ class AddTwoFunctions(FunctionGraphScene):
|
|||
for mob in g_lines, dots
|
||||
])
|
||||
self.dither()
|
||||
self.play(*map(FadeOut, [f_lines, g_lines]))
|
||||
self.add_lines(sum_lines)
|
||||
# self.play(*map(FadeOut, [f_lines, g_lines]))
|
||||
# self.add_lines(sum_lines)
|
||||
# self.dither()
|
||||
|
||||
class AddVectorsCoordinateByCoordinate(Scene):
|
||||
def construct(self):
|
||||
v1 = Matrix(["x_1", "y_1", "z_1"])
|
||||
v2 = Matrix(["x_2", "y_2", "z_2"])
|
||||
v_sum = Matrix(["x_1 + x_2", "y_1 + y_2", "z_1 + z_2"])
|
||||
for v in v1, v2, v_sum:
|
||||
v.get_entries()[0].highlight(X_COLOR)
|
||||
v.get_entries()[1].highlight(Y_COLOR)
|
||||
v.get_entries()[2].highlight(Z_COLOR)
|
||||
plus, equals = TexMobject("+=")
|
||||
VGroup(v1, plus, v2, equals, v_sum).arrange_submobjects()
|
||||
|
||||
self.add(v1, plus, v2)
|
||||
self.dither()
|
||||
self.play(
|
||||
Write(equals),
|
||||
Write(v_sum.get_brackets())
|
||||
)
|
||||
self.play(
|
||||
Transform(v1.get_entries().copy(), v_sum.get_entries()),
|
||||
Transform(v2.get_entries().copy(), v_sum.get_entries()),
|
||||
)
|
||||
self.dither()
|
||||
|
||||
class ScaleFunction(FunctionGraphScene):
|
||||
def construct(self):
|
||||
graph = self.get_function_graph()
|
||||
graph = self.get_function_graph(
|
||||
lambda x : 0.7*self.default_functions[0](x),
|
||||
animate = False
|
||||
)
|
||||
scaled_graph = self.get_function_graph(
|
||||
lambda x : graph.get_function()(x)*2,
|
||||
add = False
|
||||
animate = False, add = False
|
||||
)
|
||||
graph_lines = self.get_output_lines(graph)
|
||||
scaled_lines = self.get_output_lines(scaled_graph, nudge = False)
|
||||
|
||||
f_label = self.label_graph(graph, "f", animate = False)
|
||||
two_f_label = self.label_graph(scaled_graph, "(2f)", animate = False)
|
||||
self.remove(two_f_label)
|
||||
|
||||
title = TexMobject("(2f)", "(x) = 2", "f", "(x)")
|
||||
title.highlight_by_tex("(2f)", scaled_graph.get_color())
|
||||
title.highlight_by_tex("f", graph.get_color())
|
||||
title.next_to(ORIGIN, LEFT, buff = MED_BUFF)
|
||||
title.to_edge(UP)
|
||||
self.add(title)
|
||||
|
||||
self.add_lines(graph_lines)
|
||||
self.dither()
|
||||
self.play(Transform(graph_lines, scaled_lines))
|
||||
self.play(ShowCreation(scaled_graph))
|
||||
self.play(Write(two_f_label))
|
||||
self.play(FadeOut(graph_lines))
|
||||
self.dither()
|
||||
|
||||
class ScaleVectorByCoordinates(Scene):
|
||||
def construct(self):
|
||||
two, dot, equals = TexMobject("2 \\cdot =")
|
||||
v1 = Matrix(list("xyz"))
|
||||
v1.get_entries().gradient_highlight(X_COLOR, Y_COLOR, Z_COLOR)
|
||||
v2 = v1.copy()
|
||||
two_targets = VGroup(*[
|
||||
two.copy().next_to(entry, LEFT)
|
||||
for entry in v2.get_entries()
|
||||
])
|
||||
v2.get_brackets()[0].next_to(two_targets, LEFT)
|
||||
v2.add(two_targets)
|
||||
VGroup(two, dot, v1, equals, v2).arrange_submobjects()
|
||||
|
||||
self.add(two, dot, v1)
|
||||
self.play(
|
||||
Write(equals),
|
||||
Write(v2.get_brackets())
|
||||
)
|
||||
self.play(
|
||||
Transform(two.copy(), two_targets),
|
||||
Transform(v1.get_entries().copy(), v2.get_entries())
|
||||
)
|
||||
self.dither()
|
||||
|
||||
class ShowSlopes(Animation):
|
||||
CONFIG = {
|
||||
"line_color" : YELLOW,
|
||||
"dx" : 0.01,
|
||||
"rate_func" : None,
|
||||
"run_time" : 5
|
||||
}
|
||||
def __init__(self, graph, **kwargs):
|
||||
digest_config(self, kwargs, locals())
|
||||
line = Line(LEFT, RIGHT, color = self.line_color)
|
||||
line.save_state()
|
||||
Animation.__init__(self, line, **kwargs)
|
||||
|
||||
def update_mobject(self, alpha):
|
||||
f = self.graph.point_from_proportion
|
||||
low, high = map(f, np.clip([alpha-self.dx, alpha+self.dx], 0, 1))
|
||||
slope = (high[1]-low[1])/(high[0]-low[0])
|
||||
self.mobject.restore()
|
||||
self.mobject.rotate(np.arctan(slope))
|
||||
self.mobject.move_to(f(alpha))
|
||||
|
||||
class FromVectorsToFunctions(VectorScene):
|
||||
def construct(self):
|
||||
self.show_vector_addition_and_scaling()
|
||||
self.bring_in_functions()
|
||||
self.show_derivative()
|
||||
|
||||
def show_vector_addition_and_scaling(self):
|
||||
self.plane = self.add_plane()
|
||||
self.plane.fade()
|
||||
words1 = TextMobject("Vector", "addition")
|
||||
words2 = TextMobject("Vector", "scaling")
|
||||
for words in words1, words2:
|
||||
words.add_background_rectangle()
|
||||
words.next_to(ORIGIN, RIGHT).to_edge(UP)
|
||||
self.add(words1)
|
||||
|
||||
v = self.add_vector([2, -1], color = MAROON_B)
|
||||
w = self.add_vector([3, 2], color = YELLOW)
|
||||
w.save_state()
|
||||
self.play(w.shift, v.get_end())
|
||||
vw_sum = self.add_vector(w.get_end(), color = PINK)
|
||||
self.dither()
|
||||
self.play(
|
||||
Transform(words1, words2),
|
||||
FadeOut(vw_sum),
|
||||
w.restore
|
||||
)
|
||||
self.add(
|
||||
v.copy().fade(),
|
||||
w.copy().fade()
|
||||
)
|
||||
self.play(v.scale, 2)
|
||||
self.play(w.scale, -0.5)
|
||||
self.dither()
|
||||
|
||||
def bring_in_functions(self):
|
||||
everything = VGroup(*self.get_mobjects())
|
||||
axes = Axes()
|
||||
axes.shift(2*SPACE_WIDTH*LEFT)
|
||||
|
||||
fg_scene_config = FunctionGraphScene.CONFIG
|
||||
graph = FunctionGraph(fg_scene_config["default_functions"][0])
|
||||
graph.highlight(MAROON_B)
|
||||
func_tex = TexMobject("\\frac{1}{9}x^3 - x")
|
||||
func_tex.highlight(graph.get_color())
|
||||
func_tex.shift(5.5*RIGHT+2*UP)
|
||||
|
||||
words = VGroup(*[
|
||||
TextMobject(words).add_background_rectangle()
|
||||
for words in [
|
||||
"Linear transformations",
|
||||
"Null space",
|
||||
"Dot products",
|
||||
"Eigen-everything",
|
||||
]
|
||||
])
|
||||
words.gradient_highlight(BLUE_B, BLUE_D)
|
||||
words.arrange_submobjects(DOWN, aligned_edge = LEFT)
|
||||
words.to_corner(UP+LEFT)
|
||||
self.play(FadeIn(
|
||||
words,
|
||||
submobject_mode = "lagged_start",
|
||||
run_time = 3
|
||||
))
|
||||
self.dither()
|
||||
self.play(*[
|
||||
ApplyMethod(mob.shift, 2*SPACE_WIDTH*RIGHT)
|
||||
for mob in axes, everything
|
||||
] + [Animation(words)]
|
||||
)
|
||||
self.play(ShowCreation(graph), Animation(words))
|
||||
self.play(Write(func_tex, run_time = 2))
|
||||
self.dither(2)
|
||||
|
||||
top_word = words[0]
|
||||
words.remove(top_word)
|
||||
self.play(
|
||||
FadeOut(words),
|
||||
top_word.shift, top_word.get_center()[0]*LEFT
|
||||
)
|
||||
self.dither()
|
||||
self.func_tex = func_tex
|
||||
self.graph = graph
|
||||
|
||||
def show_derivative(self):
|
||||
func_tex, graph = self.func_tex, self.graph
|
||||
new_graph = FunctionGraph(lambda x : (x**2)/3.-1)
|
||||
new_graph.highlight(YELLOW)
|
||||
|
||||
func_tex.generate_target()
|
||||
lp, rp = parens = TexMobject("()")
|
||||
parens.scale_to_fit_height(func_tex.get_height())
|
||||
L, equals = TexMobject("L=")
|
||||
deriv = TexMobject("\\frac{d}{dx}")
|
||||
new_func = TexMobject("\\frac{1}{3}x^2 - 1")
|
||||
new_func.highlight(YELLOW)
|
||||
group = VGroup(
|
||||
L, lp, func_tex.target, rp,
|
||||
equals, new_func
|
||||
)
|
||||
group.arrange_submobjects()
|
||||
group.shift(2*UP).to_edge(LEFT, buff = 2*MED_BUFF)
|
||||
rect = BackgroundRectangle(group)
|
||||
group.add_to_back(rect)
|
||||
deriv.move_to(L, aligned_edge = RIGHT)
|
||||
|
||||
self.play(
|
||||
MoveToTarget(func_tex),
|
||||
*map(Write, [L, lp, rp, equals, new_func])
|
||||
)
|
||||
self.remove(func_tex)
|
||||
self.add(func_tex.target)
|
||||
self.dither()
|
||||
faded_graph = graph.copy().fade()
|
||||
self.add(faded_graph)
|
||||
self.play(
|
||||
Transform(graph, new_graph, run_time = 2),
|
||||
Animation(group)
|
||||
)
|
||||
self.dither()
|
||||
self.play(Transform(L, deriv))
|
||||
self.play(ShowSlopes(faded_graph))
|
||||
self.dither()
|
||||
|
||||
class WhatDoesLinearMean(TeacherStudentsScene):
|
||||
def construct(self):
|
||||
words = TextMobject("""
|
||||
What does it mean for
|
||||
a transformation of functions
|
||||
to be """, "linear", "?",
|
||||
arg_separator = ""
|
||||
)
|
||||
words.highlight_by_tex("linear", BLUE)
|
||||
self.student_says(words)
|
||||
self.change_student_modes("pondering")
|
||||
self.random_blink(4)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue