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Further in chapter 2 of eola

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This commit is contained in:
Grant Sanderson
2016-07-19 11:08:58 -07:00
parent b4eac6d6a9
commit a9c3f1e13d
3 changed files with 106 additions and 40 deletions
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6
animation/transform.py
View File

@ -93,9 +93,15 @@ class ApplyMethod(Transform):
)
class FadeOut(ApplyMethod):
CONFIG = {
"remover" : True,
}
def __init__(self, mobject, **kwargs):
ApplyMethod.__init__(self, mobject.fade, 1, **kwargs)
def cleanup(self):
self.update(0)
class FadeIn(Transform):
def __init__(self, mobject, **kwargs):
target = mobject.copy()

92
eola/chapter2.py
View File

@ -31,7 +31,6 @@ class OpeningQuote(Scene):
words.to_edge(UP)
for mob in words.submobjects[49:49+18]:
mob.highlight(GREEN)
words.show()
author = TextMobject("-Angus K. Rodgers")
author.highlight(YELLOW)
author.next_to(words, DOWN, buff = 0.5)
@ -53,17 +52,21 @@ class CoordinatesWereFamiliar(TeacherStudentsScene):
class CoordinatesAsScalars(VectorScene):
CONFIG = {
"vector_coords" : [3, -2]
}
def construct(self):
self.axes = self.add_axes()
vector = self.add_vector([3, -2])
vector = self.add_vector(self.vector_coords)
array, x_line, y_line = self.vector_to_coords(vector)
self.add(array)
self.dither()
new_array = self.general_idea_of_scalars(array)
new_array = self.general_idea_of_scalars(array, vector)
self.scale_basis_vectors(new_array)
self.show_symbolic_sum(new_array, vector)
def general_idea_of_scalars(self, array):
def general_idea_of_scalars(self, array, vector):
starting_mobjects = self.get_mobjects()
title = TextMobject("Think of each coordinate as a scalar")
@ -76,14 +79,23 @@ class CoordinatesAsScalars(VectorScene):
new_y.move_to(3*RIGHT+2*UP)
i_hat, j_hat = self.get_basis_vectors()
new_i_hat = Vector(3*i_hat.get_end(), color = X_COLOR)
new_j_hat = Vector(-2*j_hat.get_end(), color = Y_COLOR)
new_i_hat = Vector(
self.vector_coords[0]*i_hat.get_end(),
color = X_COLOR
)
new_j_hat = Vector(
self.vector_coords[1]*j_hat.get_end(),
color = Y_COLOR
)
VMobject(i_hat, new_i_hat).shift(3*LEFT)
VMobject(j_hat, new_j_hat).shift(3*RIGHT)
new_array = Matrix([new_x.copy(), new_y.copy()])
new_array.replace(array)
new_array.shift(0.5*DOWN)
new_array.scale(0.5)
new_array.shift(
-new_array.get_boundary_point(-vector.get_end()) + \
1.1*vector.get_end()
)
self.remove(*starting_mobjects)
self.play(
@ -95,15 +107,16 @@ class CoordinatesAsScalars(VectorScene):
self.dither()
self.play(
Transform(i_hat, new_i_hat),
Transform(j_hat, new_j_hat)
Transform(j_hat, new_j_hat),
run_time = 3
)
self.dither()
starting_mobjects.remove(array)
new_x, new_y = new_array.get_mob_matrix().flatten()
self.play(
Transform(
VMobject(x, y),
VMobject(*new_array.get_mob_matrix().flatten())
),
Transform(x, new_x),
Transform(y, new_y),
FadeOut(i_hat),
FadeOut(j_hat),
Write(new_array.get_brackets()),
@ -117,8 +130,6 @@ class CoordinatesAsScalars(VectorScene):
def scale_basis_vectors(self, new_array):
self.play(ApplyMethod(self.axes.highlight, GREY))
i_hat, j_hat = self.get_basis_vectors()
for mob in i_hat, j_hat:
mob.set_stroke(width = 6)
self.add_vector(i_hat)
i_hat_label = self.label_vector(
i_hat, "\\hat{\\imath}",
@ -131,19 +142,20 @@ class CoordinatesAsScalars(VectorScene):
color = Y_COLOR,
label_scale_val = 1
)
self.dither()
x, y = new_array.get_mob_matrix().flatten()
for coord, v, label, factor, shift_right in [
(x, i_hat, i_hat_label, 3, False),
(y, j_hat, j_hat_label, -2, True)
(x, i_hat, i_hat_label, self.vector_coords[0], False),
(y, j_hat, j_hat_label, self.vector_coords[1], True)
]:
faded_v = v.copy().fade(0.5)
faded_v = v.copy().fade(0.7)
scaled_v = Vector(factor*v.get_end(), color = v.get_color())
scaled_label = VMobject(coord.copy(), label.copy())
scaled_label.arrange_submobjects(RIGHT, buff = 0.1)
scaled_label.move_to(label, DOWN+RIGHT)
scaled_label.shift(scaled_v.get_center()-v.get_center())
scaled_label.shift((scaled_v.get_end()-v.get_end())/2)
coord_copy = coord.copy()
self.play(
Transform(v.copy(), faded_v),
@ -153,15 +165,20 @@ class CoordinatesAsScalars(VectorScene):
self.dither()
if shift_right:
group = VMobject(v, coord_copy, label)
self.play(ApplyMethod(group.shift, 3*RIGHT))
self.play(ApplyMethod(
group.shift, self.vector_coords[0]*RIGHT
))
self.dither()
def show_symbolic_sum(self, new_array, vector):
new_mob = TexMobject([
"3\\hat{\\imath}", "+", "(-2)\\hat{\\jmath}"
"(%d)\\hat{\\imath}"%self.vector_coords[0],
"+",
"(%d)\\hat{\\jmath}"%self.vector_coords[1]
])
new_mob.shift(vector.get_end()-new_mob.get_corner(UP+LEFT))
new_mob.move_to(new_array)
new_mob.shift_onto_screen()
i_hat, plus, j_hat = new_mob.split()
i_hat.highlight(X_COLOR)
j_hat.highlight(Y_COLOR)
@ -171,13 +188,30 @@ class CoordinatesAsScalars(VectorScene):
class CoordinatesAsScalarsExample2(CoordinatesAsScalars):
CONFIG = {
"vector_coords" : [-5, 2]
}
def construct(self):
self.add_axes()
basis_vectors = self.get_basis_vectors()
labels = self.get_basis_vector_labels()
self.add(*basis_vectors)
self.add(*labels)
text = TextMobject("""
$\\hat{\\imath}$ and $\\hat{\\jmath}$
are the ``basis vectors'' \\\\
of the $xy$ coordinate system
""")
text.scale_to_fit_width(SPACE_WIDTH-1)
text.to_corner(UP+RIGHT)
VMobject(*text.split()[:2]).highlight(X_COLOR)
VMobject(*text.split()[5:7]).highlight(Y_COLOR)
self.play(Write(text))
self.dither(2)
self.remove(*basis_vectors + labels)
CoordinatesAsScalars.construct(self)

48
eola/two_d_space.py
View File

@ -110,6 +110,9 @@ class LinearTransformationScene(Scene):
class VectorScene(Scene):
CONFIG = {
"basis_vector_stroke_width" : 6
}
def add_plane(self, animate = False, **kwargs):
plane = NumberPlane(**kwargs)
if animate:
@ -133,13 +136,35 @@ class VectorScene(Scene):
return vector
def get_basis_vectors(self):
i_hat = Vector([1, 0], color = X_COLOR)
j_hat = Vector([0, 1], color = Y_COLOR)
return i_hat, j_hat
return [
Vector(
vect, color = color,
stroke_width = self.basis_vector_stroke_width
)
for vect, color in [
([1, 0], X_COLOR),
([0, 1], Y_COLOR)
]
]
def get_basis_vector_labels(self, animate = False, **kwargs):
i_hat, j_hat = self.get_basis_vectors()
return [
self.label_vector(
vect, label, color = color,
animate = animate,
label_scale_val = 1,
**kwargs
)
for vect, label , color in [
(i_hat, "\\hat{\\imath}", X_COLOR),
(j_hat, "\\hat{\\jmath}", Y_COLOR),
]
]
def label_vector(self, vector, label, animate = True,
direction = "left", rotate = False,
color = WHITE, add_to_vector = True,
color = WHITE, add_to_vector = False,
buff_factor = 2,
label_scale_val = VECTOR_LABEL_SCALE_VAL):
if len(label) == 1:
@ -155,10 +180,10 @@ class VectorScene(Scene):
rot_angle = -np.pi/2
else:
rot_angle = np.pi/2
label.shift(-buff_factor*label.get_critical_point(
rotate_vector(vector_vect, rot_angle)
))
label.shift(vector_vect/2)
boundary_dir = -np.round(rotate_vector(vector_vect, rot_angle))
boundary_point = label.get_critical_point(boundary_dir)
label.shift(buff_factor*boundary_point)
label.shift(vector_vect/2.)
if add_to_vector:
vector.add(label)
@ -202,8 +227,9 @@ class VectorScene(Scene):
),
FadeOut(array.get_brackets())
)
y_coord, brackets = self.get_mobjects_from_last_animation()
self.play(ShowCreation(y_line))
self.play(ShowCreation(arrow, submobject_mode = "one_at_a_time"))
self.play(ShowCreation(arrow))
self.dither()
if cleanup:
self.clear()
@ -253,8 +279,8 @@ class VectorScene(Scene):
)
self.dither()
self.remove(x_coord_start, y_coord_start)
self.add(x_coord, y_coord)
self.remove(x_coord_start, y_coord_start, brackets)
self.add(array)
if cleanup:
self.clear()
self.add(*starting_mobjects)